Vector Calculus,9780716749929

Vector Calculus

by ;
Edition: 5th
ISBN13: 9780716749929
ISBN10: 0716749920
Format: Hardcover
Pub. Date: 2003-08-01
Publisher(s): W. H. Freeman
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Summary

Now in its "Fifth Edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing its readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

Table of Contents

Preface vii
Historical Introduction xiii
The Geometry of Euclidean Space
1(93)
Vectors in Two- and Three-Dimensional Space
1(22)
The Inner Product, Length, and Distance
23(15)
Matrices, Determinants, and the Cross Product
38(27)
Cylindrical and Spherical Coordinates
65(9)
n-Dimensional Euclidean Space
74(20)
Review Exercises for Chapter 1
88(6)
Differentiation
94(87)
The Geometry of Real-Valued Functions
94(13)
Limits and Continuity
107(20)
Differentiation
127(14)
Introduction to Paths and Curves
141(9)
Properties of the Derivative
150(13)
Gradients and Directional Derivatives
163(18)
Review Exercises for Chapter 2
173(8)
Higher-Order Derivatives; Maxima and Minima
181(80)
Iterated Partial Derivatives
182(11)
Taylor's Theorem
193(10)
Extrema of Real-Valued Functions
203(22)
Constrained Extrema and Lagrange Multipliers
225(21)
The Implicit Function Theorem
246(15)
Review Exercises for Chapter 3
255(6)
Vector-Valued Functions
261(56)
Acceleration and Newton's Second Law
261(13)
Arc Length
274(11)
Vector Fields
285(9)
Divergence and Curl
294(23)
Review Exercises for Chapter 4
313(4)
Double and Triple Integrals
317(51)
Introduction
317(10)
The Double Integral Over a Rectangle
327(14)
The Double Integral Over More General Regions
341(8)
Changing the Order of Integration
349(5)
The Triple Integral
354(14)
Review Exercises for Chapter 5
365(3)
The Change of Variables Formula and Applications of Integration
368(53)
The Geometry of Maps from R2 to R2
369(7)
The Change of Variables Theorem
376(17)
Applications
393(13)
Improper Integrals
406(15)
Review Exercises for Chapter 6
417(4)
Integrals Over Paths and Surfaces
421(97)
The Path Integral
421(8)
Line Integrals
429(22)
Parametrized Surfaces
451(10)
Area of a Surface
461(13)
Integrals of Scalar Functions Over Surfaces
474(9)
Surface Integrals of Vector Fields
483(17)
Applications to Differential Geometry, Physics, and Forms of Life
500(18)
Review Exercises for Chapter 7
514(4)
The Integral Theorems of Vector Analysis
518(91)
Green's Theorem
518(14)
Stokes' Theorem
532(18)
Conservative Fields
550(11)
Gauss' Theorem
561(15)
Some Differential Equations of Mechanics and Technology
576(12)
Differential Forms
588(21)
Review Exercises for Chapter 8
605(4)
Answers to Odd-Numbered Exercises 609(59)
Index 668(8)
Illustration Credits 676

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