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Vector Calculus

by: Marsden, Jerrold E.; Tromba, Anthony

Vector Calculus

by: Marsden, Jerrold E.; Tromba, Anthony

ISBN 13:
9780716749929
ISBN 10:
0716749920
Edition: 5th
Format: Hardcover
Copyright: 08/01/2003
Publisher: 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.

Preface

vii

Historical Introduction

xiii

The Geometry of Euclidean Space

(93)

Vectors in Two- and Three-Dimensional Space

(22)

The Inner Product, Length, and Distance

(15)

Matrices, Determinants, and the Cross Product

(27)

Cylindrical and Spherical Coordinates

(9)

n-Dimensional Euclidean Space

(20)

Review Exercises for Chapter 1

(6)

Differentiation

(87)

The Geometry of Real-Valued Functions

(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

Amazon no longer offers textbook rentals. We do!

Vector Calculus

Vector Calculus

9780716749929

0716749920

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Vector Calculus

Vector Calculus

9780716749929

0716749920

Summary

Table of Contents

Supplemental Materials

Write a Review

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