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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