* [https://www.youtube.com/watch?v=HAb9JbBD2ig Solving Linear First-Order Differential Equations] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=T3puDZ21Rg4 Ex 1: Solve a Linear First-Order Differential Equation] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=zN0TmKEXFh8 Ex 2: Solve a Linear First-Order Differential Equation] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=dffzCHGO0Og Ex 3: Solve a Linear First-Order Differential Equation] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=RDt5vfXX9OA Ex 1: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=PiG_NqC-RuM Ex 2: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=TpjDYubgLNY Ex 3: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=p-kzJdg1z20 Ex 4: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=KHnzaR_Wd78 Ex 5: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=w1GvJQckli8 Ex 6: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=TiRaAxGarVU Ex 7: Solve a Linear First-Order Differential Equation Using an Integrating Factor] Video by James Sousa, Math is Power 4U

* [https://www.youtube.com/watch?v=j511hg7Hlbg Integrating Factors 1] Video by Khan Academy
* [https://www.youtube.com/watch?v=0NyeDUhKwBE Integrating Factors 2] Video by Khan Academy

* [https://www.youtube.com/watch?v=Et4Y41ZNyao First Order Linear Differential Equations] Video by PatrickJMT
* [https://www.youtube.com/watch?v=eWLgWazTc-0 Integrating Factor to Solve a First Order Linear Differential Equation] Video by PatrickJMT

* [https://www.youtube.com/watch?v=gd1FYn86P0c First Order Linear Differential Equations] Video by The Organic Chemistry Tutor

First-Order Linear Equations

2021-05-15T15:26:26Z

Glenn.lahodny:

First-Order Linear Equations

2021-05-15T15:22:56Z

Glenn.lahodny: Created page with "* [https://www.youtube.com/watch?v=HAb9JbBD2ig Solving Linear First-Order Differential Equations] Video by James Sousa, Math is Power 4U * [https://www.youtube.com/watch?v=T3p..."

MAT1224

2021-05-15T14:56:55Z

Glenn.lahodny:

The textbook for this course is
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">1.3</div>

||

[[The Fundamental Theorem of Calculus]]

||

* [[Differentiation Rules]] 
* [[Chain Rule|The Chain Rule]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 

||
*
* Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
* Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
* Explain the relationship between differentiation and integration.

|-

|Week 1

||

<div style="text-align: center;">1.5</div>

||

[[Integration by Substitution]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 

||

* Recognize when to use integration by substitution.
* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 2

||

<div style="text-align: center;">2.1</div>

||

[[Area between Curves]]

||

* [[Toolkit Functions|Graphing Elementary Functions]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the area of a region between two curves by integrating with respect to the independent variable.
* Find the area of a compound region.
* Determine the area of a region between two curves by integrating with respect to the dependent variable.

|-

|Week 2

||

<div style="text-align: center;">2.2</div>

||

[[Determining Volumes by Slicing]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the volume of a solid by integrating a cross-section (the slicing method).
* Find the volume of a solid of revolution using the disk method.
* Find the volume of a solid of revolution with a cavity using the washer method.

||

|-

|Week 3

||

<div style="text-align: center;">2.3</div>

||

[[Volumes of Revolution, Cylindrical Shells]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[Determining Volumes by Slicing]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Calculate the volume of a solid of revolution by using the method of cylindrical shells.
* Compare the different methods for calculating a volume of revolution.

||

|-

|Week 3
||

<div style="text-align: center;">2.4</div>

||

[[Arc Length and Surface Area]]

||

* [[Differentiation Rules]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the length of a plane curve between two points.
* Find the surface area of a solid of revolution.

||

|-

|Week 4

||

<div style="text-align: center;">2.5</div>

||

[[Physical Applications]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* '''[[Basic Physics (Mass, Force, Work, Newton's Second Law, Hooke's Law)]]''' 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the mass of a one-dimensional object from its linear density function.
* Determine the mass of a two-dimensional circular object from its radial density function.
* Calculate the work done by a variable force acting along a line.
* Calculate the work done in pumping a liquid from one height to another.
* Find the hydrostatic force against a submerged vertical plate.

||

|-

|Week 4

||

<div style="text-align: center;">2.6</div>

||

[[Moments and Center of Mass]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Find the center of mass of objects distributed along a line.
* Locate the center of mass of a thin plate.
* Use symmetry to help locate the centroid of a thin plate.

