vector calculus 6th edition by Jerrold E. Marsden and Anthony Tromba

【实例简介】
向量微积分经典教材第六版影印版。vector calculus 6th edition by Jerrold E. Marsden and Anthony Tromba。全文593页。
chegg Copyright o W.H. Freeman Vector calculus Edition: Publisher,: Ruth Baruth jimmy Executive editor. Terri ward Printed 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 Ilustration coordinator. bill page Illustrations: Network Graphics Photo Editor: Ted Szczepanski Compositor: MPS Linited, a Macmillan Cuinpanly Manufacturer Quad graphics chegg Cover/mage. Robert wilson Copyright (c W. H. Freeman Vector calculus Edition: 6 Politics is for the moment iimmybo2@gmail.com An equation is for eternity Printedfromwww.chegg.com A EINSTEIN Some calculus tricks are quite easy Suine are enormously difficulL. The fool 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 cheo Copyrig isbn-13:978-1-4292-1508-4 Vector CIsBN-10:1-4292-1508-9 Edition: 6 immyb (2012, 2003, 1996, 1988, 1981, 1976 by W H. Freeman and Company Printedfromwww.chegg.com All rights reserved Printed in the united stales of america First printin W H. Freeman and Company Publishers 41 Madison avenue New York. NY 10010 Houndmills, Basingstoke RG21 6XS, England wwwwhfreeman.com chegg Copyright o W.H. Freeman Vector calculus Edition: 6 jimmybo2@gmail.com Printedtromwww.chegg.co chegg Copyright o W.H. Freeman Vector calculus Edition: 6 jimmybo2@dmail Printed from Contents Prefaceⅸ Acknowledgements xi Historical introduction :a Brief account xiii Prerequisites and Notation xXii 1 The Geometry of Euclidean Space chegg 1.1 Vectors in Two-and Three-Dimensional Space t l calculus, reeman 1.2 The Inner Product, Length, and Distance 19 ton.b 1.3MatricesDeterminantsandtheCrossPraductte31omwww.chegg.com 1. 4 Cylindrical and spherical coordinates 52 1.5 n-Dimensional Euclidean Space 60 Review Exercises for Chapter 1 70 2 Differentiation 75 2.1 The Geometry of Real-Valued Functions 76 2.2 Limits and Continuity 88 2. 3 Differentiation 105 chegg 2.4 Introduction to paths and curves 116 Copyright (o W. H. Freeman Vector calculus 2.5 Properties of the Derivative 124 Edition: 6 iimmybo2@gmail.com 2.6 Gradients and Directional Derivatives 13.5 Printedfromwww.chegg.com Review EXercises for Chapter 2 144 3 Higher-Order Derivatives Maxima and minima 149 3. Iterated partial Derivatives 50 3.2 Taylor's Theorem 158 3.3 Extrema of Real-valued functions 166 3.4 Constrained Extrema and Lagrange Multipliers 185 3.5 The Implicit Function Theorem(Optional) 203 right o W.H. Freeman Review Exercises for Chopter 3 211 Vector calculus Edition: 6 jimmybo2@gmail.com PrintedTromwww.ciegg.col chOgo Copyright o W.H. Freeman Vector calculus Edition: 6 iimmybo2@ gmail.cor 4 Vector-Valued Functions 217 Printedfromwww.chegg.com 4. Acceleration and Newtons second law 217 4.2 ArC Length 228 4.3 Vector fields 236 4.4 Divergence and Curl 245 Review Exercises for Chapter 4 260 5 Double and Triple Integrals 263 5.1 Introduction 263 chegg 5.2 The Double Integral Over a Rectangle 271 Copyright C W.H. Freeman Vector calculus 5.3 The Double Integral Over More General Regions 6 immybo2@gmail 5. 4 Changing the Order of Integration 289 Printedfromwww.chegg.com 5.5 The Triple Integral 294 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 R2308 6.2 The Change of Variables Theorem 314 chegg 6.3 Applications 329 6.4 Improper Integrals [Optional) 339 Copyright (o W. H. Freeman Vector calculus Review Exercises for Chapter 6 347 Edition: 6 iimmybo2@gmail.com Printedfromwww.chegg.com 7 Integrals Over Paths and Surfaces 35 1 7.1 The Path Integral 351 7.2 Line Integrals 7.3 Parametrized surfaces 375 7.4 Area of a surface 383 7.5 Integrals of Scalar Functions Over Surfaces 393 7.6 Surface Integrals of Vector Fields 400 7.7 Applications to Diferential Geometry, Physics, Chegg and forms of life 413 Copyright o W.H. Freeman Review Exercises for Chapter 7 423 Vector calculus Edition: 6 jimmybo2@gmail.com Printedtromwww.chegg.co chegg Copyright o W.H. Freeman Vector calculus Edition: 6 iimmybo2@ gmail.cor 8 The Integral Theorems of Vector Analysis 427 Printedfromwww.chegg.com 8.1 Greens Theorem 428 8.2 Stokes Theorem 439 8.3 Conservative fields 453 8. 4 Gauss Theorem 461 8.5 Differential Forms 476 Review Exercises for Chapter 8 490 Answers to odd-Numbered exercises 493 chegg Index 533 Copyright W. H. Freeman Vector calculus Photo credits 545 Edition: 6 2@gmail Printedfromwww.chegg.com chegg Copyright (o W. H. Freeman Vector calculus Edition: 6 iimmybo2@gmail.com Printedfromwww.chegg.com chegg Copyright o W.H. Freeman Vector calculus Edition: 6 jimmybo2@gmail.com Printedtromwww.chegg.co chegg Copyright o W.H. Freeman Vector calculus Edition: 6 iimmybo2@ gmail.cor Printedfromwww.chegg.com chegg Copyright (c W. H. Freeman Vector calculus Edition: 6 2@gmail Printedfromwww.chegg.com this page left intentionally blank chegg Copyright (o W. H. Freeman Vector calculus Edition: 6 iimmybo2@gmail.com Printedfromwww.chegg.com chegg Copyright o W.H. Freeman Vector calculus Edition: 6 jimmybo2@gmail.com Printedtromwww.chegg.co chegg Copyright o W.H. Freeman Vector calculus Edition: 6 iimmybo2@ gmail.cor Printedfromwww.chegg.com To Jerrold E. marsden. 