Calculus, 3rd Edition, Single Variable, 3rd Edition,9780471408253

Calculus, 3rd Edition, Single Variable, 3rd Edition

by ; ; ; ; ; ;
Edition: 3rd
ISBN13: 9780471408253
ISBN10: 0471408255
Format: Hardcover
Pub. Date: 2001-07-01
Publisher(s): Wiley
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Summary

The new edition exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.

Table of Contents

A Library of Functions
1(54)
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(8)
Introduction to Continuity
45(10)
Review Problems
48(4)
Check Your Understanding
52(2)
Projects
54(1)
Key Concept: The Derivative
55(50)
How do We Measure Speed?
56(6)
Limits
62(8)
The Derivative at a Point
70(8)
The Derivative Function
78(7)
Interpretations of the Derivative
85(4)
The Second Derivative
89(6)
Continuity and Differentiability
95(10)
Review Problems
99(4)
Check Your Understanding
103(1)
Projects
104(1)
Short-Cuts to Differentiation
105(60)
Powers and Polynomials
106(7)
The Exponential Function
113(5)
The Product and Quotient Rules
118(5)
The Chain Rule
123(5)
The Trigonometric Functions
128(5)
Applications of the Chain Rule
133(5)
Implicit Functions
138(3)
Parametric Equations
141(9)
Linear Approximation and the Derivative
150(4)
Using Local Linearity to Find Limits
154(11)
Review Problems
159(3)
Check Your Understanding
162(1)
Projects
163(2)
Using the Derivative
165(56)
Using First and Second Derivatives
166(10)
Families of Curves
176(4)
Optimization
180(9)
Applications to Marginality
189(7)
Optimization and Modeling
196(7)
Hyperbolic Functions
203(4)
Theorems About Continuous and Differentiable Functions
207(14)
Review Problems
212(4)
Check Your Understanding
216(1)
Projects
217(4)
Key Concept: The Definite Integral
221(40)
How Do We Measure Distance Traveled?
222(7)
The Definite Integral
229(7)
Interpretations of the Definite Integral
236(8)
Theorems About Definite Integrals
244(17)
Review Problems
252(5)
Check Your Understanding
257(1)
Projects
258(3)
Constructing Antiderivatives
261(28)
Antiderivatives Graphically and Numerically
262(6)
Constructing Antiderivatives Analytically
268(5)
Differential Equations
273(5)
Second Fundamental Theorem of Calculus
278(4)
The Equations of Motion
282(7)
Review Problems
284(3)
Check Your Understanding
287(1)
Projects
288(1)
Integration
289(56)
Integration by Substitution
290(8)
Integration by Parts
298(6)
Tables of Integrals
304(5)
Algebraic Identities and Trigonometric Substitutions
309(8)
Approximating Definite Integrals
317(5)
Approximation Errors and Simpson's Rule
322(4)
Improper Integrals
326(8)
Comparison of Improper Integrals
334(11)
Review Problems
338(4)
Check Your Understanding
342(1)
Projects
343(2)
Using the Definite Integral
345(60)
Areas and Volumes
346(6)
Applications to Geometry
352(8)
Density and Center of Mass
360(8)
Applications to Physics
368(9)
Applications to Economics
377(6)
Distribution Functions
383(7)
Probability, Mean, and Median
390(15)
Review Problems
397(4)
Check Your Understanding
401(1)
Projects
402(3)
Series
405(28)
Geometric Series
406(6)
Convergence of Sequences and Series
412(5)
Tests for Convergence
417(6)
Power Series
423(10)
Review Problems
429(2)
Check Your Understanding
431(1)
Projects
431(2)
Approximating Functions
433(44)
Taylor Polynomials
434(7)
Taylor Series
441(5)
Finding and Using Taylor Series
446(7)
The Error in Taylor Polynomial Approximations
453(4)
Fourier Series
457(20)
Review Problems
470(3)
Check Your Understanding
473(1)
Projects
474(3)
Differential Equations
477(82)
What is a Differential Equation?
478(4)
Slope Fields
482(6)
Euler's Method
488(4)
Separation of Variables
492(5)
Growth and Decay
497(9)
Applications and Modeling
506(8)
Models of Population Growth
514(9)
Systems of Differential Equations
523(9)
Analyzing the Phase Plane
532(5)
Second-Order Differential Equations: Oscillations
537(7)
Linear Second-Order Differential Equations
544(15)
Review Problems
552(3)
Check Your Understanding
555(1)
Projects
556(3)
APPENDIX 559(22)
A Roots, Accuracy, and Bounds
560(8)
B Polar Coordinates
568(2)
C Complex Numbers
570(7)
D Newton's Method
577(4)
Ready Reference 581(17)
Answers to Odd Numbered Problems 598(17)
Index 615

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