Difference between revisions of "MAT1223"

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(→‎Topics List: Modifed content per input by Calc II instructors)
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==Topics List==
 
==Topics List==
{| class="wikitable sortable"
+
{| class="wikitable"
 
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
 
|-
 
|-
 
+
| Week 1 || <div style="text-align: center;">1.5</div> || [[Integration by Substitution]] || * [[Differentiation Rules]] < || -- 1214-3.3 -->
 
+
* [[Linear Approximations and Differentials
|Week&nbsp;1  
 
 
 
||
 
 
 
<div style="text-align: center;">1.5</div>
 
 
 
||
 
 
 
[[Integration by Substitution]]  
 
 
 
||
 
 
 
* [[Differentiation Rules]] <!-- 1214-3.3 -->
 
* [[Linear Approximations and Differentials|Differentials]] <!-- 1214-4.2 -->
 
* [[Antiderivatives]] <!-- 1214-4.10 -->
 
* [[The Definite Integral]] <!-- 1214-5.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
 
 
||
 
 
 
* Recognize when to use integration by substitution.
 
* Use substitution to evaluate indefinite integrals.
 
* Use substitution to evaluate definite integrals.
 
 
 
 
|-
 
|-
 
+
| Week 1 & 2 || <div style="text-align: center;">2.1</div> || [[Area between Curves]] || * [[Toolkit Functions || Graphing Elementary Functions]] <
 
 
|Week&nbsp;2
 
 
 
||
 
 
 
<div style="text-align: center;">2.1</div>
 
 
 
||
 
 
 
[[Area between Curves]]  
 
 
 
||
 
 
 
* [[Toolkit Functions|Graphing Elementary Functions]] <!-- 1073-Mod 1.2 -->
 
* [[The Definite Integral]] <!-- 1214-5.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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]]''' < || -- Grades 6-12 -->
 
+
* '''[[Volume of a cylinder]]''' <
|Week&nbsp;2  
 
 
 
||
 
 
 
<div style="text-align: center;">2.2</div>
 
 
 
||
 
 
 
[[Determining Volumes by Slicing]]  
 
 
 
||
 
 
 
* '''[[Areas of basic shapes]]''' <!-- Grades 6-12 -->
 
* '''[[Volume of a cylinder]]''' <!-- Grades 6-12 -->
 
* [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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]] <
 
 
|Week&nbsp;3  
 
 
 
||
 
 
 
<div style="text-align: center;">2.3</div>
 
 
 
||
 
 
 
[[Volumes of Revolution, Cylindrical Shells]]  
 
 
 
||
 
 
 
* [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 -->
 
* [[Determining Volumes by Slicing]] <!-- 1224-2.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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]] < || -- 1214-3.3 -->
 
+
* [[The Fundamental Theorem of Calculus]] <
|Week&nbsp;3
 
||
 
 
 
<div style="text-align: center;">2.4</div>
 
 
 
||
 
 
 
[[Arc Length and Surface Area]]  
 
 
 
||
 
 
 
* [[Differentiation Rules]] <!-- 1214-3.3 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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]]''' < || -- Grades 6-12 -->
 
+
* '''[[Volume of a cylinder]]''' <
|Week&nbsp;4
 
 
 
||
 
 
 
<div style="text-align: center;">2.5</div>
 
 
 
||
 
 
 
[[Physical Applications]]
 
 
 
||
 
 
 
* '''[[Areas of basic shapes]]''' <!-- Grades 6-12 -->
 
* '''[[Volume of a cylinder]]''' <!-- Grades 6-12 -->
 
* '''[[Basic Physics (Mass, Force, Work, Newton's Second Law, Hooke's Law)]]''' <!-- Grades 6-12 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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 stretching/compressing a spring.
 
* Calculate the work done in lifting a rope/cable.
 
* Calculate the work done in pumping a liquid from one height to another.
 
* Find the hydrostatic force against a submerged vertical plate.
 
