Department of Mathematics at UTSA - User contributions [en]

MAT3233

2020-08-25T19:30:23Z

Rylee.taylor:

==Modern Algebra==

MAT 3233. Modern Algebra. (3-0) 3 Credit Hours.

Prerequisite: [[MAT3013]]. Topics will include the development of groups, integral domains, fields, and number systems, including the complex numbers. Divisibility, congruences, primes, perfect numbers, and some other problems of number theory will be considered. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Example || Chapter 1 || Preliminaries || Example || Example
|-
| Example || Chapter 2 || The Integers || Example || Example
|-
| Example || Chapter 3 || Groups || Example || Example
|-
| Example || Chapter 4 || Cyclic Groups || Example || Example
|-
| Example || Chapter 5 || Permutation Groups || Example || Example
|-
| Example || Chapter 6 || Cosets and Lagrange’s Theorem || Example || Example
|-
| Example || Chapter 9 || Isomorphisms || Example || Example
|-
| Example || Chapter 10 || Normal Subgroups and Factor Groups || Example || Example
|-
| Example || Chapter 11 || Homomorphisms || Example || Example
|-
| Example || Chapter 13 || The Structure of Groups || Example || Example
|-
| Example || Chapter 16 || Rings || Example || Example
|-
| Example || Chapter 17 || Polynomials || Example || Example
|-
| Example || Chapter 18 || Integral Domains || Example || Example
|}

MAT3233

2020-08-25T19:29:39Z

Rylee.taylor:

==Modern Algebra==

[[MAT3233]]. Modern Algebra. (3-0) 3 Credit Hours.

Prerequisite: [[MAT3013]]. Topics will include the development of groups, integral domains, fields, and number systems, including the complex numbers. Divisibility, congruences, primes, perfect numbers, and some other problems of number theory will be considered. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Example || Chapter 1 || Preliminaries || Example || Example
|-
| Example || Chapter 2 || The Integers || Example || Example
|-
| Example || Chapter 3 || Groups || Example || Example
|-
| Example || Chapter 4 || Cyclic Groups || Example || Example
|-
| Example || Chapter 5 || Permutation Groups || Example || Example
|-
| Example || Chapter 6 || Cosets and Lagrange’s Theorem || Example || Example
|-
| Example || Chapter 9 || Isomorphisms || Example || Example
|-
| Example || Chapter 10 || Normal Subgroups and Factor Groups || Example || Example
|-
| Example || Chapter 11 || Homomorphisms || Example || Example
|-
| Example || Chapter 13 || The Structure of Groups || Example || Example
|-
| Example || Chapter 16 || Rings || Example || Example
|-
| Example || Chapter 17 || Polynomials || Example || Example
|-
| Example || Chapter 18 || Integral Domains || Example || Example
|}

MAT3233

2020-08-25T19:28:56Z

Rylee.taylor: Creating MAT3233 table

==Modern Algebra==

[MAT3233]. Modern Algebra. (3-0) 3 Credit Hours.

Prerequisite: [MAT3013]. Topics will include the development of groups, integral domains, fields, and number systems, including the complex numbers. Divisibility, congruences, primes, perfect numbers, and some other problems of number theory will be considered. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Example || Chapter 1 || Preliminaries || Example || Example
|-
| Example || Chapter 2 || The Integers || Example || Example
|-
| Example || Chapter 3 || Groups || Example || Example
|-
| Example || Chapter 4 || Cyclic Groups || Example || Example
|-
| Example || Chapter 5 || Permutation Groups || Example || Example
|-
| Example || Chapter 6 || Cosets and Lagrange’s Theorem || Example || Example
|-
| Example || Chapter 9 || Isomorphisms || Example || Example
|-
| Example || Chapter 10 || Normal Subgroups and Factor Groups || Example || Example
|-
| Example || Chapter 11 || Homomorphisms || Example || Example
|-
| Example || Chapter 13 || The Structure of Groups || Example || Example
|-
| Example || Chapter 16 || Rings || Example || Example
|-
| Example || Chapter 17 || Polynomials || Example || Example
|-
| Example || Chapter 18 || Integral Domains || Example || Example
|}

Finding Vertical asymptotes of rational functions

2020-08-18T21:02:52Z

Rylee.taylor: adding links to other courses

* [[Rational Functions]] ([[MAT1073]])
* [[Graphs of Rational Functions]] ([[MAT1073]])

MAT1093

2020-08-18T21:01:53Z

Rylee.taylor: linking pre reqs

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* [[Interval notation]]
* [[Solving linear equations and inequalities]]
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: [[Even and Odd Functions]]
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]]
||
* [[Algebraic graphing technics]]
* [[Transformations]]
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || [[Finding Vertical asymptotes of rational functions]] || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]]
||
* [[Algebraic graphing technics]]
* [[Transformations]]
|| Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions|Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

Algebraic graphing techniques

2020-08-18T20:59:29Z

Rylee.taylor: adding links to other courses

* [[Graphs]] ([[MAT1073]])
* [[Domain of a Function]] ([[MAT1073]])
* [[Range of a Function]] ([[MAT1073]])
* [[Graphs of Polynomials]] ([[MAT1073]])
* [[Graphs of Rational Functions]] ([[MAT1073]])

Transformations

2020-08-18T20:56:47Z

Rylee.taylor: adding links to other courses

* [[Single Transformations of Functions]] ([[MAT1073]])
* [[Multiple Transformations of Functions]] ([[MAT1073]])

MAT1093

2020-08-18T20:55:59Z

Rylee.taylor: linking pre reqs

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* [[Interval notation]]
* [[Solving linear equations and inequalities]]
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: [[Even and Odd Functions]]
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]]
||
* [[Algebraic graphing technics]]
* [[Transformations]]
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions|Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

Even and Odd Functions

2020-08-18T20:54:21Z

Rylee.taylor: adding links to other courses

* [[Single Transformations of Functions]] ([[MAT1073]])

MAT1093

2020-08-18T20:53:53Z

Rylee.taylor: linking pre reqs

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* [[Interval notation]]
* [[Solving linear equations and inequalities]]
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: [[Even and Odd Functions]]
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions|Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

MAT1093

2020-08-18T20:52:18Z

Rylee.taylor:

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* [[Interval notation]]
* [[Solving linear equations and inequalities]]
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions|Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

Solving linear equations and inequalities

2020-08-18T20:51:16Z

Rylee.taylor: adding links to other courses

* [[Solving Equations and Inequalities]] ([[MAT1073]])
* [[Linear Equations]] ([[MAT1073]])

