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

|-


|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&nbsp;1/2

||

<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&nbsp;2/3

||

<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&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&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 -->

||

* 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.


|-


|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&nbsp;6 

||

<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).
* Solve problems involving applications of integration using trigonometric integrals.


|-


|Week&nbsp;6/7

||

<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 -->

||

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


|-


|Week&nbsp;7/8

||

<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 -->

||

* Recognize when to use partial fraction decomposition.
* 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&nbsp;8

||

<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&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&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 convergent telescoping series.

|-


|Week&nbsp;10/11

||

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

||  

[[The Divergence and Integral Tests]]

||

* [[The Limit Laws]] <!-- 1214-2.3 -->
* [[Limits at Infinity and Asymptotes| 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.

|-


|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&nbsp;12    

||

<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.
* Explain the meaning of absolute convergence and conditional convergence.

|-


|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&nbsp;13   

||

<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;14

||

<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 -->

||

* Differentiate and integrate power series term-by-term.
* Use differentiation and integration of power series to represent certain functions as power series.

|-


|Week&nbsp;14/15  

||

<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.

|-

|}