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

by Deborah Hughes-Hallett (Univ. of Arizona); Andrew M. Gleason (Harvard Univ.); Daniel E. Flath (Univ. of South Alabama); Patti Frazer Lock (St. Lawrence Univ.); Sheldon P. Gordon (SUNY at Framingdale); David O. Lomen (Univ. of Arizona); David Lovelock

• ISBN13: 9780471408253
• ISBN10: 0471408255
• Edition: 3rd
• Format: Hardcover
• Copyright: 2001-07-01
• Publisher: Wiley

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