||

|-

|Week 5

||

<div style="text-align: center;">3.1</div>

||

[[Integration by Parts]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Recognize when to use integration by parts.
* Use the integration-by-parts formula to evaluate indefinite integrals.
* Use the integration-by-parts formula to evaluate definite integrals.
* Integrate products of functions, logarithmic functions, and inverse trigonometric functions.
* Solve problems involving applications of integration using integration by parts.

||

|-

|Week 5

||

<div style="text-align: center;">3.2</div>

||

[[Trigonometric Integrals]]

||

* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Evaluate integrals involving products and powers of sin(x) and cos(x).
* Evaluate integrals involving products and powers of sec(x) and tan(x).
* Evaluate integrals involving products of sin(ax), sin(bx), cos(ax), and cos(bx).
* Solve problems involving applications of integration using trigonometric integrals.

||

|-

|Week 6

||

<div style="text-align: center;">3.3</div>

||

[[Trigonometric Substitution]]

||

* [[Completing the Square]] 
* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 

||

* Evaluate integrals involving the square root of a sum or difference of two squares.
* Solve problems involving applications of integration using trigonometric substitution.

|-

|Week 6

||

<div style="text-align: center;">3.4</div>

||

[[Partial Fractions]]

||

* [[Factoring Polynomials]] 
* [[Completing the Square]] 
* [[Dividing Polynomials|Long Division of Polynomials]] 
* [[Systems of Linear Equations]] 
* [[Antiderivatives]] 
* [[Integration by Substitution]] 

||

* Integrate a rational function whose denominator is a product of linear and quadratic polynomials.
* Recognize distinct linear factors in a rational function.
* Recognize repeated linear factors in a rational function.
* Recognize distinct irreducible quadratic factors in a rational function.
* Recognize repeated irreducible quadratic factors in a rational function.
* Solve problems involving applications of integration using partial fractions.

|-

|Week 7

||

<div style="text-align: center;">3.7</div>

||

[[Improper Integrals]]

||

* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 
* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Recognize improper integrals and determine their convergence or divergence.
* Evaluate an integral over an infinite interval.
* Evaluate an integral over a closed interval with an infinite discontinuity within the interval.
* Use the comparison theorem to determine whether an improper integral is convergent or divergent.

|-

|Week 7

||

<div style="text-align: center;">4.3</div>

||

[[Separation of Variables]]

||

* [[Factoring Polynomials]] 
* [[Exponential Properties]] 
* [[Logarithmic Properties]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives|Initial-Value Problems]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 

||

* Recognize separable differential equations.
* Use separation of variables to solve a differential equation.
* Develop and analyze elementary mathematical models.

|-

|Week 8

||

<div style="text-align: center;">2.8</div>

||

[[Exponential Growth and Decay]]

||

* [[Separation of Variables]] 

||

* The exponential growth model
* The concept of doubling time
* The exponential decay model
* The concept of half-life

|-

|Week 8

||

<div style="text-align: center;">4.4</div>

||

[[The Logistic Equation]]

||

* [[Partial Fractions]] 
* [[Separation of Variables]] 
* [[Exponential Growth and Decay]] 

||

* Describe the concept of environmental carrying capacity in the logistic model of population growth.
* Solve a logistic equation and interpret the results.

|-

|Week 8

||

<div style="text-align: center;">4.5</div>

||

[[First-Order Linear Equations]]

||

* [[Separation of Variables]] 

||

* Write a first-order linear differential equation in standard form.
* Find an integrating factor and use it to solve a first-order linear differential equation.
* Solve applied problems involving first-order linear differential equations.

|-

|Week 9

||

<div style="text-align: center;">5.1</div>

||

[[Sequences]]

||

* [[The Limit Laws| The Limit Laws and Squeeze Theorem]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 

||

* Find a formula for the general term of a sequence.
* Find a recursive definition of a sequence.
* Determine the convergence or divergence of a given sequence.
* Find the limit of a convergent sequence.
* Determine whether a sequence is bounded and/or monotone.
* Apply the Monotone Convergence Theorem.

|-

|Week 10

||

<div style="text-align: center;">5.2</div>

||

[[Infinite Series]]

||

* '''[[Sigma notation]]''' 
* [[Sequences]] 
* [[Partial Fractions]] 

||

* Define the convergence or divergence of an infinite series.
* Find the sum of a geometric or telescoping series.

