Calculus for AP 2e Notes
P Preparation for Calculus
- Graphs and Models
- Linear Model and Rates of Change
- Functions and Their Graphs
- Inverse Functions
- Exponential and Logarithmic Functions
1 Limits and Their Properties
- A Preview of Calculus
- Finding Limits Graphically and Numerically
- Evaluating Limits Analytically
- Continuity and One-Sided Limits
- Infinite Limits
- Limits at Infinity
2 Differentiation
- The Derivative and the Tangent Line Problem
- Basic Differentiation Rules and Rates of Change
- Product and Quotient Rules and Higher-Order Derivatives
- The Chain Rule
- Implicit Differentiation
- Derivatives of Inverse Functions
- Related Rates
We will cover 3.7 and 7.7 at this point, before moving to 3.1.
3 Applications of Differentiation
- Extrema on an Interval
- Rolle’s Theorem and the Mean Value Theorem
- Increasing and Decreasing Functions and the First Derivative Test
- Concavity and the Second Derivative Test
- A Summary of Curve Sketching
- Optimization Problems
- Linear Approximation and Differentials
4 Integration
- Antiderivatives and Indefinite Integration
- Area
- Riemann Sums and Definite Integrals
- The Fundamental Theorem of Calculus
- The Net Change Theorem
- Integration by Substitution
- The Natural Logarithmic Function: Integration
- Inverse Trigonometric Functions: Integration
We will cover 7.1 at this point, before moving to 5.1.