Calculus, 3rd Edition, Single and Multivariable, 3rd Edition

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

• ISBN13: 9780471408277
• ISBN10: 0471408271
• Edition: 3rd
• Format: Hardcover
• Copyright: 2001-09-01
• Publisher: Wiley

Summary

The Third Edition of CALCULUS reflects the strong consensus within the mathematics community for a new balance between the contemporary ideas of the original editions of this book and ideas and topics from earlier calculus books. Building on previous work, this Third Edition has the same philosophy as earlier editions but represents a new balance of topics. CALCULUS 3/e brings together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful to students going into mathematics and those going into the sciences and engineering. The authors believe the new edition will work well for those departments who are looking for a calculus book that offers a middle ground for their calculus instructors.CALCULUS 3/e 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)
Logrithmic 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 Functions	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 Functions	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)
Algebric 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)
Functions of Several Variables	559	(46)
Functions of Two Variables	560	(7)
Graphs of Functions of Two Variables	567	(8)
Contour Diagrams	575	(10)
Linear Functions	585	(6)
Functions of Three Variables	591	(4)
Limits and Continuity	595	(10)
Review Problems	600	(2)
Check Your Understanding	602	(1)
Projects	603	(2)
A Fundamental Tool: Vectors	605	(34)
Displacement Vectors	606	(8)
Vectors in General	614	(6)
The Dot Product	620	(9)
The Cross Product	629	(10)
Review Problems	635	(2)
Check Your Understanding	637	(1)
Projects	638	(1)
Differentiating Functions of Several Variables	639	(62)
The Partial Derivative	640	(7)
Computing Partial Derivatives Algebraically	647	(4)
Local Linearity and the Differential	651	(7)
Gradients and Directional Derivatives in the Plane	658	(8)
Gradients and Directional Derivatives in Space	666	(6)
The Chain Rule	672	(9)
Second-Order Partial Derivatives	681	(8)
Differentiability	689	(12)
Review Problems	695	(3)
Check Your Understanding	698	(1)
Projects	699	(2)
Optimization: Local and Global Extrema	701	(34)
Local Extrema	702	(8)
Optimization	710	(8)
Constrained Optimization: Lagrange Multipliers	718	(17)
Review Problems	728	(4)
Check Your Understanding	732	(1)
Projects	732	(3)
Integrating Functions of Several Variables	735	(48)
The Definite Integral of a Function of Two Variables	736	(7)
Integrated Integrals	743	(8)
Triple Integrals	751	(5)
Double Integrals in Polar Coordinates	756	(4)
Integrals in Cylinderical and Spherical Coordinates	760	(9)
Applications of Integration to Probability	769	(5)
Change of Variables in a Multiple Integral	774	(9)
Review Problems	777	(3)
Check Your Understanding	780	(1)
Projects	781	(2)
Parameterization and Vector Fields	783	(42)
Parameterized Curves	784	(7)
Motion, Velocity, and Acceleration	791	(8)
Vector Fields	799	(5)
The Flow of a Vector Field	804	(5)
Parameterized Surfaces	809	(16)
Review Problems	819	(3)
Check Your Understanding	822	(1)
Projects	823	(2)
Line Integrals	825	(38)
The Idea of a Line Integral	826	(8)
Computing Line Integrals over Parameterized Curves	834	(5)
Gradient Fields and Path-Independent Fields	839	(9)
Path-Dependent Vector Fields and Green's Theorem	848	(15)
Review Problems	857	(3)
Check Your Understanding	860	(1)
Projects	861	(2)
Flux Integrals	863	(24)
The Idea of a Flux Integral	864	(8)
Flux Integrals for Graphs, Cylinders, and Spheres	872	(7)
Flux Integrals over Parameterized Surfaces	879	(8)
Review Problems	882	(2)
Check Your Understanding	884	(1)
Projects	884	(3)
Calculus of Vector Fields	887	(64)
The Divergence of a Vector Field	888	(7)
The Divergence Theorem	895	(6)
The Curl of a Vector Field	901	(8)
Stokes' Theorem	909	(6)
The Three Fundamental Theorems	915	(13)
Review Problems	919	(4)
Check Your Understanding	923	(1)
Projects	924	(4)
APPENDIX
A Roots, Accuracy, and Bounds	928	(8)
B Polar Coordinates	936	(2)
C Complex Numbers	938	(7)
D Newton's Method	945	(3)
E Determinants	948	(3)
Ready Reference	951	(16)
Answers to Odd Numbered Problems	967	(26)
Index	993