|-

|Week 10

||

<div style="text-align: center;">5.3</div>

||

[[The Divergence and Integral Tests]]

||

* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[Continuity]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Improper Integrals]] 

||

* Use the Divergence Test to determine whether a series diverges.
* Use the Integral Test to determine whether a series converges or diverges.
* Use the p-Series Test to determine whether a series converges or diverges.
* Estimate the sum of a series by finding bounds on its remainder term.

|-

|Week 11

||

<div style="text-align: center;">5.4</div>

||

[[Comparison Tests]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 

||

* Use the Direct Comparison Test to determine whether a series converges or diverges.
* Use the Limit Comparison Test to determine whether a series converges or diverges.

|-

|Week 11

||

<div style="text-align: center;">5.5</div>

||

[[Alternating Series]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 
* [[Comparison Tests]] 

||

* Use the Alternating Series Test to determine the convergence of an alternating series.
* Estimate the sum of an alternating series.
* Explain the meaning of absolute convergence and conditional convergence.

|-

|Week 12

||

<div style="text-align: center;">5.6</div>

||

[[Ratio and Root Tests]]

||

* '''[[Factorials]]''' 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Use the Ratio Test to determine absolute convergence or divergence of a series.
* Use the Root Test to determine absolute convergence or divergence of a series.
* Describe a strategy for testing the convergence or divergence of a series.

|-

|Week 12

||

<div style="text-align: center;">6.1</div>

||

[[Power Series and Functions]]

||

* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests]] 
* [[Comparison Tests]] 
* [[Alternating Series]] 
* [[Ratio and Root Tests]] 

||

* Identify a power series.
* Determine the interval of convergence and radius of convergence of a power series.
* Use a power series to represent certain functions.

|-

|Week 13

||

<div style="text-align: center;">6.2</div>

||

[[Properties of Power Series]]

||

* [[Differentiation Rules]] 
* [[Antiderivatives]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Power Series and Functions]] 

||

* Combine power series by addition or subtraction.
* Multiply two power series together.
* Differentiate and integrate power series term-by-term.
* Use differentiation and integration of power series to represent certain functions as power series.

|-

|Week 14

||

<div style="text-align: center;">6.3</div>

||

[[Taylor and Maclaurin Series]]

||

* [[The Derivative as a Function|Higher-Order Derivatives]] 
* [[Power Series and Functions]] 
* [[Properties of Power Series]] 

||

* Find a Taylor or Maclaurin series representation of a function.
* Find the radius of convergence of a Taylor Series or Maclaurin series.
* Finding a Taylor polynomial of a given order for a function.
* Use Taylor's Theorem to estimate the remainder for a Taylor series approximation of a given function.

|-

|Week 15

||

<div style="text-align: center;">7.1</div>

||

[[Parametric Equations]]

||

* [[Toolkit Functions|Sketching Elementary Functions]] 
* '''[[Equation of a Circle]]''' 
* '''[[Equation of an Ellipse]]''' 
* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 

||

* Plot a curve described by parametric equations.
* Convert the parametric equations of a curve into the form y=f(x) by eliminating the parameter.
* Recognize the parametric equations of basic curves, such as a line and a circle.

||

|-

|Week 15

||

<div style="text-align: center;">7.2</div>

||

[[The Calculus of Parametric Equations]]

||

* [[Parametric Equations]] 
* [[Differentiation Rules]] 
* [[The Derivative as a Function|Higher-Order Derivatives]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Find the slope of the tangent line to a parametric curve at a point.
* Use the second derivative to determine the concavity of a parametric curve at a point.
* Determine the area bounded by a parametric curve.
* Determine the arc length of a parametric curve.
* Determine the area of a surface obtained by rotating a parametric curve about an axis.

||

MAT1224

2021-05-15T14:52:22Z

Glenn.lahodny:

The textbook for this course is
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">1.3</div>

||

[[The Fundamental Theorem of Calculus]]

||

* [[Differentiation Rules]] 
* [[Chain Rule|The Chain Rule]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 

||
*
* Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
* Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
* Explain the relationship between differentiation and integration.

|-

|Week 1

||

<div style="text-align: center;">1.5</div>

||

[[Integration by Substitution]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 

||

* Recognize when to use integration by substitution.
* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 2

||

<div style="text-align: center;">2.1</div>

||

[[Area between Curves]]

||

* [[Toolkit Functions|Graphing Elementary Functions]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the area of a region between two curves by integrating with respect to the independent variable.
* Find the area of a compound region.
* Determine the area of a region between two curves by integrating with respect to the dependent variable.

