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Calculus,9780534936242
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Calculus

by
Edition:
6th
ISBN13:

9780534936242

ISBN10:
0534936245
Format:
Paperback
Pub. Date:
9/25/1996
Publisher(s):
Brooks Cole
List Price: $142.33
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Summary

This is a simple, straightforward, direct calculus text. Historical strengths rest in the broad use of applications, the easy-to-understand writing style, and the wealth of examples and exercises to reinforce conceptualization of the subject matter. The inclusion of two (new) co-authors should pique interest in a book that in its heyday was the #1 best-seller. With Olinick's handle on applications (he has written a successful modeling book) and Pence's keen sense of technology (he is a guru on the HP and TI graphing calculators), we feel we have put together an unparalleled team of experts.

Table of Contents

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)
Quadratic Expressions and Miscellaneous Substitutions
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
Answers to Selected Exercises A24
Index A97


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