Preface
Guide to AP Calculus
Guide to Mathematical Practices for AP Calculus (MPACs)
AP Calculus Pacing Guide
1. Functions
1.1 Review of Functions
1.2 Representing Functions
1.3 Inverse, Exponential, and Logarithmic Functions
1.4 Trigonometric Functions and Their Inverses
Review Exercises
AP Practice Questions
2. Limits
2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definitions of Limits
Review Exercises
AP Practice Questions
3. Derivatives
3.1 Introducing the Derivative
3.2 Working with Derivatives
3.3 Rules of Differentiation
3.4 The Product and Quotient Rules
3.5 Derivatives of Trigonometric Functions
3.6 Derivatives as Rates of Change
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of Logarithmic and Exponential Functions
3.10 Derivatives of Inverse Trigonometric Functions
3.11 Related Rates
Review Exercises
AP Practice Questions
4. Applications of the Derivative
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.5 Linear Approximation and Differentials
4.6 Mean Value Theorem
4.7 L’Hôpital’s Rule
4.8 Newton’s Method
Review Exercises
AP Practice Questions
5. Integration
5.1 Antiderivatives
5.2 Approximating Areas under Curves
5.3 Definite Integrals
5.4 Fundamental Theorem of Calculus
5.5 Properties of Integrals and Average Value
5.6 Substitution Rule
5.7 Numerical Integration
Review Exercises
AP Practice Questions
6. Applications of Integration
6.1 Velocity and Net Change
6.2 Regions between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Physical Applications
Review Exercises
AP Practice Questions
7. Integration Techniques
7.1 Basic Approaches
7.2 Integration by Parts
7.3 Partial Fractions
7.4 Improper Integrals
7.5 Trigonometric Substitutions
Review Exercises
AP Practice Questions
8. Differential Equations
8.1 Basic Ideas
8.2 Slope Fields and Euler’s Method
8.3 Separable Differential Equations
8.4 Exponential Models
Review Exercises
AP Practice Questions
9. Sequences and Infinite Series
9.1 An Overview
9.2 Sequences
9.3 Infinite Series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root, and Comparison Tests
9.6 Alternating Series
Review Exercises
AP Practice Questions
10. Power Series
10.1 Approximating Functions with Polynomials
10.2 Properties of Power Series
10.3 Taylor Series
10.4 Working with Taylor Series
Review Exercises
AP Practice Questions
11. Parametric, Polar, and Vector Curves
11.1 Parametric Equations
11.2 Calculus with Parametric Equations
11.3 Polar Coordinates
11.4 Calculus in Polar Coordinates
11.5 Vectors in the Plane
11.6 Calculus of Vector-Valued Functions
11.7 Two-Dimensional Motion
Review Exercises
AP Practice Questions
Appendix A. Algebra Review
Appendix B. Conic Sections
Appendix C. Proofs of Selected Theorems
Answers
Credits
Index
Table of Integrals
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