|-

|Week 2

||

<div style="text-align: center;">2.2</div>

||

[[Determining Volumes by Slicing]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the volume of a solid by integrating a cross-section (the slicing method).
* Find the volume of a solid of revolution using the disk method.
* Find the volume of a solid of revolution with a cavity using the washer method.

||

|-

|Week 3

||

<div style="text-align: center;">2.3</div>

||

[[Volumes of Revolution, Cylindrical Shells]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[Determining Volumes by Slicing]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Calculate the volume of a solid of revolution by using the method of cylindrical shells.
* Compare the different methods for calculating a volume of revolution.

||

|-

|Week 3
||

<div style="text-align: center;">2.4</div>

||

[[Arc Length and Surface Area]]

||

* [[Differentiation Rules]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the length of a plane curve between two points.
* Find the surface area of a solid of revolution.

||

|-

|Week 4

||

<div style="text-align: center;">2.5</div>

||

[[Physical Applications]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* '''[[Basic Physics (Mass, Force, Work, Newton's Second Law, Hooke's Law)]]''' 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the mass of a one-dimensional object from its linear density function.
* Determine the mass of a two-dimensional circular object from its radial density function.
* Calculate the work done by a variable force acting along a line.
* Calculate the work done in pumping a liquid from one height to another.
* Find the hydrostatic force against a submerged vertical plate.

||

|-

|Week 4

||

<div style="text-align: center;">2.6</div>

||

[[Moments and Center of Mass]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Find the center of mass of objects distributed along a line.
* Locate the center of mass of a thin plate.
* Use symmetry to help locate the centroid of a thin plate.

||

|-

|Week 5

||

<div style="text-align: center;">3.1</div>

||

[[Integration by Parts]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Recognize when to use integration by parts.
* Use the integration-by-parts formula to evaluate indefinite integrals.
* Use the integration-by-parts formula to evaluate definite integrals.
* Integrate products of functions, logarithmic functions, and inverse trigonometric functions.
* Solve problems involving applications of integration using integration by parts.

||

|-

|Week 5

||

<div style="text-align: center;">3.2</div>

||

[[Trigonometric Integrals]]

||

* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Evaluate integrals involving products and powers of sin(x) and cos(x).
* Evaluate integrals involving products and powers of sec(x) and tan(x).
* Evaluate integrals involving products of sin(ax), sin(bx), cos(ax), and cos(bx).
* Solve problems involving applications of integration using trigonometric integrals.

||

|-

|Week 6

||

<div style="text-align: center;">3.3</div>

||

[[Trigonometric Substitution]]

||

* [[Completing the Square]] 
* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 

||

* Evaluate integrals involving the square root of a sum or difference of two squares.
* Solve problems involving applications of integration using trigonometric substitution.

|-

|Week 6

||

<div style="text-align: center;">3.4</div>

||

[[Partial Fractions]]

||

* [[Factoring Polynomials]] 
* [[Completing the Square]] 
* [[Dividing Polynomials|Long Division of Polynomials]] 
* [[Systems of Linear Equations]] 
* [[Antiderivatives]] 
* [[Integration by Substitution]] 

||

* Integrate a rational function whose denominator is a product of linear and quadratic polynomials.
* Recognize distinct linear factors in a rational function.
* Recognize repeated linear factors in a rational function.
* Recognize distinct irreducible quadratic factors in a rational function.
* Recognize repeated irreducible quadratic factors in a rational function.
* Solve problems involving applications of integration using partial fractions.

|-

|Week 7

||

<div style="text-align: center;">3.7</div>

||

[[Improper Integrals]]

||

* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 
* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Recognize improper integrals and determine their convergence or divergence.
* Evaluate an integral over an infinite interval.
* Evaluate an integral over a closed interval with an infinite discontinuity within the interval.
* Use the comparison theorem to determine whether an improper integral is convergent or divergent.

|-

|Week 7

||

<div style="text-align: center;">4.3</div>

||

[[Separation of Variables]]

||

* [[Factoring Polynomials]] 
* [[Exponential Properties]] 
* [[Logarithmic Properties]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives|Initial-Value Problems]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 

||

* Recognize separable differential equations.
* Use separation of variables to solve a differential equation.
* Develop and analyze elementary mathematical models.