Interval notation

2020-08-18T20:48:28Z

Rylee.taylor: adding links to other courses

* [[Domain of a Function]] ([[MAT1073]])

MAT1093

2020-08-18T20:48:01Z

Rylee.taylor: linking pre reqs

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* [[Interval notation]]
* [[Solving linear equations and inequalities]]
* [[Evaluating algebraic expressions]]
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions|Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

Local & Global Maxima & Minima

2020-08-18T20:46:06Z

Rylee.taylor: adding links to other courses

* [[Quadratic Functions]] ([[MAT1073]])

MAT1193

2020-08-18T20:45:36Z

Rylee.taylor: adding link to pre req

== Calculus for the Biosciences ==

[https://catalog.utsa.edu/search/?P=MAT%201193 MAT 1193 Calculus for the Biosciences]. (3-0) 3 Credit Hours. (TCCN = MATH 2313)

Prerequisite: [[MAT1093|MAT 1093]] or an equivalent course or satisfactory performance on a placement examination. An introduction to calculus is presented using discrete-time dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phase-plane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $72; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable"
|-
! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
|-
| Week 1 || '''Example''' || [[Review of Functions and Change]]
||
* [[Basic graphing skills]]
* [[The idea of a function]]
* Graphs of elementary functions (lines, parabola)
* Understanding of slope
* Periodic functions
||
* Define a function and connect to a real-world dynamical model
* Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
* Understand formulas for distance, velocity and speed and make connection with slope formula
* Understand exponential functions and their graphs in terms of exponential growth/decay
* Understand logarithmic functions, graph and solve equations with log properties
* Analyze graphs of the sine and cosine by understanding amplitude and period
|-
| Week 2 || '''Example''' || [[Instantaneous Rate of Change]]
||
* Evaluating functions
* Tangent lines
* Average rate of change
* Equations of a line (slope-intercept, point-slope)
||
* Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
* Defining velocity using the idea of a limit
* Visualizing the limit with tangent lines
* Recognize graphs of derivatives from original function
* Estimate the derivative of a function given table data and graphically
* Interpret the derivative with units and alternative notations (Leibniz)
* Use derivative to estimate value of a function
|-
| Week 3 || '''Example''' || [[Limits]] || '''Example'''
||
* Use the limit definition to define the derivative at a particular point and to define the derivative function
* Understand the definition of continuity
* Apply derivatives to biological functions
|-
| Week 4 & 5 || '''Example''' || [[Derivative Formulas]]
||
* Equations of lines
* [[Limits]]
* [[Composite functions]]
* [[Exponential]]
* [[Logarithmic]]
* [[Trigonometric]]
* [[Applications]]
||
* Use constant formula and power formula to differentiate functions along with the sum and difference rule
* Use differentiation to find the equation of a tangent line to make predictions using tangent line approximation
* Differentiate exponential and logarithmic functions
* Differentiate composite functions using the chain rule
* Differentiate products and quotients
* Differentiate trigonometric functions
* Applications of trigonometric function derivatives
|-
| Week 6 || '''Example''' || [[Applications]]
||
* [[Local & Global Maxima & Minima]]
* Concavity
||
* Detecting a local maximum or minimum from graph and function values
* Test for both local and global maxima and minima using first derivative test (finding critical points)
* Test for both local and global maxima and minima using second derivative test (testing concavity)
* Using concavity for finding inflection points
* Apply max and min techniques in real world applications in the field of Biology (logistic growth)
|-
| Week 7 || '''Example''' || [[Accumulated Change]]
||
* Distance formula
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
|-
| Week 7 & 9 || '''Example''' || [[The Definite Integral]]
||
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
* Use the limit formula to compute a definite integral
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 8 || '''Example''' || [[Antiderivatives]] || Basics in graphing
||
* Be able to analyze area under the curve with antiderivatives graphically and numerically
* Use formulas for finding antiderivatives of constants and powers
* Use formulas for finding antiderivatives of trigonometric functions
|-
| Week 9 || '''Example''' || [[The Fundamental Theorem of Calculus]] || Average formula
||
* Use the limit formula to compute a definite integral
* Compute area with the fundamental theorem of calculus (FTC)
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 10 || '''Example''' || [[Integration Applications]] || '''Example''' || Solve various biology applications using the fundamental theorem of calculus
|-
| Week 10 || '''Example''' || [[Substitution Method]] || '''Example''' || Applying integration by substitution formulas
|-
| Week 11 || '''Example''' || [[Integration by Parts and further applications]] || '''Example'''
||
* Applying integration by integration by parts formulas
* Recognize which integration formulas to use
|-
| Week 12 || '''Example''' || [[Differential Equations (Mathematical Modeling)]] || Word problem setup and understanding of mathematical models
||
* Understand how to take information to set up a mathematical model
* Examine the basic parts of differential equations
|-
| Week 13 || '''Example''' || [[Differential Equations]] || Graphing and factoring
||
* Examine differential equations graphically with slope fields
* Use separation of variables for solving differential equations
|-
| Week 14 || '''Example''' || [[Exponential Growth and Decay & Surge Function]] || [[Exponential functions]]
||
* Apply differential equations to exponential growth & decay functions for population models
* Apply differential equations to surge functions for drug models
|}

Exponential functions

2020-08-18T20:42:01Z

Rylee.taylor: adding links to other courses

* [[Logarithmic and Exponential Equations]] ([[MAT1093]])
* [[Exponential growth and decay models]] ([[MAT1093]])

MAT1193

2020-08-18T20:40:34Z

Rylee.taylor: adding link to pre req

== Calculus for the Biosciences ==

[https://catalog.utsa.edu/search/?P=MAT%201193 MAT 1193 Calculus for the Biosciences]. (3-0) 3 Credit Hours. (TCCN = MATH 2313)

