Difference between revisions of "MAT1223"

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The textbook for this course is
+
==Topics List==
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]
+
{| class="wikitable sortable"
 +
! 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|Differentials]] <!-- 1214-4.2 -->
 +
* [[Antiderivatives]] <!-- 1214-4.10 -->
 +
* [[The Definite Integral]] <!-- 1214-5.2 -->
 +
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
  
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].
+
* Recognize when to use integration by substitution.
 +
* Use substitution to evaluate indefinite integrals.
 +
* Use substitution to evaluate definite integrals.
  
{| class="wikitable"
 
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
 
|-
 
|-
| Week 1 || 1.5 || [[Integration by Substitution]] || * [[Differentiation Rules]] ||
+
 
* [[Linear Approximations and Differentials]]
+
 
 +
|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 1 & 2 || 2.1 || [[Area between Curves]] || * [[Toolkit Functions]] || [[Graphing Elementary Functions]]  
+
 
 +
 
 +
|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 2 || 2.2 || [[Determining Volumes by Slicing]] || * '''[[Areas of basic shapes]]'''  ||  
+
 
* '''[[Volume of a cylinder]]'''
+
 
 +
|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 || 2.3 || [[Volumes of Revolution, Cylindrical Shells]] || * [[Toolkit Functions]] || [[Graphing elementary functions]]  
+
 
 +
 
 +
|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 3 || 2.4 || [[Arc Length and Surface Area]] || * [[Differentiation Rules]] ||  
+
 
* [[The Fundamental Theorem of Calculus]]  
+
 
 +
|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 4 || 2.5 || [[Physical Applications]] || * '''[[Areas of basic shapes]]'''  ||
+
 
* '''[[Volume of a cylinder]]'''
+
 
 +
|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 4 & 5 || 2.6 || [[Moments and Center of Mass]] || * [[Toolkit Functions]] || [[Graphing elementary functions]]  
+
 
 +
 
 +
|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 5 || 3.1 || [[Integration by Parts]] || * [[Differentiation Rules]] ||  
+
 
* [[Linear Approximations and Differentials]]
+
 
 +
|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 6 || 3.2 || [[Trigonometric Integrals]] || * [[Trigonometric Functions]] ||  
+
 
* [[Properties of the Trigonometric Functions]]
+
 
 +
|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 6 & 7 || 3.3 || [[Trigonometric Substitution]] || * [[Completing the Square]] ||  
+
 
* [[Trigonometric Functions]]  
+
 
 +
|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 7 || 3.4 || [[Partial Fractions]] || * [[Factoring Polynomials]] ||
+
 
* [[Completing the Square]]  
+
 
 +
|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 || 3.7 || [[Improper Integrals]] || * [[The Fundamental Theorem of Calculus]] ||  
+
 
* [[Integration by Substitution]]  
+
 
 +
|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 9 || 5.1 || [[Sequences]] || * [[The Limit Laws]] || [[The Limit Laws and Squeeze Theorem]]  
+
 
 +
 
 +
|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 10 || 5.2 || [[Infinite Series]] || * '''[[Sigma notation]]'''  ||  
+
 
* [[Sequences]]  
+
 
 +
|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 11 || 5.3 || [[The Divergence and Integral Tests]] || * [[The Limit Laws]] ||
+
 
* [[Limits at Infinity and Asymptotes]]
+
 
 +
|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 11 || 5.4 || [[Comparison Tests]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]]  
+
 
 +
|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 12 || 5.5 || [[Alternating Series]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]]  
+
 
 +
 
 +
|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 12 || 5.6 || [[Ratio and Root Tests]] || * '''[[Factorials]]'''  ||
+
 
* [[Limits at Infinity and Asymptotes]]
+
 
 +
|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.
 +
 
 
|-
 
|-
| Week 13 || 6.1 || [[Power Series and Functions]] || * [[Infinite Series]] || [[The Geometric Series Test]]
+
 
|-
 
| Week 14 || 6.2 || [[Properties of Power Series]] || * [[Differentiation Rules]]  ||
 
* [[Antiderivatives]] 
 
|-
 
| Week 15 || 6.3 || [[Taylor and Maclaurin Series]] || * [[The Derivative as a Function]] || [[Higher-Order Derivatives]]
 
 
|}
 
|}

Latest revision as of 09:34, 11 June 2024

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
1.5

Integration by Substitution

  • Recognize when to use integration by substitution.
  • Use substitution to evaluate indefinite integrals.
  • Use substitution to evaluate definite integrals.
Week 1/2
2.1

Area between Curves

  • 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 2/3
2.2

Determining Volumes by Slicing

  • 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
2.3

Volumes of Revolution, Cylindrical Shells

  • 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 4
2.5

Physical Applications

  • 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 5
3.1

Integration by Parts

  • 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
3.2

Trigonometric Integrals

  • 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 6/7
3.3

Trigonometric Substitution

  • 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 7/8
3.4

Partial Fractions

  • 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 8
3.7

Improper Integrals

  • 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
5.1

Sequences

  • 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
5.2

Infinite Series

  • 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 10/11
5.3

The Divergence and Integral Tests

  • 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 11
5.4

Comparison Tests

  • 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 12
5.5

Alternating Series

  • Use the Alternating Series Test to determine the convergence of an alternating series.
  • Explain the meaning of absolute convergence and conditional convergence.
Week 12
5.6

Ratio and Root Tests

  • 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 13
6.1

Power Series and Functions

  • 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 14
6.2

Properties of Power Series

  • Differentiate and integrate power series term-by-term.
  • Use differentiation and integration of power series to represent certain functions as power series.
Week 14/15
6.3

Taylor and Maclaurin Series

  • Find a Taylor or Maclaurin series representation of a function.
  • Find the radius of convergence of a Taylor Series or Maclaurin series.