|-

|Week 8

||

<div style="text-align: center;">2.8</div>

||

[[Exponential Growth and Decay]]

||

* [[Separation of Variables]] 

||

* The exponential growth model
* The concept of doubling time
* The exponential decay model
* The concept of half-life

|-

|Week 8

||

<div style="text-align: center;">4.4</div>

||

[[The Logistic Equation]]

||

* [[Partial Fractions]] 
* [[Separation of Variables]] 
* [[Exponential Growth and Decay]] 

||

* Describe the concept of environmental carrying capacity in the logistic model of population growth.
* Solve a logistic equation and interpret the results.

|-

|Week 9

||

<div style="text-align: center;">5.1</div>

||

[[Sequences]]

||

* [[The Limit Laws| The Limit Laws and Squeeze Theorem]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 

||

* Find a formula for the general term of a sequence.
* Find a recursive definition of a sequence.
* Determine the convergence or divergence of a given sequence.
* Find the limit of a convergent sequence.
* Determine whether a sequence is bounded and/or monotone.
* Apply the Monotone Convergence Theorem.

|-

|Week 10

||

<div style="text-align: center;">5.2</div>

||

[[Infinite Series]]

||

* '''[[Sigma notation]]''' 
* [[Sequences]] 
* [[Partial Fractions]] 

||

* Define the convergence or divergence of an infinite series.
* Find the sum of a geometric or telescoping series.

|-

|Week 10

||

<div style="text-align: center;">5.3</div>

||

[[The Divergence and Integral Tests]]

||

* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[Continuity]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Improper Integrals]] 

||

* Use the Divergence Test to determine whether a series diverges.
* Use the Integral Test to determine whether a series converges or diverges.
* Use the p-Series Test to determine whether a series converges or diverges.
* Estimate the sum of a series by finding bounds on its remainder term.

|-

|Week 11

||

<div style="text-align: center;">5.4</div>

||

[[Comparison Tests]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 

||

* Use the Direct Comparison Test to determine whether a series converges or diverges.
* Use the Limit Comparison Test to determine whether a series converges or diverges.

|-

|Week 11

||

<div style="text-align: center;">5.5</div>

||

[[Alternating Series]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 
* [[Comparison Tests]] 

||

* Use the Alternating Series Test to determine the convergence of an alternating series.
* Estimate the sum of an alternating series.
* Explain the meaning of absolute convergence and conditional convergence.

|-

|Week 12

||

<div style="text-align: center;">5.6</div>

||

[[Ratio and Root Tests]]

||

* '''[[Factorials]]''' 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Use the Ratio Test to determine absolute convergence or divergence of a series.
* Use the Root Test to determine absolute convergence or divergence of a series.
* Describe a strategy for testing the convergence or divergence of a series.

|-

|Week 12

||

<div style="text-align: center;">6.1</div>

||

[[Power Series and Functions]]

||

* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests]] 
* [[Comparison Tests]] 
* [[Alternating Series]] 
* [[Ratio and Root Tests]] 

||

* Identify a power series.
* Determine the interval of convergence and radius of convergence of a power series.
* Use a power series to represent certain functions.

|-

|Week 13

||

<div style="text-align: center;">6.2</div>

||

[[Properties of Power Series]]

||

* [[Differentiation Rules]] 
* [[Antiderivatives]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Power Series and Functions]] 

||

* Combine power series by addition or subtraction.
* Multiply two power series together.
* Differentiate and integrate power series term-by-term.
* Use differentiation and integration of power series to represent certain functions as power series.

|-

|Week 14

||

<div style="text-align: center;">6.3</div>

||

[[Taylor and Maclaurin Series]]

||

* [[The Derivative as a Function|Higher-Order Derivatives]] 
* [[Power Series and Functions]] 
* [[Properties of Power Series]] 

||

* Find a Taylor or Maclaurin series representation of a function.
* Find the radius of convergence of a Taylor Series or Maclaurin series.
* Finding a Taylor polynomial of a given order for a function.
* Use Taylor's Theorem to estimate the remainder for a Taylor series approximation of a given function.