 
 
 
 
 
|-
 
|-
 
+
| Week 4 & 5 || <div style="text-align: center;">2.6</div> || [[Moments and Center of Mass]] || * [[Toolkit Functions || Graphing elementary functions]] <
 
 
|Week&nbsp;4
 
 
 
||
 
 
 
<div style="text-align: center;">2.6</div>
 
 
 
||  
 
 
 
[[Moments and Center of Mass]]
 
 
 
||
 
 
 
* [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* Find the center of mass of objects distributed along a line.
 
* Find the center of mass of objects distributed in a plane.
 
* 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]] < || -- 1214-3.3 -->
 
+
* [[Linear Approximations and Differentials
|Week&nbsp;5
 
 
 
||
 
 
 
<div style="text-align: center;">3.1</div>
 
 
 
||
 
 
 
[[Integration by Parts]]
 
 
 
||
 
 
 
* [[Differentiation Rules]] <!-- 1214-3.3 -->
 
* [[Linear Approximations and Differentials|Differentials]] <!-- 1214-4.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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.
 
* Use the tabular method to perform integration by parts.
 
* Solve problems involving applications of integration using integration by parts.
 
 
 
 
|-
 
|-
 
+
| Week 6 || <div style="text-align: center;">3.2</div> || [[Trigonometric Integrals]] || * [[Trigonometric Functions]] < || -- 1093-2.2 -->
 
+
* [[Properties of the Trigonometric Functions
|Week&nbsp;5
 
 
 
||
 
 
 
<div style="text-align: center;">3.2</div>
 
 
 
||  
 
 
 
[[Trigonometric Integrals]]
 
 
 
||
 
 
 
* [[Trigonometric Functions]] <!-- 1093-2.2 -->
 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
* [[Integration by Parts]] <!-- 1224-3.1 -->
 
 
 
||
 
 
 
* 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 & 7 || <div style="text-align: center;">3.3</div> || [[Trigonometric Substitution]] || * [[Completing the Square]] < || -- 1073-Mod 3.2-->
 
+
* [[Trigonometric Functions]] <
|Week&nbsp;6
 
 
 
||
 
 
 
<div style="text-align: center;">3.3</div>
 
 
 
||
 
 
 
[[Trigonometric Substitution]]
 
 
 
||
 
 
 
* [[Completing the Square]] <!-- 1073-Mod 3.2-->
 
* [[Trigonometric Functions]] <!-- 1093-2.2 -->
 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
* [[Integration by Parts]] <!-- 1224-3.1 -->
 
* [[Trigonometric Integrals]] <!-- 1224-3.2 -->
 
 
 
||
 
 
 
* Evaluate integrals involving the square root of a sum or difference of two squares.
 
* Solve problems involving applications of integration using trigonometric substitution.
 
 
 
 
 
 
|-
 
|-
 
+
| Week 7 || <div style="text-align: center;">3.4</div> || [[Partial Fractions]] || * [[Factoring Polynomials]] < || -- 1073-Mod 0.2 -->
 
+
* [[Completing the Square]] <
|Week&nbsp;6
 
 
 
||
 
 
 
<div style="text-align: center;">3.4</div>
 
 
 
||
 
 
 
[[Partial Fractions]]
 
 
 
||
 
 
 
* [[Factoring Polynomials]] <!-- 1073-Mod 0.2 -->
 
* [[Completing the Square]] <!-- 1073-Mod 3.2-->
 
* [[Dividing Polynomials|Long Division of Polynomials]] <!-- 1073-Mod 4.1 -->
 
* [[Systems of Linear Equations]] <!-- 1073-Mod 12.1 and 12.2 -->
 
* [[Antiderivatives]] <!-- 1214-4.10 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
||
 
 
 
* 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 || <div style="text-align: center;">3.7</div> || [[Improper Integrals]] || * [[The Fundamental Theorem of Calculus]] < || -- 1214-5.3 -->
 
+
* [[Integration by Substitution]] <
|Week&nbsp;7
 
 
 
||
 
 
 
<div style="text-align: center;">3.7</div>
 
 
 
||
 
 
 
[[Improper Integrals]]
 
 
 
||
 
 
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
* [[Integration by Parts]] <!-- 1224-3.1 -->
 