Prerequisite: [[MAT1093|MAT 1093]] or an equivalent course or satisfactory performance on a placement examination. An introduction to calculus is presented using discrete-time dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phase-plane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $72; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable"
|-
! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
|-
| Week 1 || '''Example''' || [[Review of Functions and Change]]
||
* [[Basic graphing skills]]
* [[The idea of a function]]
* Graphs of elementary functions (lines, parabola)
* Understanding of slope
* Periodic functions
||
* Define a function and connect to a real-world dynamical model
* Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
* Understand formulas for distance, velocity and speed and make connection with slope formula
* Understand exponential functions and their graphs in terms of exponential growth/decay
* Understand logarithmic functions, graph and solve equations with log properties
* Analyze graphs of the sine and cosine by understanding amplitude and period
|-
| Week 2 || '''Example''' || [[Instantaneous Rate of Change]]
||
* Evaluating functions
* Tangent lines
* Average rate of change
* Equations of a line (slope-intercept, point-slope)
||
* Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
* Defining velocity using the idea of a limit
* Visualizing the limit with tangent lines
* Recognize graphs of derivatives from original function
* Estimate the derivative of a function given table data and graphically
* Interpret the derivative with units and alternative notations (Leibniz)
* Use derivative to estimate value of a function
|-
| Week 3 || '''Example''' || [[Limits]] || '''Example'''
||
* Use the limit definition to define the derivative at a particular point and to define the derivative function
* Understand the definition of continuity
* Apply derivatives to biological functions
|-
| Week 4 & 5 || '''Example''' || [[Derivative Formulas]]
||
* Equations of lines
* [[Limits]]
* [[Composite functions]]
* [[Exponential]]
* [[Logarithmic]]
* [[Trigonometric]]
* [[Applications]]
||
* Use constant formula and power formula to differentiate functions along with the sum and difference rule
* Use differentiation to find the equation of a tangent line to make predictions using tangent line approximation
* Differentiate exponential and logarithmic functions
* Differentiate composite functions using the chain rule
* Differentiate products and quotients
* Differentiate trigonometric functions
* Applications of trigonometric function derivatives
|-
| Week 6 || '''Example''' || [[Applications]]
||
* Local & Global Maxima & Minima
* Concavity
||
* Detecting a local maximum or minimum from graph and function values
* Test for both local and global maxima and minima using first derivative test (finding critical points)
* Test for both local and global maxima and minima using second derivative test (testing concavity)
* Using concavity for finding inflection points
* Apply max and min techniques in real world applications in the field of Biology (logistic growth)
|-
| Week 7 || '''Example''' || [[Accumulated Change]]
||
* Distance formula
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
|-
| Week 7 & 9 || '''Example''' || [[The Definite Integral]]
||
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
* Use the limit formula to compute a definite integral
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 8 || '''Example''' || [[Antiderivatives]] || Basics in graphing
||
* Be able to analyze area under the curve with antiderivatives graphically and numerically
* Use formulas for finding antiderivatives of constants and powers
* Use formulas for finding antiderivatives of trigonometric functions
|-
| Week 9 || '''Example''' || [[The Fundamental Theorem of Calculus]] || Average formula
||
* Use the limit formula to compute a definite integral
* Compute area with the fundamental theorem of calculus (FTC)
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 10 || '''Example''' || [[Integration Applications]] || '''Example''' || Solve various biology applications using the fundamental theorem of calculus
|-
| Week 10 || '''Example''' || [[Substitution Method]] || '''Example''' || Applying integration by substitution formulas
|-
| Week 11 || '''Example''' || [[Integration by Parts and further applications]] || '''Example'''
||
* Applying integration by integration by parts formulas
* Recognize which integration formulas to use
|-
| Week 12 || '''Example''' || [[Differential Equations (Mathematical Modeling)]] || Word problem setup and understanding of mathematical models
||
* Understand how to take information to set up a mathematical model
* Examine the basic parts of differential equations
|-
| Week 13 || '''Example''' || [[Differential Equations]] || Graphing and factoring
||
* Examine differential equations graphically with slope fields
* Use separation of variables for solving differential equations
|-
| Week 14 || '''Example''' || [[Exponential Growth and Decay & Surge Function]] || [[Exponential functions]]
||
* Apply differential equations to exponential growth & decay functions for population models
* Apply differential equations to surge functions for drug models
|}

Trigonometric

2020-08-18T20:38:14Z

Rylee.taylor: adding links to other courses

* [[Trigonometric Equations]] ([[MAT1093]])
* [[Trigonometric Identities]] ([[MAT1093]])

Logarithmic

2020-08-18T20:35:25Z

Rylee.taylor: adding links to other courses

* [[Logarithmic Functions]] ([[MAT1073]])
* [[Logarithmic Properties]] ([[MAT1073]])
* [[Logarithmic and Exponential Equations]] ([[MAT1093]])

Exponential

2020-08-18T20:34:50Z

Rylee.taylor: adding links to other courses

* [[Exponential Properties]] ([[MAT1073]])
* [[Exponential Functions]] ([[MAT1073]])
* [[Logarithmic and Exponential Equations]] ([[MAT1093]])

The idea of a function

2020-08-18T20:32:09Z

Rylee.taylor: adding course

* [[Functions]] ([[MAT1073]])
* [[Function Notation]] ([[MAT1073]])
* [[Domain of a Function]] ([[MAT1073]])
* [[Range of a Function]] ([[MAT1073]])

Exponential

2020-08-18T20:30:59Z

Rylee.taylor: adding course

* [[Exponential Properties]] ([[MAT1073]])
* [[Exponential Functions]] ([[MAT1073]])

Composite functions

2020-08-18T20:29:59Z

Rylee.taylor: adding course

* [[Composition of Functions]] ([[MAT1073]])

Basic graphing skills

2020-08-18T20:29:15Z

Rylee.taylor:

* [[Graphs]] ([[MAT1073]])
* [[Graph of equations]] ([[MAT1023]])
* [[Functions and their graphs]] ([[MAT1093]])
* [[One-to-one functions]] ([[MAT1093]])
* [[Inverse functions]] ([[MAT1093]])

Logarithmic

2020-08-18T20:28:13Z

Rylee.taylor: adding links to other courses

* [[Logarithmic Functions]] ([[MAT1073]])
* [[Logarithmic Properties]] ([[MAT1073]])

Exponential

2020-08-18T20:26:23Z

Rylee.taylor: adding links to other courses

* [[Exponential Properties]]
* [[Exponential Functions]]

Composite functions

2020-08-18T20:25:47Z

Rylee.taylor: adding links to other courses

* [[Composition of Functions]]

MAT1193

2020-08-18T20:25:11Z

Rylee.taylor: adding link to pre reqs

== Calculus for the Biosciences ==

[https://catalog.utsa.edu/search/?P=MAT%201193 MAT 1193 Calculus for the Biosciences]. (3-0) 3 Credit Hours. (TCCN = MATH 2313)

