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Tables of Contents for Multivariable Calculus
Chapter/Section Title
Page #
Page Count
Preface
vii
Parametric Equations and Polar Coordinates
686
50
Curves Defined by Parametric Equations
687
9
Laboratory Project Running Circles around Circles
695
1
Calculus with Parametric Curves
696
9
Laboratory Project Bezier Curves
705
1
Polar Coordinates
705
10
Areas and Lengths in Polar Coordinates
715
5
Conic Sections
720
8
Conic Sections in Polar Coordinates
728
8
Review
732
3
Problems Plus
735
1
Infinite Sequences and Series
736
92
Sequences
737
12
Laboratory Project Logistic Sequences
749
1
Series
749
10
The Integral Test and Estimates of Sums
759
7
The Comparison Tests
766
5
Alternating Series
771
5
Absolute Convergence and the Ratio and Root Tests
776
7
Strategy for Testing Series
783
2
Power Series
785
5
Representations of Functions as Power Series
790
6
Taylor and Maclaurin Series
796
12
Laboratory Project An Elusive Limit
808
1
The Binomial Series
808
4
Writing Project How Newton Discovered the Binomial Series
812
1
Applications of Taylor Polynomials
812
16
Applied Project Radiation from the Stars
875
Review
822
3
Problems Plus
825
3
Vectors and the Geometry of Space
828
56
Three-Dimensional Coordinate Systems
829
5
Vectors
834
9
The Dot Product
843
7
The Cross Product
850
8
Discovery Project The Geometry of a Tetrahedron
858
1
Equations of Lines and Planes
858
10
Laboratory Project Putting 3D in Perspective
868
1
Cylinders and Quadric Surfaces
868
7
Cylindrical and Spherical Coordinates
875
9
Laboratory Project Families of Surfaces
880
1
Review
880
3
Problems Plus
883
1
Vector Functions
884
38
Vector Functions and Space Curves
885
7
Derivatives and Integrals of Vector Functions
892
6
Arc Length and Curvature
898
8
Motion in Space: Velocity and Acceleration
906
16
Applied Project Kepler's Laws
916
1
Review
917
3
Problems Plus
920
2
Partial Derivatives
922
94
Functions of Several Variables
923
15
Limits and Continuity
938
7
Partial Derivatives
945
14
Tangent Planes and Linear Approximations
959
8
The Chain Rule
967
9
Directional Derivatives and the Gradient Vector
976
13
Maximum and Minimum Values
989
12
Applied Project Designing a Dumpster
999
1
Discovery Project Quadratic Approximations and Critical Points
1000
1
Lagrange Multipliers
1001
15
Applied Project Rocket Science
1008
1
Applied Project Hydro-Turbine Optimization
1009
1
Review
1010
4
Problems Plus
1014
2
Multiple Integrals
1016
74
Double Integrals over Rectangles
1017
8
Iterated Integrals
1025
6
Double Integrals over General Regions
1031
8
Double Integrals in Polar Coordinates
1039
6
Applications of Double Integrals
1045
10
Surface Area
1055
4
Triple Integrals
1059
10
Discovery Project Volumes of Hyperspheres
1068
1
Triple Integrals in Cylindrical and Spherical Coordinates
1069
8
Applied Project Roller Derby
1075
1
Discovery Project The Intersection of Three Cylinders
1076
1
Change of Variables in Multiple Integrals
1077
13
Review
1085
3
Problems Plus
1088
2
Vector Calculus
1090
86
Vector Fields
1091
7
Line Integrals
1098
12
The Fundamental Theorem for Line Integrals
1110
9
Green's Theorem
1119
7
Curl and Divergence
1126
8
Parametric Surfaces and Their Areas
1134
11
Surface Integrals
1145
12
Stokes' Theorem
1157
6
Writing Project Three Men and Two Theorems
1162
1
The Divergence Theorem
1163
7
Summary
1170
6
Review
1171
3
Problems Plus
1174
2
Second-Order Differential Equations
1176
1
Second-Order Linear Equations
1177
6
Nonhomogeneous Linear Equations
1183
8
Applications of Second-Order Differential Equations
1191
8
Series Solutions
1199
4
Review
1203
Appendixes
1
42
F Proofs of Theorems
2
3
G Complex Numbers
5
8
H Answers to Odd-Numbered Exercises
13
30
Index
43