* [[Trigonometric Integrals]] <!-- 1224-3.2 -->
 
* [[Trigonometric Substitution]] <!-- 1224-3.3 -->
 
* [[Partial Fractions]] <!-- 1224-3.4 -->
 
* [[The Limit Laws]] <!-- 1214-2.3 -->
 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] <!-- 1224-4.6 -->
 
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
 
 
 
||
 
 
 
* 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 9 || <div style="text-align: center;">5.1</div> || [[Sequences]] || * [[The Limit Laws || The Limit Laws and Squeeze Theorem]] <
 
 
|Week&nbsp;8
 
 
 
||
 
 
 
<div style="text-align: center;">4.3</div>
 
 
 
||
 
 
 
[[Separation of Variables]]
 
 
 
||
 
 
 
* [[Factoring Polynomials]] <!-- 1073-Mod 0.2 -->
 
* [[Exponential Properties]] <!-- 1073-Mod 9.1 -->
 
* [[Logarithmic Properties]] <!-- 1073-Mod 10.2 -->
 
* [[Linear Approximations and Differentials|Differentials]] <!-- 1214-4.2 -->
 
* [[Initial Value Problem]] <!-- 1214-4.10 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
* [[Integration by Parts]] <!-- 1224-3.1 -->
 
* [[Trigonometric Integrals]] <!-- 1224-3.2 -->
 
* [[Trigonometric Substitution]] <!-- 1224-3.3 -->
 
* [[Partial Fractions]] <!-- 1224-3.4 -->
 
 
 
||
 
 
 
* Recognize separable differential equations.
 
* Use separation of variables to solve a differential equation.
 
* Develop and analyze elementary mathematical models.
 
 
 
 
|-
 
|-
 
+
| Week 10 || <div style="text-align: center;">5.2</div> || [[Infinite Series]] || * '''[[Sigma notation]]''' < || -- DNE (recommend 1093) -->
 
+
* [[Sequences]] <
|Week&nbsp;8   
 
 
 
||
 
 
 
<div style="text-align: center;">4.5</div>
 
 
 
||
 
 
 
[[First-Order Linear Equations]]
 
 
 
||
 
 
 
* [[Separation of Variables]] <!-- 1224-4.3 -->
 
 
 
||
 
 
 
* 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 11 || <div style="text-align: center;">5.3</div> || [[The Divergence and Integral Tests]] || * [[The Limit Laws]] < || -- 1214-2.3 -->
 
+
* [[Limits at Infinity and Asymptotes
|Week&nbsp;9 
 
 
 
||
 
 
 
<div style="text-align: center;">5.1</div>
 
 
 
||
 
 
 
[[Sequences]]
 
 
 
||
 
 
 
* [[The Limit Laws| The Limit Laws and Squeeze Theorem]] <!-- 1214-2.3 -->
 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] <!-- 1214-4.6 -->
 
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
 
 
 
||
 
 
 
* 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 11 || <div style="text-align: center;">5.4</div> || [[Comparison Tests]] || * [[Limits at Infinity and Asymptotes || Limits at Infinity]] <
 
 
|Week&nbsp;10
 
 
 
||
 
 
 
<div style="text-align: center;">5.2</div>
 
 
 
||
 
 
 
[[Infinite Series]]
 
 
 
||
 
 
 
* '''[[Sigma notation]]''' <!-- DNE (recommend 1093) -->
 
* [[Sequences]] <!-- 10224-5.1-->
 
* [[Partial Fractions]] <!-- 1224-3.4-->
 
 
 
||
 
 
 
* Write an infinite series using sigma notation.
 
* Find the nth partial sum of an infinite series.
 
* Define the convergence or divergence of an infinite series.
 
* Identify a geometric series.
 
* Apply the Geometric Series Test.
 
* Find the sum of a convergent geometric series.
 
* Identify a telescoping series.
 
* Find the sum of a telescoping series.
 