|-

|Week 15

||

<div style="text-align: center;">7.1</div>

||

[[Parametric Equations]]

||

* [[Toolkit Functions|Sketching Elementary Functions]] 
* '''[[Equation of a Circle]]''' 
* '''[[Equation of an Ellipse]]''' 
* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 

||

* Plot a curve described by parametric equations.
* Convert the parametric equations of a curve into the form y=f(x) by eliminating the parameter.
* Recognize the parametric equations of basic curves, such as a line and a circle.

||

|-

|Week 15

||

<div style="text-align: center;">7.2</div>

||

[[The Calculus of Parametric Equations]]

||

* [[Parametric Equations]] 
* [[Differentiation Rules]] 
* [[The Derivative as a Function|Higher-Order Derivatives]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Find the slope of the tangent line to a parametric curve at a point.
* Use the second derivative to determine the concavity of a parametric curve at a point.
* Determine the area bounded by a parametric curve.
* Determine the arc length of a parametric curve.
* Determine the area of a surface obtained by rotating a parametric curve about an axis.

||

Conservative Vector Fields

2021-05-05T11:57:33Z

Glenn.lahodny:

<strong>Conservative Vector Fields</strong>

* [https://www.youtube.com/watch?v=cVTcsHcispQ Conservative Vector Fields] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=VLTUku45Qs4 Conservative Vector Fields - The Definition and a Few Remarks] Video by Patrick JMT
* [https://www.youtube.com/watch?v=gAb1ZTD41wo Showing a Vector Field on R^2 is Conservative] Video by Patrick JMT

<strong>Finding a Potential Function of a Conservative Vector Field</strong>
* [https://www.youtube.com/watch?v=nQkHh2psLck Determining the Potential Function of a Conservative Vector Field] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=iLAK2IsQ_Uo Finding a Potential for a Conservative Vector Field] Video by Patrick JMT
* [https://www.youtube.com/watch?v=tslJEOnt9aY Finding a Potential for a Conservative Vector Field Ex 2] Video by Patrick JMT
* [https://www.youtube.com/watch?v=nY4mW_R-T40 Potential Function of a Conservative Vector Field] Video by Krista King
* [https://www.youtube.com/watch?v=Rb12YouJXyA Potential Function of a Conservative Vector Field in 3D] Video by Krista King

<strong>The Fundamental Theorem of Line Integrals</strong>
* [https://www.youtube.com/watch?v=Td6g2bvJh18 The Fundamental Theorem of Line Integrals Part 1] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=I8BtXV-xgxM The Fundamental Theorem of Line Integrals Part 2] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=00RN-hw9BXc The Fundamental Theorem of Line Integrals on a Closed Path] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=62oBGKSjYiY Ex 1: Fundamental Theorem of Line Integrals in the Plane] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=Eh6OinLiGWg Ex 2: Fundamental Theorem of Line Integrals in the Plane] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=pbHlZR2TD7M Ex 3: Fundamental Theorem of Line Integrals in the Plane] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=e2g7321ne48 Ex 4: Fundamental Theorem of Line Integrals in Space] Video by James Sousa, Math is Power 4U
* [https://www.youtube.com/watch?v=xVhHow_usMQ The Fundamental Theorem for Line Integrals] Video by Patrick JMT
* [https://www.youtube.com/watch?v=hT3YSXQaUHQ Potential Function of a Conservative Vector Field to Evaluate a Line Integral] Video by Krista King

2020-11-16T16:35:39Z

Glenn.lahodny: /* Topics List */

The textbook for this course is
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">1.3</div>

||

[[The Fundamental Theorem of Calculus]]

||

* [[Differentiation Rules]] 
* [[Chain Rule|The Chain Rule]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 

||
*
* Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
* Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
* Explain the relationship between differentiation and integration.

|-

|Week 1

||

<div style="text-align: center;">1.5</div>

||

[[Integration by Substitution]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 

||

* Recognize when to use integration by substitution.
* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 2

||

<div style="text-align: center;">2.1</div>

||

[[Area between Curves]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the area of a region between two curves by integrating with respect to the independent variable.
* Find the area of a compound region.
* Determine the area of a region between two curves by integrating with respect to the dependent variable.

|-

|Week 2

||

<div style="text-align: center;">2.2</div>

||

[[Determining Volumes by Slicing]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the volume of a solid by integrating a cross-section (the slicing method).
* Find the volume of a solid of revolution using the disk method.
* Find the volume of a solid of revolution with a cavity using the washer method.

