Multivariable Calculus (with Tools for Enriching Calculus, Video Skillbuilder CD-ROM, iLrn™ Homework, and Personal Tutor)

by Stewart, James

• ISBN13: 9780534393571
• ISBN10: 0534393578
• Edition: 5th
• Format: Hardcover
• Copyright: 2002-12-26
• Publisher: Brooks Cole

Summary

Stewart's CALCULUS, Fifth Edition has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. Stewart retains the focus on problem solving and the pedagogical system that has made the book a favorite of students and instructors in a wide variety of colleges and universities throughout the world. In this Fifth Edition, he has made hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and references to the TEC CD (Tools for Enriching Calculus). These refinements ensure that students and instructors have the best materials available. The number of pages in the book, however, remains unchanged from the 4th edition. Further support for students and instructors is now available through a vast array of supplementary material.

Table of Contents

Preface	vii
Parametric Equations and Polar Coordinates	686	(50)
Curves Defined by Parametric Equations	687	(9)
Laboratory Project Running Circles around Circles	695	(1)
Calculus with Parametric Curves	696	(9)
Laboratory Project Bezier Curves	705	(1)
Polar Coordinates	705	(10)
Areas and Lengths in Polar Coordinates	715	(5)
Conic Sections	720	(8)
Conic Sections in Polar Coordinates	728	(8)
Review	732	(3)
Problems Plus	735	(1)
Infinite Sequences and Series	736	(92)
Sequences	737	(12)
Laboratory Project Logistic Sequences	749	(1)
Series	749	(10)
The Integral Test and Estimates of Sums	759	(7)
The Comparison Tests	766	(5)
Alternating Series	771	(5)
Absolute Convergence and the Ratio and Root Tests	776	(7)
Strategy for Testing Series	783	(2)
Power Series	785	(5)
Representations of Functions as Power Series	790	(6)
Taylor and Maclaurin Series	796	(12)
Laboratory Project An Elusive Limit	808	(1)
The Binomial Series	808	(4)
Writing Project How Newton Discovered the Binomial Series	812	(1)
Applications of Taylor Polynomials	812	(16)
Applied Project Radiation from the Stars	875
Review	822	(3)
Problems Plus	825	(3)
Vectors and the Geometry of Space	828	(56)
Three-Dimensional Coordinate Systems	829	(5)
Vectors	834	(9)
The Dot Product	843	(7)
The Cross Product	850	(8)
Discovery Project The Geometry of a Tetrahedron	858	(1)
Equations of Lines and Planes	858	(10)
Laboratory Project Putting 3D in Perspective	868	(1)
Cylinders and Quadric Surfaces	868	(7)
Cylindrical and Spherical Coordinates	875	(9)
Laboratory Project Families of Surfaces	880	(1)
Review	880	(3)
Problems Plus	883	(1)
Vector Functions	884	(38)
Vector Functions and Space Curves	885	(7)
Derivatives and Integrals of Vector Functions	892	(6)
Arc Length and Curvature	898	(8)
Motion in Space: Velocity and Acceleration	906	(16)
Applied Project Kepler's Laws	916	(1)
Review	917	(3)
Problems Plus	920	(2)
Partial Derivatives	922	(94)
Functions of Several Variables	923	(15)
Limits and Continuity	938	(7)
Partial Derivatives	945	(14)
Tangent Planes and Linear Approximations	959	(8)
The Chain Rule	967	(9)
Directional Derivatives and the Gradient Vector	976	(13)
Maximum and Minimum Values	989	(12)
Applied Project Designing a Dumpster	999	(1)
Discovery Project Quadratic Approximations and Critical Points	1000	(1)
Lagrange Multipliers	1001	(15)
Applied Project Rocket Science	1008	(1)
Applied Project Hydro-Turbine Optimization	1009	(1)
Review	1010	(4)
Problems Plus	1014	(2)
Multiple Integrals	1016	(74)
Double Integrals over Rectangles	1017	(8)
Iterated Integrals	1025	(6)
Double Integrals over General Regions	1031	(8)
Double Integrals in Polar Coordinates	1039	(6)
Applications of Double Integrals	1045	(10)
Surface Area	1055	(4)
Triple Integrals	1059	(10)
Discovery Project Volumes of Hyperspheres	1068	(1)
Triple Integrals in Cylindrical and Spherical Coordinates	1069	(8)
Applied Project Roller Derby	1075	(1)
Discovery Project The Intersection of Three Cylinders	1076	(1)
Change of Variables in Multiple Integrals	1077	(13)
Review	1085	(3)
Problems Plus	1088	(2)
Vector Calculus	1090	(86)
Vector Fields	1091	(7)
Line Integrals	1098	(12)
The Fundamental Theorem for Line Integrals	1110	(9)
Green's Theorem	1119	(7)
Curl and Divergence	1126	(8)
Parametric Surfaces and Their Areas	1134	(11)
Surface Integrals	1145	(12)
Stokes' Theorem	1157	(6)
Writing Project Three Men and Two Theorems	1162	(1)
The Divergence Theorem	1163	(7)
Summary	1170	(6)
Review	1171	(3)
Problems Plus	1174	(2)
Second-Order Differential Equations	1176	(1)
Second-Order Linear Equations	1177	(6)
Nonhomogeneous Linear Equations	1183	(8)
Applications of Second-Order Differential Equations	1191	(8)
Series Solutions	1199	(4)
Review	1203
Appendixes	1	(42)
F Proofs of Theorems	2	(3)
G Complex Numbers	5	(8)
H Answers to Odd-Numbered Exercises	13	(30)
Index	43