Calculus: Single Variable, 4th Edition,9780471484813

Calculus: Single Variable, 4th Edition

by ; ; ; ; ; ;
Edition: 4th
ISBN13: 9780471484813
ISBN10: 0471484814
Format: Hardcover
Pub. Date: 2004-11-01
Publisher(s): WILEY
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Summary

Now in its fourth edition,Calculus reflects the strong consensus within the mathematics community for a balance between contemporary and traditional ideas. Building on previous work, it brings together the best of both new and traditional curricula in an effort to meet the needs of instructors and students alike. The text exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that is easy to understand, and a flexible approach to technology.

Table of Contents

A Library of Functions
1(64)
Functions and Change
2(7)
Exponential Functions
9(8)
New Functions From Old
17(6)
Logarithmic Functions
23(6)
Trigonometric Functions
29(8)
Powers, Polynomials, and Rational Functions
37(7)
Introduction to Continuity
44(4)
Limits
48(17)
Review Problems
58(4)
Check Your Understanding
62(2)
Projects
64(1)
Key Concept: The Derivative
65(44)
How Do We Measure Speed?
66(6)
The Derivative at a Point
72(8)
The Derivative Function
80(8)
Interpretations of the Derivative
88(5)
The Second Derivative
93(6)
Differentiability
99(10)
Review Problems
103(3)
Check Your Understanding
106(1)
Projects
107(2)
Short-Cuts to Differentiation
109(56)
Powers and Polynomials
110(7)
The Exponential Function
117(4)
The Product and Quotient Rules
121(6)
The Chain Rule
127(6)
The Trigonometric Functions
133(5)
The Chain Rule and Inverse Functions
138(5)
Implicit Functions
143(3)
Hyperbolic Functions
146(4)
Linear Approximation and the Derivative
150(5)
Theorems About Differentiable Functions
155(10)
Review Problems
159(4)
Check Your Understanding
163(1)
Projects
164(1)
Using the Derivative
165(74)
Using First and Second Derivatives
166(9)
Families of Curves
175(6)
Optimization
181(9)
Applications to Marginality
190(8)
Optimization and Modeling
198(8)
Rates and Related Rates
206(8)
L'Hopital's Rule, Growth, and Dominance
214(5)
Parametric Equations
219(20)
Review Problems
229(5)
Check Your Understanding
234(1)
Projects
235(4)
Key Concept: The Definite Integral
239(42)
How Do We Measure Distance Traveled?
240(8)
The Definite Integral
248(7)
The Fundamental Theorem and Interpretations
255(9)
Theorems About Definite Integrals
264(17)
Review Problems
272(6)
Check Your Understanding
278(1)
Projects
279(2)
Constructing Antiderivatives
281(30)
Antiderivatives Graphically and Numerically
282(6)
Constructing Antiderivatives Analytically
288(5)
Differential Equations
293(6)
Second Fundamental Theorem of Calculus
299(4)
The Equations of Motion
303(8)
Review Problems
306(3)
Check Your Understanding
309(1)
Projects
310(1)
Integration
311(56)
Integration by Substitution
312(8)
Integration by Parts
320(6)
Tables of Integrals
326(5)
Algebraic Identities and Trigonometric Substitutions
331(8)
Approximating Definite Integrals
339(5)
Approximation Errors and Simpson's Rule
344(4)
Improper Integrals
348(8)
Comparison of Improper Integrals
356(11)
Review Problems
361(3)
Check Your Understanding
364(1)
Projects
365(2)
Using the Definite Integral
367(70)
Areas and Volumes
368(6)
Applications to Geometry
374(8)
Area and Arc Length in Polar Coordinates
382(8)
Density and Center of Mass
390(9)
Applications to Physics
399(9)
Applications to Economics
408(6)
Distribution Functions
414(7)
Probability, Mean, and Median
421(16)
Review Problems
428(5)
Check Your Understanding
433(2)
Projects
435(2)
Sequences and Series
437(40)
Sequences
438(6)
Geometric Series
444(6)
Convergence of Series
450(5)
Tests for Convergence
455(8)
Power Series and Interval of Convergence
463(14)
Review Problems
471(3)
Check Your Understanding
474(1)
Projects
475(2)
Approximating Functions Using Series
477(44)
Taylor Polynomials
478(7)
Taylor Series
485(5)
Finding and Using Taylor Series
490(7)
The Error in Taylor Polynomial Approximations
497(5)
Fourier Series
502(19)
Review Problems
514(3)
Check Your Understanding
517(1)
Projects
518(3)
Differential Equations
521(82)
What is a Differential Equation?
522(4)
Slope Fields
526(6)
Euler's Method
532(3)
Separation of Variables
535(5)
Growth and Decay
540(9)
Applications and Modeling
549(9)
Models of Population Growth
558(8)
Systems of Differential Equations
566(9)
Analyzing the Phase Plane
575(5)
Second-Order Differential Equations: Oscillations
580(7)
Linear Second-Order Differential Equations
587(16)
Review Problems
595(4)
Check Your Understanding
599(1)
Projects
600(3)
APPENDIX
603(20)
A Roots, Accuracy, and Bounds
604(8)
B Complex Numbers
612(7)
C Newton's Method
619(4)
READY REFERENCE
623(11)
Ready Reference
624(10)
Answers to Odd Numbered Problems 634(31)
Index 665

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