Course Topics

Limits and Continuity
- Introduction to limits
- Evaluating limits algebraically and graphically
- One-sided limits and infinite limits
- Continuity and discontinuity
- Intermediate Value Theorem
Differentiation: Definition and Basic Techniques
- Definition of the derivative
- Interpretation of the derivative as a rate of change
- Differentiation rules for polynomials, exponentials, logarithms, and trigonometric functions
- Implicit differentiation
- Related rates problems
Applications of Derivatives
- Analysis of graphs using derivatives
- Optimization problems
- Modeling rates of change
- Derivatives of inverse functions
- Linear approximation and differentials
Integration and Accumulation
- Antiderivatives and indefinite integrals
- Integration by substitution
- Definite integrals and areas under curves
- The Fundamental Theorem of Calculus
- Average value of a function
Applications of Integration
- Area between curves
- Volumes of solids of revolution
- Work, average value, and accumulation
- Differential equations and slope fields
- Applications to physics and economics
Exam Preparation
- Review of all topics covered in the course
- Practice with AP-style multiple-choice and free-response questions
- Test-taking strategies and time management tips

Calculus I