||

|-

|Week 3

||

<div style="text-align: center;">2.3</div>

||

[[Volumes of Revolution, Cylindrical Shells]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[Determining Volumes by Slicing]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Calculate the volume of a solid of revolution by using the method of cylindrical shells.
* Compare the different methods for calculating a volume of revolution.

||

|-

|Week 3
||

<div style="text-align: center;">2.4</div>

||

[[Arc Length and Surface Area]]

||

* [[Differentiation Rules]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the length of a plane curve between two points.
* Find the surface area of a solid of revolution.

||

|-

|Week 4

||

<div style="text-align: center;">2.5</div>

||

[[Physical Applications]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* '''[[Basic Physics (Mass, Force, Work, Newton's Second Law, Hooke's Law)]]''' 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the mass of a one-dimensional object from its linear density function.
* Determine the mass of a two-dimensional circular object from its radial density function.
* Calculate the work done by a variable force acting along a line.
* Calculate the work done in pumping a liquid from one height to another.
* Find the hydrostatic force against a submerged vertical plate.

||

|-

|Week 4

||

<div style="text-align: center;">2.6</div>

||

[[Moments and Center of Mass]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Find the center of mass of objects distributed along a line.
* Locate the center of mass of a thin plate.
* Use symmetry to help locate the centroid of a thin plate.

||

|-

|Week 5

||

<div style="text-align: center;">3.1</div>

||

[[Integration by Parts]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Recognize when to use integration by parts.
* Use the integration-by-parts formula to evaluate indefinite integrals.
* Use the integration-by-parts formula to evaluate definite integrals.
* Integrate products of functions, logarithmic functions, and inverse trigonometric functions.
* Solve problems involving applications of integration using integration by parts.

||

|-

|Week 5

||

<div style="text-align: center;">3.2</div>

||

[[Trigonometric Integrals]]

||

* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Evaluate integrals involving products and powers of sin(x) and cos(x).
* Evaluate integrals involving products and powers of sec(x) and tan(x).
* Evaluate integrals involving products of sin(ax), sin(bx), cos(ax), and cos(bx).
* Solve problems involving applications of integration using trigonometric integrals.

||

|-

|Week 6

||

<div style="text-align: center;">3.3</div>

||

[[Trigonometric Substitution]]

||

* [[Completing the Square]] 
* [[Trigonometric Functions: Unit Circle Approach|Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 

||

* Evaluate integrals involving the square root of a sum or difference of two squares.
* Solve problems involving applications of integration using trigonometric substitution.

|-

|Week 6

||

<div style="text-align: center;">3.4</div>

||

[[Partial Fractions]]

||

* [[Factoring Polynomials]] 
* [[Completing the Square]] 
* [[Dividing Polynomials|Long Division of Polynomials]] 
* [[Systems of Linear Equations]] 
* [[Antiderivatives]] 
* [[Integration by Substitution]] 

||

* Integrate a rational function whose denominator is a product of linear and quadratic polynomials.
* Recognize distinct linear factors in a rational function.
* Recognize repeated linear factors in a rational function.
* Recognize distinct irreducible quadratic factors in a rational function.
* Recognize repeated irreducible quadratic factors in a rational function.
* Solve problems involving applications of integration using partial fractions.

|-

|Week 7

||

<div style="text-align: center;">3.7</div>

||

[[Improper Integrals]]

||

* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 
* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Recognize improper integrals and determine their convergence or divergence.
* Evaluate an integral over an infinite interval.
* Evaluate an integral over a closed interval with an infinite discontinuity within the interval.
* Use the comparison theorem to determine whether an improper integral is convergent or divergent.

|-

|Week 7

||

<div style="text-align: center;">4.3</div>

||

[[Separation of Variables]]

||

* [[Factoring Polynomials]] 
* [[Exponential Properties]] 
* [[Logarithmic Properties]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives|Initial-Value Problems]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 

||

* Recognize separable differential equations.
* Use separation of variables to solve a differential equation.
* Develop and analyze elementary mathematical models.

|-

|Week 8

||

<div style="text-align: center;">2.8</div>

||

[[Exponential Growth and Decay]]

||

* [[Separation of Variables]] 

||

* The exponential growth model
* The concept of doubling time
* The exponential decay model
* The concept of half-life

|-

|Week 8

||

<div style="text-align: center;">4.4</div>

||

[[The Logistic Equation]]

||

* [[Partial Fractions]] 
* [[Separation of Variables]] 
* [[Exponential Growth and Decay]] 

||

* Describe the concept of environmental carrying capacity in the logistic model of population growth.
* Solve a logistic equation and interpret the results.