Prerequisite: [[MAT1093|MAT 1093]] or an equivalent course or satisfactory performance on a placement examination. An introduction to calculus is presented using discrete-time dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phase-plane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $72; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable"
|-
! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
|-
| Week 1 || '''Example''' || [[Review of Functions and Change]]
||
* [[Basic graphing skills]]
* [[The idea of a function]]
* Graphs of elementary functions (lines, parabola)
* Understanding of slope
* Periodic functions
||
* Define a function and connect to a real-world dynamical model
* Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
* Understand formulas for distance, velocity and speed and make connection with slope formula
* Understand exponential functions and their graphs in terms of exponential growth/decay
* Understand logarithmic functions, graph and solve equations with log properties
* Analyze graphs of the sine and cosine by understanding amplitude and period
|-
| Week 2 || '''Example''' || [[Instantaneous Rate of Change]]
||
* Evaluating functions
* Tangent lines
* Average rate of change
* Equations of a line (slope-intercept, point-slope)
||
* Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
* Defining velocity using the idea of a limit
* Visualizing the limit with tangent lines
* Recognize graphs of derivatives from original function
* Estimate the derivative of a function given table data and graphically
* Interpret the derivative with units and alternative notations (Leibniz)
* Use derivative to estimate value of a function
|-
| Week 3 || '''Example''' || [[Limits]] || '''Example'''
||
* Use the limit definition to define the derivative at a particular point and to define the derivative function
* Understand the definition of continuity
* Apply derivatives to biological functions
|-
| Week 4 & 5 || '''Example''' || [[Derivative Formulas]]
||
* Equations of lines
* [[Limits]]
* [[Composite functions]]
* [[Exponential]]
* [[Logarithmic]]
* [[Trigonometric]]
* [[Applications]]
||
* Use constant formula and power formula to differentiate functions along with the sum and difference rule
* Use differentiation to find the equation of a tangent line to make predictions using tangent line approximation
* Differentiate exponential and logarithmic functions
* Differentiate composite functions using the chain rule
* Differentiate products and quotients
* Differentiate trigonometric functions
* Applications of trigonometric function derivatives
|-
| Week 6 || '''Example''' || [[Applications]]
||
* Local & Global Maxima & Minima
* Concavity
||
* Detecting a local maximum or minimum from graph and function values
* Test for both local and global maxima and minima using first derivative test (finding critical points)
* Test for both local and global maxima and minima using second derivative test (testing concavity)
* Using concavity for finding inflection points
* Apply max and min techniques in real world applications in the field of Biology (logistic growth)
|-
| Week 7 || '''Example''' || [[Accumulated Change]]
||
* Distance formula
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
|-
| Week 7 & 9 || '''Example''' || [[The Definite Integral]]
||
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
* Use the limit formula to compute a definite integral
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 8 || '''Example''' || [[Antiderivatives]] || Basics in graphing
||
* Be able to analyze area under the curve with antiderivatives graphically and numerically
* Use formulas for finding antiderivatives of constants and powers
* Use formulas for finding antiderivatives of trigonometric functions
|-
| Week 9 || '''Example''' || [[The Fundamental Theorem of Calculus]] || Average formula
||
* Use the limit formula to compute a definite integral
* Compute area with the fundamental theorem of calculus (FTC)
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 10 || '''Example''' || [[Integration Applications]] || '''Example''' || Solve various biology applications using the fundamental theorem of calculus
|-
| Week 10 || '''Example''' || [[Substitution Method]] || '''Example''' || Applying integration by substitution formulas
|-
| Week 11 || '''Example''' || [[Integration by Parts and further applications]] || '''Example'''
||
* Applying integration by integration by parts formulas
* Recognize which integration formulas to use
|-
| Week 12 || '''Example''' || [[Differential Equations (Mathematical Modeling)]] || Word problem setup and understanding of mathematical models
||
* Understand how to take information to set up a mathematical model
* Examine the basic parts of differential equations
|-
| Week 13 || '''Example''' || [[Differential Equations]] || Graphing and factoring
||
* Examine differential equations graphically with slope fields
* Use separation of variables for solving differential equations
|-
| Week 14 || '''Example''' || [[Exponential Growth and Decay & Surge Function]] || Exponential functions
||
* Apply differential equations to exponential growth & decay functions for population models
* Apply differential equations to surge functions for drug models
|}

The idea of a function

2020-08-18T20:21:23Z

Rylee.taylor: adding links to other courses

* [[Functions]]
* [[Function Notation]]
* [[Domain of a Function]]
* [[Range of a Function]]

MAT1193

2020-08-18T20:19:44Z

Rylee.taylor: adding links to other courses

== Calculus for the Biosciences ==

[https://catalog.utsa.edu/search/?P=MAT%201193 MAT 1193 Calculus for the Biosciences]. (3-0) 3 Credit Hours. (TCCN = MATH 2313)