1942-2010 chegg Copyright W. H. Freeman Vector calculus Edition: 6 2@gmail Printedfromwww.chegg.com Jerry Marsden, Carl F Braun distinguished Professor at the California lnslitule of Technology, Fellow of the Royal Sociely chegg (as was Isaac Newton), and one of the world's pre-eminent applied mathematicians, passed away on September 21, 2010, Copyright (o W. H. Freeman while working on the sixth edition of Vector Calculus. Jerry's Vector calculus Edition: 6 interests were unusually broad; hiis work influenced physicists, iimmybo2@gmail.com engineers. life scientists. and mathematicians across the scientifi Printedfromwww.chegg.com and engineering spectrum. In addition to his many publications (over 400 archival and conference papers and 2l 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 pcrson and a close friend for almost half century. He will he sorely missed Anthony Tromba chegg Copyright o W.H. Freeman Vector calculus Edition: 6 jimmybo2@gmail.com Printedtromwww.chegg.co chegg Copyright o W.H. Freeman Vector calculus Edition: 6 iimmybo2@ gmail.cor Printedfromwww.chegg.com chegg Copyright (c W. H. Freeman Vector calculus Edition: 6 2@gmail Printedfromwww.chegg.com this page left intentionally blank chegg Copyright (o W. H. Freeman Vector calculus Edition: 6 iimmybo2@gmail.com Printedfromwww.chegg.com chegg Copyright o W.H. Freeman Vector calculus Edition: 6 jimmybo2@gmail.com Printedtromwww.chegg.co chegg Copyright o W.H. Freeman Vector calculus Edition: 6 iimmybo2 Printed fro Preface This text is intended for a one semester course in the calculus of functions of several variables and vector analysis, which is normally taught at the sophomore level. In addi- lion tU Illakinig changes and ilnlpruveinents throughout tie texl. we have also at leInpled to convey a sense of excitement, relevance, and importance of the subject matter Prerequisites Sometimes courses in vector calculus are preceded by a first course in linear algebra but this is not an essential prerequisite. We require only the bare rudiments of matrix algebra, and the necessary concepts are developed in thc text. If this course is preceded by a course in linear algebra, the instructor will have no difficulty enhancing the material. man However we do assume a knowledge of the fundamentals of one-variable calculus--the process of differentiation and integration and their geometric and physical meaning as wellasaknowledgeofthestandardfunctionssuchasthetrigonometricandexponentialgg.com functions The Role of Theory The text includes much of the basic theory as well as many concrete examples and problems. Some of the technical proofs for theorems in Chapters 2 and 5 are given in optional sections that are readily available on the book Companion Web Site at wwwwhfreeman.com'marsdenvcbe(seethedescriptiononthenextpage).Section2.2, on limits and continuity, is designed to be treated lightly and is deliberately hrief. More sophisticated theoretical topics, such as compactness and delicate proofs in integration theory, have been omitted, because they usually belong to a more advanced course in chegg Concrete and student-Oriented Copyright (o W. H. Freeman Computational skills and intuitive understanding are irnportant at this level, and we Vector calculus have tried to meet this need by making the book concrete and student-oriented. For Edition: 6 example, al though we formulate the definition of the derivative correctly, it is done iimmybo2@gmail.com by using matrices of partial derivatives rather than abstract linear transformations. We Printedfromwww.chegg.com also include a number of physical illustrations such as fuid mechanics, gravitation, and electromagnetic theory, and from economics as well, although knowledge of these Order of Topics A special feature of the text is the early introduction of vector fields, divergence, and curl in Chapter 4, hefore integration. Vector analysis often suffers in a course of this type and the present arrangement is designed to offset this tendency. To go even further, one might consider teaching Chapter 3 (Taylors theorems, maxima and minima, Lagrange multipliers)after Chapter &(the integral theorems of vector analysis New to This edition chegg This sixth edition was completely redesigned, but retains and iimproves on the balanceeman between theory, applications, optional material, and historical notes that was present in earlier editions jimmybo2@gmail.com Printedtromwww.cixgg.co 【实例截图】
【核心代码】