Preface
Chapter 1  Integration
Introduction
1.1 Approximating Areas
1.2 The Definite Integral
1.3 The Fundamental Theorem of Calculus
1.4 Integration Formulas and the Net Change Theorem
1.5 Substitution
1.6 Integrals Involving Exponential and Logarithmic Functions
1.7 Integrals Resulting in Inverse Trigonometric Functions
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 2  Applications of Integration
Introduction
2.1 Areas between Curves
2.2 Determining Volumes by Slicing
2.3 Volumes of Revolution: Cylindrical Shells
2.4 Arc Length of a Curve and Surface Area
2.5 Physical Applications
2.6 Moments and Centers of Mass
2.7 Integrals, Exponential Functions, and Logarithms
2.8 Exponential Growth and Decay
2.9 Calculus of the Hyperbolic Functions
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 3  Techniques of Integration
Introduction
3.1 Integration by Parts
3.2 Trigonometric Integrals
3.3 Trigonometric Substitution
3.4 Partial Fractions
3.5 Other Strategies for Integration
3.6 Numerical Integration
3.7 Improper Integrals
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 4  Introduction to Differential Equations
Introduction
4.1 Basics of Differential Equations
4.2 Direction Fields and Numerical Methods
4.3 Separable Equations
4.4 The Logistic Equation
4.5 First-order Linear Equations
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 5  Sequences and Series
Introduction
5.1 Sequences
5.2 Infinite Series
5.3 The Divergence and Integral Tests
5.4 Comparison Tests
5.5 Alternating Series
5.6 Ratio and Root Tests
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 6  Power Series
Introduction
6.1 Power Series and Functions
6.2 Properties of Power Series
6.3 Taylor and Maclaurin Series
6.4 Working with Taylor Series
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Chapter 7  Parametric Equations and Polar Coordinates
Introduction
7.1 Parametric Equations
7.2 Calculus of Parametric Curves
7.3 Polar Coordinates
7.4 Area and Arc Length in Polar Coordinates
7.5 Conic Sections
Chapter Review
Key Terms
Key Equations
Key Concepts
Review Exercises
Appendix A Table of Integrals
Appendix B Table of Derivatives
Appendix C Review of Pre-Calculus
Answer Key
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Index