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: Functions and Graphs
- Review of Functions
- Basic Classes of Functions
- Trigonometric Functions
- Inverse Functions
- Exponential and Logarithmic Functions
Module 2: Limits
- A Preview of Calculus
- The Limit of a Function
- The Limit Laws
- Continuity
- The Precise Definition of a Limit
Module 3: Derivatives
- Defining the Derivative
- The Derivative as a Function
- Differentiation Rules
- Derivatives as Rates of Change
- Derivatives of Trigonometric Functions
- The Chain Rule
- Derivatives of Inverse Functions
- Implicit Differentiation
- Derivatives of Exponential and Logarithmic Functions
Module 4: Applications of Derivatives
- Related Rates
- Linear Approximations and Differentials
- Maxima and Minima
- The Mean Value Theorem
- Derivatives and the Shape of a Graph
- Limits at Infinity and Asymptotes
- Applied Optimization Problems
- L’Hôpital’s Rule
- Newton’s Method
- Antiderivatives
Module 5: 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
- Approximating Integrals
Module 6: 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
