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Tables of Contents for Calculus of Several Variables

Chapter/Section Title

Page #

Page Count

Preface

ix

Acknowledgments

xiii

Ancillaries

xvii

For the Student

xxi

Major Results from Calculus of a Single Variable

xxiii

Infinite Series

692

92

Sequences

694

15

Convergent or Divergent Series

709

14

Positive-term Series

723

11

The Ratio and Root Tests

734

5

Alternating Series and Absolute Convergence

739

8

Power Series

747

8

Power Series Representations of Functions

755

9

Maclaurin and Taylor Series

764

12

Applications of Taylor Polynomials

776

8

Review Exercises

782

1

Extended Problems and Group Projects

783

1

Parametric Equations and Polar Coordinates

784

60

Parametric Equations

786

17

Arc Length and Surface Area

803

8

Polar Coordinates

811

11

Integrals in Polar Coordinates

822

10

Translation and Rotation of Axes

832

12

Review Exercises

840

1

Extended Problems and Group Projects

841

3

Vectors and Surfaces

844

76

Vectors in Two Dimensions

846

11

Vectors in Three Dimensions

857

9

The Dot Product

866

10

The Vector Product

876

9

Lines and Planes

885

13

Surfaces

898

22

Review Exercises

918

1

Extended Problems and Group Projects

919

1

Vector-Valued Functions

920

52

Vector-Valued Functions and Space Curves

922

7

Limits, Derivatives, and Integrals

929

8

Curvilinear Motion

937

10

Curvature

947

12

Tangential and Normal Components of Acceleration

959

6

Kepler's Laws

965

7

Review Exercises

970

1

Extended Problems and Group Projects

971

1

Partial Differentiation

972

104

Functions of Several Variables

974

12

Limits and Continuity

986

12

Partial Derivatives

998

9

Increments and Differentials

1007

14

Chain Rules

1021

9

Directional Derivatives

1030

12

Tangent Planes and Normal Lines

1042

8

Extrema of Functions of Several Variables

1050

12

Lagrange Multipliers

1062

14

Review Exercises

1071

3

Extended Problems and Group Projects

1074

2

Multiple Integrals

1076

90

Double Integrals

1078

12

Area and Volume

1090

13

Double Integrals in Polar Coordinates

1103

8

Surface Area

1111

4

Triple Integrals

1115

12

Moments and Center of Mass

1127

9

Cylindrical Coordinates

1136

8

Spherical Coordinates

1144

8

Change of Variables and Jacobians

1152

14

Chapter 13 Review Exercises

1163

2

Extended Problems and Group Projects

1165

1

Vector Calculus

1166

68

Vector Fields

1168

8

Line Integrals

1176

12

Independence of Path

1188

11

Green's Theorem

1199

7

Surface Integrals

1206

10

The Divergence Theorem

1216

7

Stokes's Theorem

1223

11

Review Exercises

1232

1

Extended Problems and Group Projects

1233

1

Differential Equations

1234

2

Separable Differential Equations

1236

9

First-Order Linear Differential Equations

1245

12

Second-Order Linear Differential Equations

1257

5

Nonhomogeneous Linear Differential Equations

1262

6

Vibrations

1268

9

Review Exercises

1277

1

Extended Problems and Group Projects

1278

Appendices

I Theorems on Limits and Integrals

1

13

II Table of Integrals

14

5

III The Binomial Series

19

5

Answers to Selected Exercises

24

73

Index

97