AP Calculus AB Syllabus

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

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 Related Rates

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 Limits at Infinity

3.6 A Summary of Curve Sketching

3.7 Optimization Problems

3.8 Newton's Method

3.9 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 Integration by Substitution

4.6 Numerical Integration

5 Logarithmic, Exponential, and Other Transcendental Functions

5.1 The Natural Logarithmic Function: Differentiation

5.2 The Natural Logarithmic Function: Integration

5.3 Inverse Functions

5.4 Exponential Functions: Differentiation and Integration

5.5 Bases Other Than e and Applications

5.6 Inverse Trigonometric Functions: Differentiation

5.7 Inverse Trigonometric Functions: Integration

5.8 Hyperbolic Functions

6 Differential Equations

6.1 Slope Fields and Euler's Method

6.2 Differential Equations: Growth and Decay

7 Applications of Integration

7.1 Area of a Region Between Two Curves

7.2 Volume: The Disk Method

7.3 Volume: The Shell Method

8 Integration Techniques, L'Hopital's Rule, and Improper Integrals

8.1 Basic Integration Rules

8.2 Indeterminate Forms and L' Hopital's Rule

• This course is suitable for students who have completed Algebra2 and Pre Calculus.