|-

|Week 9

||

<div style="text-align: center;">5.1</div>

||

[[Sequences]]

||

* [[The Limit Laws| The Limit Laws and Squeeze Theorem]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 

||

* Find a formula for the general term of a sequence.
* Find a recursive definition of a sequence.
* Determine the convergence or divergence of a given sequence.
* Find the limit of a convergent sequence.
* Determine whether a sequence is bounded and/or monotone.
* Apply the Monotone Convergence Theorem.

|-

|Week 10

||

<div style="text-align: center;">5.2</div>

||

[[Infinite Series]]

||

* '''[[Sigma notation]]''' 
* [[Sequences]] 
* [[Partial Fractions]] 

||

* Define the convergence or divergence of an infinite series.
* Find the sum of a geometric or telescoping series.

|-

|Week 10

||

<div style="text-align: center;">5.3</div>

||

[[The Divergence and Integral Tests]]

||

* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[Continuity]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Improper Integrals]] 

||

* Use the Divergence Test to determine whether a series diverges.
* Use the Integral Test to determine whether a series converges or diverges.
* Use the p-Series Test to determine whether a series converges or diverges.
* Estimate the sum of a series by finding bounds on its remainder term.

|-

|Week 11

||

<div style="text-align: center;">5.4</div>

||

[[Comparison Tests]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 

||

* Use the Direct Comparison Test to determine whether a series converges or diverges.
* Use the Limit Comparison Test to determine whether a series converges or diverges.

|-

|Week 11

||

<div style="text-align: center;">5.5</div>

||

[[Alternating Series]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 
* [[Comparison Tests]] 

||

* Use the Alternating Series Test to determine the convergence of an alternating series.
* Estimate the sum of an alternating series.
* Explain the meaning of absolute convergence and conditional convergence.

|-

|Week 12

||

<div style="text-align: center;">5.6</div>

||

[[Ratio and Root Tests]]

||

* '''[[Factorials]]''' 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Use the Ratio Test to determine absolute convergence or divergence of a series.
* Use the Root Test to determine absolute convergence or divergence of a series.
* Describe a strategy for testing the convergence or divergence of a series.

|-

|Week 12

||

<div style="text-align: center;">6.1</div>

||

[[Power Series and Functions]]

||

* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests]] 
* [[Comparison Tests]] 
* [[Alternating Series]] 
* [[Ratio and Root Tests]] 

||

* Identify a power series.
* Determine the interval of convergence and radius of convergence of a power series.
* Use a power series to represent certain functions.

|-

|Week 13

||

<div style="text-align: center;">6.2</div>

||

[[Properties of Power Series]]

||

* [[Antiderivatives|Indefinite integrals]] 
* [[The Limit Laws]] 
* [[Power Series and Functions]] 

||

* Differentiate and integrate power series term-by-term.
* Recognize certain continuous functions as power series on their radius of convergence.

|-

|Week 14

||

<div style="text-align: center;">6.3</div>

||

[[Taylor and Maclaurin Series]]

||

* [[The Derivative of a Function]] 
* [[Power Series and Functions]] 
* [[Properties of Power Series]] 

||

* Find the Taylor or Maclaurin series representation of a function.
* Find the radius of convergence of a Taylor Series.
* Estimate the remainder in a Taylor polynomial approximation.

|-

|Week 15

||

<div style="text-align: center;">7.1</div>

||

[[Parametric Equations]]

||

* [[Trigonometric Functions]] 
* [[Exponential Functions]] 
* [[Toolkit Functions|Sketching Common Functions]] 

||

* Sketch the graph of a parametric curve

||

|-

|Week 15

||

<div style="text-align: center;">7.2</div>

||

[[The Calculus of Parametric Equations]]

||

* [[Parametric Equations]] 
* [[The Derivative as a Function]] 
* [[Integration by Substitution]] 
* [[The Definite Integral]] 

||

* Find the slope of the tangent line to a parametric curve at a point
* Find the second derivative of a parametric curve
* Determine the area bounded by a parametric curve
* Determine the arc length of a parametric curve
* Calculating the area of a surface obtained by rotating a parametric curve about an axis

||