Vector Calculus 6ed, Marsden.pdf

发布时间：2022-06-19 发布人：admin 分类：说明书资料大小：27.65M 资料格式：pdf 举报版权申诉

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第1页.png

第1页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第2页.png

第2页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第3页.png

第3页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第4页.png

第4页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第5页.png

第5页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第6页.png

第6页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第7页.png

第7页 / 共578页

be1569fc-1e08-4ca5-827b-5618456ea30e.pdf-第8页.png

第8页 / 共578页

Cover Page

Title Page

Contents

Preface

Acknowledgements

Historical Introduction: A Brief Acco

Prerequisites and Notation

1 The Geometry of Euclidean Space

1.1 Vectors in Two- and Three-Dimensional Space

1.2 The Inner Product, Length, and Distance

1.3 Matrices, Determinants, and the Cross Product

1.4 Cylindrical and Spherical Coordinates

1.5 n-Dimensional Euclidean Space

Review Exercises for Chapter 1

2 Differentiation

2.1 The Geometry of Real-Valued Functions

2.2 Limits and Continuity

2.3 Differentiation

2.4 Introduction to Paths and Curves

2.5 Properties of the Derivative

2.6 Gradients and Directional Derivatives

Review Exercises for Chapter 2

3 Higher-Order Derivatives: Maxima and Minima

3.1 Iterated Partial Derivatives

3.2 Taylor’s Theorem

3.3 Extrema of Real-Valued Functions

3.4 Constrained Extrema and Lagrange Multipliers

3.5 The Implicit Function Theorem [Optional]

Review Exercises for Chapter 3

4 Vector-Valued Functions

4.1 Acceleration and Newton’s Second Law

4.2 Arc Length

4.3 Vector Fields

4.4 Divergence and Curl

Review Exercises for Chapter 4

5 Double and Triple Integrals

5.1 Introduction

5.2 The Double Integral Over a Rectangle

5.3 The Double Integral Over More General Regions

5.4 Changing the Order of Integration

5.5 The Triple Integral

Review Exercises for Chapter 5

6 The Change of Variables Formula and Applications of Integration

6.1 The Geometry of Maps from R2 to R2

6.2 The Change of Variables Theorem

6.3 Applications

6.4 Improper Integrals [Optional]

Review Exercises for Chapter 6

7 Integrals Over Paths and Surfaces

7.1 The Path Integral

7.2 Line Integrals

7.3 Parametrized Surfaces

7.4 Area of a Surface

7.5 Integrals of Scalar Functions Over Surfaces

7.6 Surface Integrals of Vector Fields

7.7 Applications to Differential Geometry, Physics, and Forms of Life

Review Exercises for Chapter 7

8 The Integral Theorems of Vector Analysis

8.1 Green’s Theorem

8.2 Stokes’ Theorem

8.3 Conservative Fields

8.4 Gauss’ Theorem

8.5 Differential Forms

Review Exercises for Chapter 8

Answers to Odd-Numbered Exercises

Index

Photo Credits

Marsden-3620111 VC˙FM September 27, 2011 9:49 i SIXTH EDITION Jerrold E. Marsden California Institute of Technology, Pasadena Anthony Tromba University of California, Santa Cruz W. H. Freeman and Company · New York

Marsden-3620111 VC˙FM September 27, 2011 9:49 ii Publisher: Ruth Baruth Executive Editor: Terri Ward Executive Marketing Manager: Jennifer Somerville Associate Editor: Katrina Wilhelm Senior Media Editor: Laura Capuano Editorial Assistant: Tyler Holzer Project Editor: Vivien Weiss Art Director: Diana Blume Director of Production: Ellen Cash Illustration Coordinator: Bill Page Illustrations: Network Graphics Photo Editor: Ted Szczepanski Compositor: MPS Limited, a Macmillan Company Manufacturer: Quad Graphics Cover Image: Robert Wilson Politics is for the moment. An equation is for eternity. A. EINSTEIN Some calculus tricks are quite easy. Some are enormously difﬁcult. The fools who write the textbooks of advanced mathematics seldom take the trouble to show you how easy the easy calculations are. SILVANUS P. THOMPSON, CALCULUS MADE EASY, MACMILLAN (1910) Library of Congress Control Number: 2011931725 ISBN-13: 978-1-4292-1508-4 ISBN-10: 1-4292-1508-9 c2012, 2003, 1996, 1988, 1981, 1976 by W. H. Freeman and Company All rights reserved. Printed in the United States of America First printing W. H. Freeman and Company Publishers 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com

