Calculus for AP 2e Notes
P Preparation for Calculus
- P.1 Graphs and Models
- P.2 Linear Model and Rates of Change
- P.3 Functions and Their Graphs
- P.4 Inverse Functions
- P.5 Exponential and Logarithmic Functions
1 Limits and Their Properties
- 1.1 A Preview of Calculus
- 1.2 Finding Limits Graphically and Numerically
- 1.3 Evaluating Limits Analytically
- 1.4 Continuity and One-Sided Limits
- 1.5 Infinite Limits
- 1.6 Limits at Infinity
2 Differentiation
- 2.1 The Derivative and the Tangent Line Problem
- 2.2 Basic Differentiation Rules and Rates of Change
- 2.3 Product and Quotient Rules and Higher-Order Derivatives
- 2.4 The Chain Rule
- 2.5 Implicit Differentiation
- 2.6 Derivatives of Inverse Functions
- 2.7 Related Rates
- Differentiation Cheat Sheet
3 Applications of Differentiation
- 3.1 Extrema on an Interval
- 3.2 Rolle’s Theorem and the Mean Value Theorem
- 3.3 Increasing and Decreasing Functions and the First Derivative Test
- 3.4 Concavity and the Second Derivative Test
- 3.5 A Summary of Curve Sketching
- 3.6 Optimization Problems
- 3.7 Linear Approximation and Differentials
4 Integration
- 4.1 Antiderivatives and Indefinite Integration
- 4.2 Area
- 4.3 Riemann Sums and Definite Integrals
- 4.4 The Fundamental Theorem of Calculus
- 4.5 The Net Change Theorem
- 4.6 Integration by Substitution
- 4.7 The Natural Logarithmic Function: Integration
- 4.8 Inverse Trigonometric Functions: Integration
- Integration Cheat Sheet