 
 
 
|-
 
|-
 
+
| Week 12 || <div style="text-align: center;">5.5</div> || [[Alternating Series]] || * [[Limits at Infinity and Asymptotes || Limits at Infinity]] <
 
 
|Week&nbsp;10
 
 
 
||
 
 
 
<div style="text-align: center;">5.3</div>
 
 
 
||
 
 
 
[[The Divergence and Integral Tests]]
 
 
 
||
 
 
 
* [[The Limit Laws]] <!-- 1214-2.3 -->
 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] <!-- 1214-4.6 -->
 
* [[Continuity]] <!-- 1214-3.5 -->
 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
 
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
 
* [[Improper Integrals]] <!-- 1224-3.7 -->
 
 
 
||
 
 
 
* 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 12 || <div style="text-align: center;">5.6</div> || [[Ratio and Root Tests]] || * '''[[Factorials]]''' < || -- Grades 6-12 -->
 
+
* [[Limits at Infinity and Asymptotes
|Week&nbsp;11 
 
 
 
||
 
 
 
<div style="text-align: center;">5.4</div>
 
 
 
||  
 
 
 
[[Comparison Tests]]
 
 
 
||
 
 
 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6-->
 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
 
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
 
* [[Infinite Series|The Geometric Series Test]] <!-- 1224-5.2 -->
 
* [[The Divergence and Integral Tests|The p-Series Test]] <!-- 1224-5.3 -->
 
 
 
||
 
 
 
* 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 13 || <div style="text-align: center;">6.1</div> || [[Power Series and Functions]] || * [[Infinite Series || The Geometric Series Test]] <
 
 
|Week&nbsp;11   
 
 
 
||
 
 
 
<div style="text-align: center;">5.5</div>
 
 
 
||
 
 
 
[[Alternating Series]]
 
 
 
||
 
 
 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6-->
 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
 
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
 
* [[Infinite Series|The Geometric Series Test]] <!-- 1224-5.2 -->
 
* [[The Divergence and Integral Tests|The p-Series Test]] <!-- 1224-5.3 -->
 
* [[Comparison Tests]] <!-- 1224-5.4 -->
 
 
 
||
 
 
 
* 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 14 || <div style="text-align: center;">6.2</div> || [[Properties of Power Series]] || * [[Differentiation Rules]] < || -- 1214-3.3 -->
 
+
* [[Antiderivatives]] <
|Week&nbsp;12
 
 
 
||
 
 
 
<div style="text-align: center;">5.6</div>
 
 
 
||  
 
 
 
[[Ratio and Root Tests]]
 
 
 
||
 
 
 
* '''[[Factorials]]''' <!-- Grades 6-12 -->
 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6-->
 
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
 
 
 
||
 
 
 
* 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 15 || <div style="text-align: center;">6.3</div> || [[Taylor and Maclaurin Series]] || * [[The Derivative as a Function || Higher-Order Derivatives]] <
|Week&nbsp;12 
 
 
 
||
 
 
 
<div style="text-align: center;">6.1</div>
 
 
 
||
 
 
 
[[Power Series and Functions]]
 
 
 
||
 
 
 
* [[Infinite Series|The Geometric Series Test]] <!-- 1224-5.2 -->
 
* [[The Divergence and Integral Tests]] <!-- 1224-5.3 -->
 
* [[Comparison Tests]] <!-- 1224-5.4 -->
 
* [[Alternating Series]] <!-- 1224-5.5 -->
 
* [[Ratio and Root Tests]] <!-- 1224-5.6 -->
 
 
 
||
 
 
 
* 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&nbsp;13
 
 
 
||
 
 
 
<div style="text-align: center;">6.2</div>
 
 
 
||  
 
 
 
[[Properties of Power Series]]
 
 
 
||
 
 
 
* [[Differentiation Rules]] <!-- 1214-3.3 -->
 
* [[Antiderivatives]]  <!-- 1214-4.10 -->
 
* [[The Fundamental Theorem of Calculus]]  <!-- 1214-5.3 -->
 
* [[Power Series and Functions]] <!-- 1224-6.1 -->
 
 
 
||
 
 
 
* 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&nbsp;14 
 
 
 
||
 
 
 
<div style="text-align: center;">6.3</div>
 
 
 
|| 
 
 
 
[[Taylor and Maclaurin Series]]
 
 
 
||
 
 
 
