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Tables of Contents for Multivariable Calculus
Chapter/Section Title
Page #
Page Count
Preface
ix
Functions and Graphs
1
48
Preliminaries
2
11
Lines in the Plane
13
6
Functions and Graphs
19
14
Inverse Functions; Inverse Trigonometric Functions
33
16
Chapter 1 Review
42
4
Guest Essay: Calculus Was Inevitable, John Troutman
46
2
Mathematical Essays
48
1
Limits and Continuity
49
48
The Limit of a Function
50
11
Algebraic Computation of Limits
61
9
Continuity
70
10
Exponential and Logarithmic Functions
80
17
Chapter 2 Review
92
5
Differentiation
97
86
An Introduction to the Derivative: Tangents
98
12
Techniques of Differentiation
110
9
Derivatives of Trigonometric, Exponential, and Logarithmic Functions
119
6
Rates of Change: Modeling Rectilinear Motion
125
13
The Chain Rule
138
8
Implicit Differentiation
146
11
Related Rates and Applications
157
8
Linear Approximation and Differentials
165
18
Chapter 3 Review
177
4
Group Research Project: Chaos
181
2
Additional Applications of the Derivative
183
88
Extreme Values of a Continuous Function
184
11
The Mean Value Theorem
195
6
Using Derivatives to Sketch the Graph of a Function
201
16
Curve Sketching with Asymptotes: Limits Involving Infinity
217
12
l'Hopital's Rule
229
9
Optimization in the Physical Sciences and Engineering
238
12
Optimization in Business, Economics, and the Life Sciences
250
21
Chapter 4 Review
263
6
Group Research Project: Wine Barrel Capacity
269
2
Integration
271
84
Antidifferentiation
272
10
Area as the Limit of a Sum
282
8
Riemann Sums and the Definite Integral
290
12
The fundamental Theorems of Calculus
302
7
Integration by Substitution
309
7
Introduction to Differential Equations
316
12
The Mean Value Theorem for Integrals; Average Value
328
6
Numerical Integration: The Trapezoidal Rule and Simpson's Rule
334
8
An Alternative Approach: The logarithm as an Integral
342
13
Chapter 5 Review
346
5
Guest Essay: Kinematics of Jogging, Ralph Boas
351
1
Mathematical Essays
352
1
Cumulative Review: Chapters 1-5
353
2
Additional Applications of the Integral
355
70
Area between Two Curves
356
6
Volume
362
13
Polar Forms and Area
375
10
Arc length and Surface Area
385
10
Physical Applications: Work, Liquid Force, and Centroids
395
12
Applications to Business, Economics, and life Sciences
407
18
Chapter 6 Review
417
7
Group Research Project: Houdini's Escape
424
1
Methods of Integration
425
68
Review of Substitution and Integration by Table
426
9
Integration by Parts
435
6
Trigonometric Methods
441
7
Method of Partial Fractions
448
9
Summary of Integration Techniques
457
4
First-Order Differential Equations
461
11
Improper Integrals
472
9
Hyperbolic and Inverse Hyperbolic Functions
481
12
Chapter 7 Review
487
4
Group Research Project: Buoy Design
491
2
Infinite Series
493
80
Sequences and Their Limits
494
11
Introduction to Infinite Series: Geometric Series
505
9
The Integral Test, p-Series
514
7
Comparison Tests
521
6
The Ratio Test and the Root Test
527
6
Alternating Series; Absolute and Conditional Convergence
533
11
Power Series
544
9
Taylor and Maclaurin Series
553
20
Chapter 8 Review
566
4
Group Research Project: Elastic Tightrope
570
1
Cumulative Review: Chapters 6-8
571
2
Vectors in the Plane and in Space
573
60
Vectors in R2
574
8
Coordinates and Vectors in R3
582
6
The Dot Product
588
9
The Cross Product
597
9
Parametric Representation of Curves; lines in R3
606
9
Planes in R3
615
7
Quadric Surfaces
622
11
Chapter 9 Review
628
4
Group Research Project: Star Trek
632
1
Vector-Valued Functions
633
60
Introduction to Vector Functions
634
8
Differentiation and Integration of Vector Functions
642
9
Modeling Ballistics and Planetary Motion
651
9
Unit Tangent and Principal Unit Normal Vectors; Curvature
660
13
Tangential and Normal Components of Acceleration
673
20
Chapter 10 Review
679
5
Guest Essay: The Stimulation of Science, Howard Eves
684
3
Mathematical Essays
687
1
Cumulative Review: Chapters 1-10
688
5
Partial Differentiation
693
84
Functions of Several Variables
694
7
Limits and Continuity
701
9
Partial Derivatives
710
10
Tangent Planes, Approximations, and Differentiability
720
9
Chain Rules
729
8
Directional Derivatives and the Gradient
737
12
Extrema of Functions of Two Variables
749
12
Lagrange Multipliers
761
16
Chapter 11 Review
770
5
Group Research Project: Desertification
775
2
Multiple Integration
777
82
Double Integration over Rectangular Regions
778
9
Double Integration over Nonrectangular Regions
787
8
Double Integrals in Polar Coordinates
795
9
Surface Area
804
8
Triple Integrals
812
10
Mass, Moments, and Probability Density Functions
822
11
Cylindrical and Spherical Coordinates
833
10
Jacobians: Change of Variables
843
16
Chapter 12 Review
852
5
Group Research Project: Space-Capsule Design
857
2
Vector Analysis
859
76
Properties of a Vector Field: Divergence and Curl
860
7
Line Integrals
867
10
The Fundamental Theorem and Path Independence
877
10
Green's Theorem
887
11
Surface Integrals
898
10
Stokes' Theorem
908
8
The Divergence Theorem
916
19
Chapter 13 Review
924
5
Guest Essay: Continuous vs. Discrete Mathematics
929
1
Cumulative Review: Chapters 11-13
930
1
Mathematical Essays
931
1
Cumulative Review: Chapters 11-13
932
3
Introduction to Differential Equations
935
1
First-Order Differential Equations
936
11
Second-Order Homogeneous Linear Differential Equations
947
10
Second-Order Nonhomogeneous Linear Differential Equations
957
9
Chapter 14 Review
966
3
Group Research Project: Save the Perch Project
969
Appendices
A Introduction of The Theory of Limits
A-1
Selected Proofs
A-8
Significant Digits
A-17
Short Table of Integrals
A-21
Trigonometric Formulas
A-31
Answers to Selected Problems
A-34
Credits
A-54
Index
A-57
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