**Chapter 1 Functions**

1.1 Functions and Graphs

1.2 Combining Functions

1.3 Polynomial and Rational Functions

1.4 Transcendental Functions

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

1.7 From Words to Functions

Chapter 1 in Review

**Chapter 2 Limit of a Function**

2.1 Limits—An Informal Approach

2.2 Limit Theorems

2.3 Continuity

2.4 Trigonometric Limits

2.5 Limits That Involve Infinity

2.6 Limits—A Formal Approach

2.7 The Tangent Line Problem

Chapter 2 in Review

**Chapter 3 The Derivative**

3.1 The Derivative

3.2 Power and Sum Rules

3.3 Product and Quotient Rules

3.4 Trigonometric Functions

3.5 Chain Rule

3.6 Implicit Differentiation

3.7 Derivatives of Inverse Functions

3.8 Exponential Functions

3.9 Logarithmic Functions

3.10 Hyperbolic Functions

Chapter 3 in Review

**Chapter 4 Applications of the Derivative**

4.1 Rectilinear Motion

4.2 Related Rates

4.3 Extrema of Functions

4.4 Mean Value Theorem

4.5 Limits Revisited—L’Hôpital’s Rule

4.6 Graphing and the First Derivative

4.7 Graphing and the Second Derivative

4.8 Optimization

4.9 Linearization and Differentials

4.10 Newton’s Method

Chapter 4 in Review

**Chapter 5 Integrals**

5.1 The Indefinite Integral

5.2 Integration by the u-Substitution

5.3 The Area Problem

5.4 The Definite Integral

5.5 Fundamental Theorem of Calculus

Chapter 5 in Review

**Chapter 6 Applications of the Integral**

6.1 Rectilinear Motion Revisited

6.2 Area Revisited

6.3 Volumes of Solids: Slicing Method

6.4 Volumes of Solids: Shell Method

6.5 Length of a Graph

6.6 Area of a Surface of Revolution

6.7 Average Value of a Function

6.8 Work

6.9 Liquid Pressure and Force

6.10 Centers of Mass and Centroids

Chapter 6 in Review

**Chapter 7 Techniques of Integration**

7.1 Integration—Three Resources

7.2 Integration by Substitution

7.3 Integration by Parts

7.4 Powers of Trigonometric Functions

7.5 Trigonometric Substitutions

7.6 Partial Fractions

7.7 Improper Integrals

7.8 Approximate Integration

Chapter 7 in Review

**Chapter 8 First-Order Differential Equations**

8.1 Separable Equations

8.2 Linear Equations

8.3 Mathematical Models

8.4 Solution Curves without a Solution

8.5 Euler’s Method

Chapter 8 in Review

**Chapter 9 Sequences and Series**

9.1 Sequences

9.2 Monotonic Sequences

9.3 Series

9.4 Integral Test

9.5 Comparison Tests

9.6 Ratio and Root Tests

9.7 Alternating Series

9.8 Power Series

9.9 Representing Functions by Power Series

9.10 Taylor Series

9.11 Binomial Series

Chapter 9 in Review

**Chapter 10 Conics and Polar Coordinates**

10.1 Conic Sections

10.2 Parametric Equations

10.3 Calculus and Parametric Equations

10.4 Polar Coordinate System

10.5 Graphs of Polar Equations

10.6 Calculus in Polar Coordinates

10.7 Conic Sections in Polar Coordinates

Chapter 10 in Review

Appendix

Proofs of Selected Theorems

Answers to Test Yourself

Answers to Selected Odd-Numbered Problems

Index

Resource Pages:

Review of Algebra

Formulas from Geometry

Graphs and Functions

Review of Trigonometry

Exponential and Logarithmic Functions

Differentiation

Integration Formulas