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