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Tables of Contents for Calculus
Chapter/Section Title
Page #
Page Count
Preface
xi

Acknowledgments
xvi

Ancillaries
xx

For the Student
xxiii

Precalculus Review
2
2
Algebra
4
16
Functions and Their Graphs
20
16
Trigonometry
36
17
Exponentials and Logarithms
53
10
Conic Sections
63
19
Limits and Continuity
82
60
Introduction to Limits
84
13
Definition of Limit
97
9
Techniques for Finding Limits
106
10
Limits Involving Infinity
116
11
Continuous Functions
127
15
Chapter 1 Review Exercises
139
1
Extended Problems and Group Projects
140
2
The Derivative
142
104
Tangent Lines and Rates of Change
144
13
Definition of Derivative
157
16
Techniques of Differentiation
173
11
Derivatives of the Trigonometric Functions
184
11
The Chain Rule
195
11
Implicit Differentiation
206
8
Related Rates
214
10
Linear Approximations and Differentials
224
13
Newton's Method
237
9
Chapter 2 Review Exercises
242
3
Extended Problems and Group Projects
245
1
Applications of the Derivative
246
96
Extrema of Functions
248
13
The Mean Value Theorem
261
8
The First Derivative Test
269
10
Concavity and the Second Derivative Test
279
12
Summary of Graphical Methods
291
11
Optimization Problems
302
16
Velocity and Acceleration
318
10
Applications to Economics, Social Sciences, and Life Sciences
328
14
Chapter 3 Review Exercises
337
3
Extended Problems and Group Projects
340
2
Integrals
342
88
Antiderivatives, Indefinite Integrals, and Simple Differential Equations
344
13
Change of Variables in Indefinite Integrals
357
8
Summation Notation and Area
365
12
The Definite Integral
377
11
Properties of the Definite Integral
388
8
The Fundamental Theorem of Calculus
396
13
Numerical Integration
409
21
Chapter 4 Review Exercises
427
2
Extended Problems and Group Projects
429
1
Applications of the Definite Integral
430
84
Area
432
13
Solids of Revolution
445
12
Volumes by Cylindrical Shells
457
6
Volumes by Cross Sections
463
5
Arc Length and Surfaces of Revolution
468
12
Work
480
8
Moments and Centers of Mass
488
9
Other Applications
497
17
Chapter 5 Review Exercises
511
2
Extended Problems and Group Projects
513
1
Transcendental Functions
514
114
The Derivative of the Inverse Function
516
11
The Natural Logarithm Function
527
12
The Exponential Function
539
9
Integration Using Natural Logarithm and Exponential Functions
548
9
General Exponential and Logarithmic Functions
557
11
Separable Differential Equations and Laws of Growth and Decay
568
8
Inverse Trigonometric Functions
576
15
Hyperbolic and Inverse Hyperbolic Functions
591
19
Indeterminate Forms and I'Hopital's Rule
610
18
Chapter 6 Review Exercises
623
3
Extended Problems and Group Projects
626
2
Techniques of Integration
628
64
Integration by Parts
630
9
Trigonometric Integrals
639
5
Trigonometric Substitutions
644
6
Integrals of Rational Functions
650
10
660
8
Tables of Integrals and Computer Algebra Systems
668
6
Improper Integrals
674
18
Chapter 7 Review Exercises
689
2
Extended Problems and Group Projects
691
1
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
Chapter 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
Chapter 9 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
Chapter 10 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
Chapter 11 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
Chapter 12 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
Chapter 14 Review Exercises
1232
1
Extended Problems and Group Projects
1233
1
Differential Equations
1234

Separable Differential Equations
1236

First-Order Linear Differential Equations
1245

Second-Order Linear Differential Equations
1257

Nonhomogeneous Linear Differential Equations
1262

Vibrations
1268

Chapter 15 Review Exercises
1277

Extended Problems and Group Projects
1278

Appendices
I Theorems on Limits and Integrals
A1

II Table of Integrals
A14

III The Binomial Series
A19