## Course Contents at a Glance 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