Calculus: Single Variable, 4th Edition

by Deborah Hughes-Hallett (Univ. of Arizona); Andrew M. Gleason (Harvard University ); William G. McCallum (Univ. of Arizona); Daniel E. Flath (Macalester College ); Patti Frazer Lock (St. Lawrence Univ.); David O. Lomen (Univ. of Arizona); David Lovelo

• ISBN13: 9780471484813
• ISBN10: 0471484814
• Edition: 4th
• Format: Hardcover
• Copyright: 2004-11-01
• Publisher: WILEY

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