Marsden-3620111 VC˙FM September 27, 2011 9:49 iii Contents Preface ix Acknowledgements xi Historical Introduction: A Brief Account xiii Prerequisites and Notation xxiii 1 The Geometry of Euclidean Space 1 1.1 Vectors in Two- and Three-Dimensional Space 1 1.2 The Inner Product, Length, and Distance 19 1.3 Matrices, Determinants, and the Cross Product 1.4 Cylindrical and Spherical Coordinates 1.5 n-Dimensional Euclidean Space 60 52 31 Review Exercises for Chapter 1 70 2 Differentiation 75 88 2.1 The Geometry of Real-Valued Functions 2.2 Limits and Continuity 2.3 Differentiation 105 2.4 Introduction to Paths and Curves 2.5 Properties of the Derivative 124 2.6 Gradients and Directional Derivatives 116 76 135 Review Exercises for Chapter 2 144 3 Higher-Order Derivatives: Maxima and Minima 149 150 3.1 Iterated Partial Derivatives 3.2 Taylor’s Theorem 158 3.3 Extrema of Real-Valued Functions 3.4 Constrained Extrema and Lagrange Multipliers 3.5 The Implicit Function Theorem [Optional] 166 203 Review Exercises for Chapter 3 211 185 iii

Marsden-3620111 VC˙FM September 27, 2011 9:49 iv iv Contents 4 Vector-Valued Functions 217 4.1 Acceleration and Newton’s Second Law 217 4.2 Arc Length 228 4.3 Vector Fields 4.4 Divergence and Curl 245 236 Review Exercises for Chapter 4 260 5 Double and Triple Integrals 263 5.1 Introduction 263 5.2 The Double Integral Over a Rectangle 271 5.3 The Double Integral Over More General Regions 5.4 Changing the Order of Integration 289 5.5 The Triple Integral 294 283 Review Exercises for Chapter 5 304 6 The Change of Variables Formula and Applications of Integration 307 6.1 The Geometry of Maps from R2 to R2 6.2 The Change of Variables Theorem 314 6.3 Applications 6.4 Improper Integrals [Optional] 329 339 308 Review Exercises for Chapter 6 347 7 Integrals Over Paths and Surfaces 351 358 351 7.1 The Path Integral 7.2 Line Integrals 7.3 Parametrized Surfaces 7.4 Area of a Surface 383 7.5 Integrals of Scalar Functions Over Surfaces 7.6 Surface Integrals of Vector Fields 7.7 Applications to Differential Geometry, Physics, 375 400 393 and Forms of Life 413 Review Exercises for Chapter 7 423

Marsden-3620111 VC˙FM September 27, 2011 9:49 v 8 The Integral Theorems of Vector Analysis 427 Contents v 8.1 Green’s Theorem 428 8.2 Stokes’ Theorem 439 8.3 Conservative Fields 8.4 Gauss’ Theorem 461 8.5 Differential Forms 476 453 Review Exercises for Chapter 8 490 Answers to Odd-Numbered Exercises 493 Index 533 Photo Credits 545

Marsden-3620111 VC˙FM September 27, 2011 9:49 vi this page left intentionally blank

Marsden-3620111 VC˙FM September 27, 2011 9:49 vii To Jerrold E. Marsden, 1942--2010 Jerry Marsden, Carl F. Braun distinguished Professor at the California Institute of Technology, Fellow of the Royal Society (as was Isaac Newton), and one of the world’s pre-eminent applied mathematicians, passed away on September 21, 2010, while working on the sixth edition of Vector Calculus. Jerry’s interests were unusually broad; his work inﬂuenced physicists, engineers, life scientists, and mathematicians across the scientiﬁc and engineering spectrum. In addition to his many publications (over 400 archival and conference papers and 21 books) and major scientiﬁc prizes, he was a brilliant expositor and teacher. He motivated and encouraged colleagues and students alike, around the world and across an astonishing array of disciplines. He was a wonderful person and a close friend for almost half a century. He will be sorely missed. —Anthony Tromba

分享到：

赞收藏

资料库

Vector Calculus 6ed, Marsden.pdf

相关推荐

人工智能

热门标签

最新资料