* [[The Derivative as a Function|Higher-Order Derivatives]] <!-- 1214-3.2 -->
 
* [[Power Series and Functions]] <!-- 1224-6.1 -->
 
* [[Properties of Power Series]] <!-- 1224-6.2 -->
 
 
 
||
 
 
 
* 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&nbsp;15 
 
 
 
||
 
 
 
<div style="text-align: center;">7.1</div>
 
 
 
||
 
 
 
[[Parametric Equations]]
 
 
 
||
 
 
 
* [[Toolkit Functions|Sketching Elementary Functions]] <!-- 1073-Mod 1.2 -->
 
* '''[[Equation of a Circle]]''' <!-- Grades 6-12 -->
 
* '''[[Equation of an Ellipse]]''' <!-- Grades 6-12 -->
 
* [[Trigonometric Functions]] <!-- 1093-2.2 -->
 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 -->
 
 
 
||
 
 
 
* 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&nbsp;15 
 
 
 
||
 
 
 
<div style="text-align: center;">7.2</div>
 
 
 
||
 
 
 
[[The Calculus of Parametric Equations]]
 
 
 
||
 
 
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[Differentiation Rules]] <!-- 1214-3.3 -->
 
* [[The Derivative as a Function|Higher-Order Derivatives]] <!-- 1214-3.2 -->
 
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
* [[Integration by Parts]] <!-- 1224-3.1 -->
 
 
 
||
 
 
 
* 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.
 
 
 
 
|}
 
|}

Revision as of 13:37, 31 March 2023

The textbook for this course is Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.

A comprehensive list of all undergraduate math courses at UTSA can be found here.

The Wikipedia summary of calculus and its history.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
1.5
Integration by Substitution * Differentiation Rules < -- 1214-3.3 -->
  • [[Linear Approximations and Differentials
Week 1 & 2
2.1
Area between Curves * [[Toolkit Functions Graphing Elementary Functions]] <
Week 2
2.2
Determining Volumes by Slicing * Areas of basic shapes < -- Grades 6-12 -->
Week 3
2.3
Volumes of Revolution, Cylindrical Shells * [[Toolkit Functions Graphing elementary functions]] <
Week 3
2.4
Arc Length and Surface Area * Differentiation Rules < -- 1214-3.3 -->
Week 4
2.5
Physical Applications * Areas of basic shapes < -- Grades 6-12 -->
Week 4 & 5
2.6
Moments and Center of Mass * [[Toolkit Functions Graphing elementary functions]] <
Week 5
3.1
Integration by Parts * Differentiation Rules < -- 1214-3.3 -->
  • [[Linear Approximations and Differentials
Week 6
3.2
Trigonometric Integrals * Trigonometric Functions < -- 1093-2.2 -->
  • [[Properties of the Trigonometric Functions
Week 6 & 7
3.3
Trigonometric Substitution * Completing the Square < -- 1073-Mod 3.2-->
Week 7
3.4
Partial Fractions * Factoring Polynomials < -- 1073-Mod 0.2 -->
Week 8
3.7
Improper Integrals * The Fundamental Theorem of Calculus < -- 1214-5.3 -->
Week 9
5.1
Sequences * [[The Limit Laws The Limit Laws and Squeeze Theorem]] <
Week 10
5.2
Infinite Series * Sigma notation < -- DNE (recommend 1093) -->
Week 11
5.3
The Divergence and Integral Tests * The Limit Laws < -- 1214-2.3 -->
  • [[Limits at Infinity and Asymptotes
Week 11
5.4
Comparison Tests * [[Limits at Infinity and Asymptotes Limits at Infinity]] <
Week 12
5.5
Alternating Series * [[Limits at Infinity and Asymptotes Limits at Infinity]] <
Week 12
5.6
Ratio and Root Tests * Factorials < -- Grades 6-12 -->
  • [[Limits at Infinity and Asymptotes
Week 13
6.1
Power Series and Functions * [[Infinite Series The Geometric Series Test]] <
Week 14
6.2
Properties of Power Series * Differentiation Rules < -- 1214-3.3 -->
Week 15
6.3
Taylor and Maclaurin Series * [[The Derivative as a Function Higher-Order Derivatives]] <