The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the **Table of Contents**.

## Module 1: Integration

- Approximating Areas
- The Definite Integral
- The Fundamental Theorem of Calculus
- Integration Formulas and the Net Change Theorem
- Substitution
- Integrals Involving Exponential and Logarithmic Functions
- Integrals Resulting in Inverse Trigonometric Functions

## Module 2: Applications of Integration

- Areas Between Curves
- Determining Volumes by Slicing
- Volumes of Revolution: Cylindrical Shells
- Arc Length of a Curve and Surface Area
- Physical Applications
- Moments and Centers of Mass
- Integrals, Exponential Functions, and Logarithms
- Exponential Growth and Decay
- Calculus of the Hyperbolic Functions

## Module 3: Techniques of Integration

- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitution
- Partial Fractions
- Other Strategies for Integration
- Numerical Integration
- Improper Integrals

## Module 4: Introduction to Differential Equations

- Basics of Differential Equations
- Direction Fields and Numerical Methods
- Separable Equations
- The Logistic Equation
- First-order Linear Equations

## Module 5: Sequences and Series

- Sequences
- Infinite Series
- The Divergence and Integral Tests
- Comparison Tests
- Alternating Series
- Ratio and Root Tests

## Module 6: Power Series

- Power Series and Functions
- Properties of Power Series
- Taylor and Maclaurin Series
- Working with Taylor Series

## Module 7: Parametric Equations and Polar Coordinates

- Parametric Equations
- Calculus of Parametric Curves
- Polar Coordinates
- Area and Arc Length in Polar Coordinates
- Conic Sections