Calculus, 3rd Edition, Multivariable, 3rd Edition

by William G. McCallum (Univ. of Arizona); Daniel E. Flath (Univ. of South Alabama); Andrew M. Gleason (Harvard Univ.); Sheldon P. Gordon (SUNY at Farmingdale); Patti Frazer Lock (St. Lawrence Univ.); David Mumford (Brown Univ.); Deborah Hughes-Hallett

• ISBN13: 9780471409526
• ISBN10: 0471409529
• Edition: 3rd
• Format: Paperback
• Copyright: 2002-01-01
• 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

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)
Iterated Integrals	743	(8)
Triple Integrals	751	(5)
Double Integrals in Polar Coordinates	756	(4)
Integrals in Cylindrical 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	(40)
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	(12)
Review Problems	919	(4)
Check Your Understanding	923	(1)
Projects	924	(3)
APPENDIX	927	(24)
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	(8)
Answers to Odd Numbered Problems	959	(10)
Index	969