Prerequisite: [[MAT1093|MAT 1093]] or an equivalent course or satisfactory performance on a placement examination. An introduction to calculus is presented using discrete-time dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phase-plane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $72; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable"
|-
! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
|-
| Week 1 || '''Example''' || [[Review of Functions and Change]]
||
* [[Basic graphing skills]]
* [[The idea of a function]]
* Graphs of elementary functions (lines, parabola)
* Understanding of slope
* Periodic functions
||
* Define a function and connect to a real-world dynamical model
* Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
* Understand formulas for distance, velocity and speed and make connection with slope formula
* Understand exponential functions and their graphs in terms of exponential growth/decay
* Understand logarithmic functions, graph and solve equations with log properties
* Analyze graphs of the sine and cosine by understanding amplitude and period
|-
| Week 2 || '''Example''' || [[Instantaneous Rate of Change]]
||
* Evaluating functions
* Tangent lines
* Average rate of change
* Equations of a line (slope-intercept, point-slope)
||
* Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
* Defining velocity using the idea of a limit
* Visualizing the limit with tangent lines
* Recognize graphs of derivatives from original function
* Estimate the derivative of a function given table data and graphically
* Interpret the derivative with units and alternative notations (Leibniz)
* Use derivative to estimate value of a function
|-
| Week 3 || '''Example''' || [[Limits]] || '''Example'''
||
* Use the limit definition to define the derivative at a particular point and to define the derivative function
* Understand the definition of continuity
* Apply derivatives to biological functions
|-
| Week 4 & 5 || '''Example''' || [[Derivative Formulas]]
||
* Equations of lines
* [[Limits]]
* Composite functions
* Exponential
* Logarithmic
* Trigonometric
* Applications
||
* Use constant formula and power formula to differentiate functions along with the sum and difference rule
* Use differentiation to find the equation of a tangent line to make predictions using tangent line approximation
* Differentiate exponential and logarithmic functions
* Differentiate composite functions using the chain rule
* Differentiate products and quotients
* Differentiate trigonometric functions
* Applications of trigonometric function derivatives
|-
| Week 6 || '''Example''' || [[Applications]]
||
* Local & Global Maxima & Minima
* Concavity
||
* Detecting a local maximum or minimum from graph and function values
* Test for both local and global maxima and minima using first derivative test (finding critical points)
* Test for both local and global maxima and minima using second derivative test (testing concavity)
* Using concavity for finding inflection points
* Apply max and min techniques in real world applications in the field of Biology (logistic growth)
|-
| Week 7 || '''Example''' || [[Accumulated Change]]
||
* Distance formula
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
|-
| Week 7 & 9 || '''Example''' || [[The Definite Integral]]
||
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
* Use the limit formula to compute a definite integral
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 8 || '''Example''' || [[Antiderivatives]] || Basics in graphing
||
* Be able to analyze area under the curve with antiderivatives graphically and numerically
* Use formulas for finding antiderivatives of constants and powers
* Use formulas for finding antiderivatives of trigonometric functions
|-
| Week 9 || '''Example''' || [[The Fundamental Theorem of Calculus]] || Average formula
||
* Use the limit formula to compute a definite integral
* Compute area with the fundamental theorem of calculus (FTC)
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 10 || '''Example''' || [[Integration Applications]] || '''Example''' || Solve various biology applications using the fundamental theorem of calculus
|-
| Week 10 || '''Example''' || [[Substitution Method]] || '''Example''' || Applying integration by substitution formulas
|-
| Week 11 || '''Example''' || [[Integration by Parts and further applications]] || '''Example'''
||
* Applying integration by integration by parts formulas
* Recognize which integration formulas to use
|-
| Week 12 || '''Example''' || [[Differential Equations (Mathematical Modeling)]] || Word problem setup and understanding of mathematical models
||
* Understand how to take information to set up a mathematical model
* Examine the basic parts of differential equations
|-
| Week 13 || '''Example''' || [[Differential Equations]] || Graphing and factoring
||
* Examine differential equations graphically with slope fields
* Use separation of variables for solving differential equations
|-
| Week 14 || '''Example''' || [[Exponential Growth and Decay & Surge Function]] || Exponential functions
||
* Apply differential equations to exponential growth & decay functions for population models
* Apply differential equations to surge functions for drug models
|}

Basic graphing skills

2020-08-18T20:15:38Z

Rylee.taylor: adding links to other courses

* [[Graphs]]
* [[Graph of equations]]
* [[Functions and their graphs]]
* [[One-to-one functions]]
* [[Inverse functions]]

MAT1193

2020-08-18T20:11:56Z

Rylee.taylor: adding link

== Calculus for the Biosciences ==

[https://catalog.utsa.edu/search/?P=MAT%201193 MAT 1193 Calculus for the Biosciences]. (3-0) 3 Credit Hours. (TCCN = MATH 2313)

Prerequisite: [[MAT1093|MAT 1093]] or an equivalent course or satisfactory performance on a placement examination. An introduction to calculus is presented using discrete-time dynamical systems and differential equations to model fundamental processes important in biological and biomedical applications. Specific topics to be covered are limits, continuity, differentiation, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, differential equations, and the phase-plane. (Formerly MAT 1194. Credit can be earned for only one of the following: MAT 1193, MAT 1194, or MAT 1214.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $72; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable"
|-
! Date !! Section !! Topic !! Pre-requisite !! Student Learning Outcome
|-
| Week 1 || '''Example''' || [[Review of Functions and Change]]
||
* [[Basic graphing skills]]
* The idea of a function
* Graphs of elementary functions (lines, parabola)
* Understanding of slope
* Periodic functions
||
* Define a function and connect to a real-world dynamical model
* Estimate instantaneous rate of change by both visualization of average rate of change and calculations of the formula
* Understand formulas for distance, velocity and speed and make connection with slope formula
* Understand exponential functions and their graphs in terms of exponential growth/decay
* Understand logarithmic functions, graph and solve equations with log properties
* Analyze graphs of the sine and cosine by understanding amplitude and period
|-
| Week 2 || '''Example''' || [[Instantaneous Rate of Change]]
||
* Evaluating functions
* Tangent lines
* Average rate of change
* Equations of a line (slope-intercept, point-slope)
||
* Comparing and contrasting the average rate of change (ARC) with instantaneous rate of change (IRC)
* Defining velocity using the idea of a limit
* Visualizing the limit with tangent lines
* Recognize graphs of derivatives from original function
* Estimate the derivative of a function given table data and graphically
* Interpret the derivative with units and alternative notations (Leibniz)
* Use derivative to estimate value of a function
|-
| Week 3 || '''Example''' || [[Limits]] || '''Example'''
||
* Use the limit definition to define the derivative at a particular point and to define the derivative function
* Understand the definition of continuity
* Apply derivatives to biological functions
|-
| Week 4 & 5 || '''Example''' || [[Derivative Formulas]]
||
* Equations of lines
* [[Limits]]
* Composite functions
* Exponential
* Logarithmic
* Trigonometric
* Applications
||
* Use constant formula and power formula to differentiate functions along with the sum and difference rule
* Use differentiation to find the equation of a tangent line to make predictions using tangent line approximation
* Differentiate exponential and logarithmic functions
* Differentiate composite functions using the chain rule
* Differentiate products and quotients
* Differentiate trigonometric functions
* Applications of trigonometric function derivatives
|-
| Week 6 || '''Example''' || [[Applications]]
||
* Local & Global Maxima & Minima
* Concavity
||
* Detecting a local maximum or minimum from graph and function values
* Test for both local and global maxima and minima using first derivative test (finding critical points)
* Test for both local and global maxima and minima using second derivative test (testing concavity)
* Using concavity for finding inflection points
* Apply max and min techniques in real world applications in the field of Biology (logistic growth)
|-
| Week 7 || '''Example''' || [[Accumulated Change]]
||
* Distance formula
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
|-
| Week 7 & 9 || '''Example''' || [[The Definite Integral]]
||
* Summation formulas
||
* Approximate total change from rate of change
* Computing area with Riemann Sums
* Apply concepts of finding total change with Riemann Sums
* Use the limit formula to compute a definite integral
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 8 || '''Example''' || [[Antiderivatives]] || Basics in graphing
||
* Be able to analyze area under the curve with antiderivatives graphically and numerically
* Use formulas for finding antiderivatives of constants and powers
* Use formulas for finding antiderivatives of trigonometric functions
|-
| Week 9 || '''Example''' || [[The Fundamental Theorem of Calculus]] || Average formula
||
* Use the limit formula to compute a definite integral
* Compute area with the fundamental theorem of calculus (FTC)
* Interpreting the definite integral as area above and below the graph
* Use the definite integral to compute average value
|-
| Week 10 || '''Example''' || [[Integration Applications]] || '''Example''' || Solve various biology applications using the fundamental theorem of calculus
|-
| Week 10 || '''Example''' || [[Substitution Method]] || '''Example''' || Applying integration by substitution formulas
|-
| Week 11 || '''Example''' || [[Integration by Parts and further applications]] || '''Example'''
||
* Applying integration by integration by parts formulas
* Recognize which integration formulas to use
|-
| Week 12 || '''Example''' || [[Differential Equations (Mathematical Modeling)]] || Word problem setup and understanding of mathematical models
||
* Understand how to take information to set up a mathematical model
* Examine the basic parts of differential equations
|-
| Week 13 || '''Example''' || [[Differential Equations]] || Graphing and factoring
||
* Examine differential equations graphically with slope fields
* Use separation of variables for solving differential equations
|-
| Week 14 || '''Example''' || [[Exponential Growth and Decay & Surge Function]] || Exponential functions
||
* Apply differential equations to exponential growth & decay functions for population models
* Apply differential equations to surge functions for drug models
|}

