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  

Chapter 11  Vectors and 3-Space

11.1  Vectors in 2-Space
11.2  3-Space and Vectors
11.3  Dot Product
11.4  Cross Product
11.5  Lines in 3-Space
11.6  Planes
11.7  Cylinders and Spheres
11.8  Quadric Surfaces
 Chapter 11 in Review 

Chapter 12  Vector-Valued Functions

12.1  Vector Functions
12.2  Calculus of Vector Functions
12.3  Motion on a Curve
12.4  Curvature and Acceleration
 Chapter 12 in Review 

Chapter 13  Partial Derivatives

13.1    Functions of Several Variables
13.2    Limits and Continuity
13.3    Partial Derivatives
13.4    Linearization and Differentials
13.5    Chain Rule
13.6    Directional Derivative
13.7    Tangent Planes and Normal Lines
13.8    Extrema of Multivariable Functions
13.9    Method of Least Squares
13.10  Lagrange Multipliers
   Chapter 13 in Review 

Chapter 14  Multiple Integrals

14.1  The Double Integral
14.2  Iterated Integrals
14.3  Evaluation of Double Integrals
14.4  Center of Mass and Moments
14.5  Double Integrals in Polar Coordinates
14.6  Surface Area
14.7  The Triple Integral
14.8  Triple Integrals in Other Coordinate Systems
14.9  Change of Variables in Multiple Integrals
 Chapter 14 in Review 

Chapter 15  Vector Integral Calculus

15.1  Line Integrals
15.2  Line Integrals of Vector Fields
15.3 Independence of the Path
15.4  Green’s Theorem
15.5 Parametric Surfaces and Area
15.6  Surface Integrals
15.7  Curl and Divergence
15.8  Stokes’ Theorem
15.9  Divergence Theorem
 Chapter 15 in Review 

Chapter 16   Higher-Order Differential Equations

16.1  Exact First-Order Equations
16.2  Homogenous Linear Equations
16.3  Nonhomogenous Linear Equations
16.4  Mathematical Models
16.5  Power Series Solutions
 Chapter 16 in Review 

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