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