MAT1093

2020-08-18T20:02:45Z

Rylee.taylor: fixing typo in link

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* Interval notation
* Solving linear equations and inequalities
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions|Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

Trigonometric Functions: Unit Circle Approach

2020-08-18T20:00:04Z

Rylee.taylor: added Trigonometric Functions_ Unit Circle Approach notes by professor Esparza

* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Trigonometric%20Functions_%20Unit%20Circle%20Approach/Esparza%201093%20Notes%202.2.pdf Trigonometric Functions: Unit Circle Approach]. Written notes created by Professor Esparza, UTSA.

MAT1093

2020-08-18T19:58:03Z

Rylee.taylor:

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* Interval notation
* Solving linear equations and inequalities
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

MAT1093

2020-08-18T19:56:27Z

Rylee.taylor:

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* Interval notation
* Solving linear equations and inequalities
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [Trigonometric Functions: Unit Circle Approach]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [Trigonometric Functions: Unit Circle Approach]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [Trigonometric Functions: Unit Circle Approach]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [Trigonometric Functions: Unit Circle Approach]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [Trigonometric Functions: Unit Circle Approach]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [Trigonometric Functions: Unit Circle Approach]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [Trigonometric Functions: Unit Circle Approach] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

MAT1093

2020-08-18T19:53:15Z

Rylee.taylor:

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* Interval notation
* Solving linear equations and inequalities
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of Trigonometric Functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

MAT1093

2020-08-18T19:49:29Z

Rylee.taylor: fixing link

==Precalculus==
[https://catalog.utsa.edu/search/?P=MAT%201093|MAT 1093. Precalculus]. (3-0) 3 Credit Hours. (TCCN = MATH 2312)

Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

{| class="wikitable sortable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student learning outcomes
|-
| Week 1 || Orientation
||
* Distribute and read syllabus
* Introduction to MyMathLab
|| ||
|-
| Week 1 || 1.3 || [[Functions and their graphs]]
||
* Interval notation
* Solving linear equations and inequalities
* Evaluating algebraic expressions
||
* Determine whether a relation is a function
* Find the Difference Quotient of a simple quadratic or radical function
* Find the domain of a function defined by an equation or a graph
* Identify the graph of a function and get information from the graph
|-
| Week 2 || 1.7 || [[One-to-one functions]] || Section 1.3: [[Functions and their graphs]] || Determine when a function or its graph is one-to-one
|-
| Week 2 || 1.7 || [[Inverse functions]] || Section 1.3: [[Functions and their graphs]]
||
* Find the inverse of a function defined by a graph or an equation
* Use the composition property to verify two functions are the inverses of each other
* Find the inverse of a function algebraically or graphically
|-
| Week 2 || 2.1 || [[Angles and their measure]]
|| '''Elementary geometry and terminology'''
||
* Know the definition of an angle in standard position and when its measure is positive or negative
* Know relationship between degrees and radians and be able to sketch angles of any measure
* Be able to convert angles to and from decimal degrees and D-M-S notations
* Know formulas for finding the length of a circular arc and the area of a sector of a circle
* Find the distance between two cities at same longitudes and at different longitudes
* Know the formula relating linear speed of an object in circular motion with its angular velocity in either radians per unit of time or revolutions per unit of time or vice versa
|-
| Week 3 || 2.2 || [[Trigonometric Functions: Unit Circle Approach]]
||
* Appendix A.2: '''Geometry Essentials'''
* Section 1.2: '''Symmetry of graphs'''
||
* Learn the definitions of the six trig functions as derived from the Unit Circle and apply them to find exact values for a given point on this circle
* Use the Unit Circle definitions to find the exact values for all six trig functions for angles of π/4, π/6 and π/3 radians, and integer multiples of these angles
* Use a course-approved scientific calculator to approximate values for the six trig functions of any angle
* Learn the definitions of the six trig. functions derived from a circle of any radius '''r''', and use them to find exact and approximate values of these functions for a given point on the circle, including those in application questions
|-
| Week 3 || 2.3 || [[Properties of the Trigonometric Functions]]
||
* Section 1.3: [[Functions and their graphs]]
* Section 1.4: '''Even and Odd Functions'''
||
* Determine the domain and range of each of the six trig functions, their period, and their signs in a given quadrant of the x-y plane
* Learn the reciprocal and quotient identities based on the definitions from the Unit Circle of the six trigonometric functions
* Use the Unit Circle to derive the three Pythagorean Identities to complete the set of Fundamental Identities
* Find the exact value of the remaining trig functions, given the value of one and the sign of another, using either a circle of radius '''r''' or the Fundamental Identities
* Determine and use the Even-Odd properties to find exact values for the six trigonometric functions
|-
| Week 4 || 2.4 || [[Graphs of the Sine and Cosine Functions]] || '''Algebraic graphing technics and transformations '''
||
* Graph on the x-y plane the functions f(x) = sin x and f(x) = cos x using key points
* Graph functions of the form y = A sin (ωx) and y = A cos (ωx) using transformations
* Determine the Amplitude and Period of sinusoidal functions from equations and graphs
* Find equations of sinusoidal functions given their graphs
|-
| Week 4 || 2.5 || [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]] || '''Finding Vertical asymptotes of rational functions''' || Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed
|-
| Week 5 || 2.6 || [[Phase shift and Applications]] || '''Algebraic graphing technics and transformations''' || Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω
|-
| Week 5 || || Test 1 Review Session. '''Common Test 1: Ch.1 and 2.''' || ||
|-
| Week 6 || 3.1 || [[The inverse Sine, Cosine and Tangent functions]]
||
* Section 1.7: [[Inverse functions]]
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.4: [[Graphs of the Sine and Cosine Functions]]
* Section 2.5: [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* Solving algebraic equations
||
* Determine the inverse functions for the sine, cosine and tangent knowing their restricted domains that make these functions one-to-one
* Find the exact values of a given inverse sine, cosine or tangent function knowing that each inverse function represents an angle
* Use approved scientific calculator to estimate sine, cosine and tangent functions
* Use properties of inverse functions to find exact values for certain composite functions
* For a given sine, cosine or tangent function find the inverse function algebraically and its domain
* Solve simple equations that contain inverse trigonometric functions, including some from applications
|-
| Week 6 || 3.2 || [[The inverse Secant, Cosecant and Cotangent functions]]
||
* Section 1.7, [[Inverse functions]]
* Section 2.3: [[Properties of the Trigonometric Functions]]
* Section 2.5: [[Graphs of the Cotangent, Cosecant and Secant Functions]]
||
* Find the exact value of composite expressions involving the inverse sine, cosine or tangent function
* Know definitions for the inverse secant, cosecant and cotangent functions, including their domain and range, and determine their exact and approximate values
* Write composite functions of trigonometric and inverse trigonometric functions as an Algebraic expression
|-
| Week 6 || 3.3A || [[Trigonometric equations involving a single trig function]] || '''Section A.4: Solving algebraic equations''' || Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function
|-
| Week 7 || 3.3B || [[Trigonometric Equations]]
||
* '''Section A.4: Solving algebraic equations'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Solve linear, quadratic and other equations containing trigonometric functions, including those from application questions and those that can be solved using the Fundamental Identities
* Find exact solutions in the interval [0, 2π) and in general form
* Use a course-approved calculator to find approximate solutions of trigonometric equations that require the use of an inverse function
|-
| Week 7 || 3.4 || [[Trigonometric Identities]] ||
* Section 2.3: [[Properties of the Trigonometric Functions|Fundamental Identities and even-odd properties]]
* '''Algebraic operations with fractions, polynomials and factoring polynomials'''
|| Prove simple identities using the fundamental identities and algebraic technics
|-
| Week 8 || 3.5 || [[Sum and Difference Formulas]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Use sum and difference formulas to find exact values, establish identities and evaluate compositions with inverse functions
* Solve trigonometric equations linear in both sine and cosine
|-
| Week 8 || 3.6A || [[Double-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use double-angle formulas to find exact values
* Use double-angle formulas to solve trigonometric equations (including from applications)
* Establish identities
|-
| Week 8 || 3.6B || [[Half-angle formulas]] ||
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach|Values of trigonometric functions]]
* Section 2.3: [[Properties of the Trigonometric Functions|Finding exact values given the value of a trig function and the quadrant of the angle]]
||
* Use half-angle formulas to find exact values
* Establish identities
|-
| Week 9 || 3.7 || [[Product-to-Sum and Sum-to-Product Formulas]] || '''Basic algebra and geometry''' || Use product-to-sum and sum-to-product formulas
|-
| Week 9 || ||
* Test 2 Review Session
* '''Common Test 2: Chapter 3'''
|| ||
|-
| Week 10 || 4.1 || [[Right triangle definitions of trig functions and related applications]]
||
* '''Basic algebra and geometry'''
* Section A.2: '''Pythagorean Theorem'''
* Section 3.3: [[Trigonometric Equations]]
||
* Learn the definitions of the six trigonometric functions defined using a right triangle and apply them to solve any right triangle given or sketched from application questions
* Learn how to use bearings in application questions that generate right triangles to be solved using the right triangle definitions of the trig functions
|-
| Week 10 || 4.2 || [[The Law of Sines]]
||
* '''Basic algebra and geometry'''
* Section 3.3: [[Trigonometric Equations]]
|| Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings
|-
| Week 11 || 4.3 || [[The Law of Cosines]] || Section 3.3: [[Trigonometric Equations]] || Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings
|-
| Week 11 || 4.4 || [[Area of a Triangle]] || Section A.2: '''Geometry Essentials'''
||
* Find the area of a SAS triangle using the sine function to find the altitude
* Find the area of a SSS triangle using Heron’s Formula
|-
| Week 11 || 5.1 || [[Polar Coordinates]]
||
* '''Section 1.1: Rectangular coordinates'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
* Section 3.1: [[The inverse Sine, Cosine and Tangent functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-
| Week 11 || 5.2 || [[Polar Equations and Graphs]]
||
* '''Section A-3: Completing the square'''
* '''Section 1.2: Graphing lines and circles'''
|| Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations
|-
| Week 11/12 || 5.3 || [[The complex plane]]
||
* '''Section A.5: Complex numbers'''
* Section 2.2: [[Trigonometric Functions: Unit Circle Approach]]
||
* Plot points in the complex plane
* Convert complex numbers from rectangular to polar/trigonometric form and vice-versa
|-
| Week 12 || 5.3 || [[DeMoivere’s Theorem]] || Section 2.2: [[Trigonometric Functions: Unit Circle Approach]] || Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers
|-
| Week 12 ||
||
* Test 3 Review Session
* '''Common Test 3: Ch.4 and 5'''
|| ||
|-
| Week 13 || 7.4 || [[Logarithmic and Exponential Equations]]
||
* '''Section A-1: Law of Exponents'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms (Review in class as needed)'''
|| Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions
|-
| Week 14 || 7.6 || [[Exponential growth and decay models]]
||
* '''Section A-4: Solving quadratic equations'''
* '''Section 7.1: Exponential functions'''
* '''Section 7.2: Logarithmic functions'''
* '''Section 7.3: Properties of logarithms'''
|| Create and use exponential growth and decay models from two data points
|-
| Week 14 || 7.6 || [[Newton’s law of Cooling models]] || '''Section A-4: Solving quadratic equations''' || Create and use exponential models based on Newton’s Law of Cooling
|-
| Week 14 || 7.6 || [[Logistic growth and decay models]] || '''Section A-4: Solving quadratic equations''' || Use Logistic growth and decay models to find present and future values, and times for any future value
|-
| Week 15 || || Common Final Exam Review || All topics covered during the semester ||
|-
|}

Differential Equations

2020-08-18T19:41:03Z

Rylee.taylor: added powerpoints by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Differential%20Equations/Presentation18_SlopeFields.pptx Slope Fields]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Differential%20Equations/Presentation19_Separation%20of%20Variables.pptx Separation of variables]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Differential%20Equations/Presentation20_DiffEq_Solutions.pptx Differential Equations Solutions]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

Differential Equations (Mathematical Modeling)

2020-08-18T19:38:09Z

Rylee.taylor: added powerpoint by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Differential%20Equations%20(Mathematical%20Modeling)/Presentation17_Setting%20Up%20Differential%20Equations.pptx Setting up Differential Equations]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

Integration by Parts and further applications

2020-08-18T19:37:14Z

Rylee.taylor: added powerpoint by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Integration%20by%20Parts/Presentation16_Integration%20by%20Parts.pptx Integration by Parts]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

Substitution Method

2020-08-18T19:34:33Z

Rylee.taylor: added powerpoint by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Substitution%20Method/Presentation15_Integration%20by%20Substitution.pptx Integration by Substitution]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

Integration Applications

2020-08-18T19:33:25Z

Rylee.taylor: added powerpoint by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Integration%20Applications/Presentation14_FTC_Applications.pptx Fundamental Theorem of Calculus Applications]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

The Fundamental Theorem of Calculus

2020-08-18T19:31:53Z

Rylee.taylor: added powerpoints by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/The%20Fundamental%20Theorem%20of%20Calculus/Presentation12_DefiniteIntegral%20&%20Antiderivatives.pptx Definite Integral & Antiderivatives] (Slides 6&7). PowerPoint file created by Professor Cynthia Roberts, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/The%20Fundamental%20Theorem%20of%20Calculus/Presentation13_FTC%20Part%20I.pptx Fundamental Theorem of Calculus Part 1]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

* [https://youtu.be/jyRdHbHeUuU The Second Fundamental Theorem of Calculus] Video Lecture by James Sousa.

* [https://youtu.be/YE9jpfxEFYk Ex 1: The Second Fundamental Theorem of Calculus] Video Lecture by James Sousa.

* [https://youtu.be/gJtkTRjqM6I Ex 2: The Second Fundamental Theorem of Calculus (Reverse Order)] Video Lecture by James Sousa.

* [https://youtu.be/X5ke8bUiiQM Ex 3: The Second Fundamental Theorem of Calculus] Video Lecture by James Sousa.

* [https://youtu.be/ep52C-MUzDY Ex 4: The Second Fundamental Theorem of Calculus with Chain Rule] Video Lecture by James Sousa.

* [https://youtu.be/8IrK5JcjMvM Ex 5: The Second Fundamental Theorem of Calculus with Chain Rule] Video Lecture by James Sousa.

* [https://youtu.be/6p5NQwAeZRc Ex 6: Second Fundamental Theorem of Calculus with Chain Rule] Video Lecture by James Sousa.

* [https://youtu.be/18qhfQ2IeLU Ex 7: Second Fundamental Theorem of Calculus with Chain Rule] Video Lecture by James Sousa.

* [https://youtu.be/PGmVvIglZx8 Fundamental Theorem of Calculus Part 1] video by patrickJMT

* [https://youtu.be/yrQ6PnE6D8w PART 1 OF THE DREADED FUNDAMENTAL THEOREM OF CALCULUS!] video by Krista King

* [https://youtu.be/aeB5BWY0RlE Fundamental Theorem of Calculus Part 1] video by The Organic Chemistry Tutor

Antiderivatives

2020-08-18T19:26:12Z

Rylee.taylor: added antiderivative powerpoints by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/The%20Definite%20Integral/Presentation11_Distance_Definite_Integral.pptx Distance Definite Integral] (Slides 23-38). PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/The%20Definite%20Integral/Presentation12_DefiniteIntegral%20&%20Antiderivatives.pptx Definite Integral & Antiderivatives]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Antiderivatives/MAT1214-4.10AntiderivativesPwPt.pptx Antiderivatives] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Antiderivatives/MAT1214-4.10AntiderivativesWS1.pdf Antiderivatives Worksheet]

The Definite Integral

2020-08-18T00:35:51Z

Rylee.taylor: added the definite integral powerpoint by professor Roberts

Accumulated Change

2020-08-18T00:33:06Z

Rylee.taylor: added Accumulated Change powerpoint by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Accumulated%20Change/Presentation11_Distance_Definite_Integral.pptx Accumulated Change]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

Applications

2020-08-18T00:31:30Z

Rylee.taylor: added applications powerpoints by professor Roberts

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation3b,4,5_Limits%20&%20Derivative%20Formulas.pptx Limits & Derivative Formulas] (Slides 28 & 29). PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation5b_Exponential%20and%20Logs.pptx Exponential and Logarithms] (Slides 24-26). PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation6%20Product%20Rule%20and%20Quotient%20Rule.pptx Product Rule and Quotient Rule]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation6b%20Chain%20Rule.pptx Chain Rule]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation7_periodic%20functions.pptx Periodic Functions]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation8%20Local%20Max%20&%20Min.pptx Local Max & Min]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation8b_Inflection%20Points.pptx Inflection Points]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation9_Global%20Max%20&%20Min.pptx Global Max & Min]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Applications/Presentation10_LogisticGrowth&SurgeFunction.pptx Logistic Growth & Surge Function]. PowerPoint file created by Professor Cynthia Roberts, UTSA.

Derivative Formulas

2020-08-18T00:23:13Z

Rylee.taylor: fixing link

* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation3_DerivativeFunction%20&%20Interpretations.pptx Derivative Function & Interpretations]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation3b,4,5_Limits%20&%20Derivative%20Formulas.pptx Limits & Derivative Formulas]. PowerPoint file created by Professor Cynthia Roberts, UTSA.
* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation5b_Exponential%20and%20Logs.pptx Exponential and Logarithms]. PowerPoint file created by Professor Cynthia Roberts, UTSA.