当前: 首页 - 图书专区 - 复变函数及应用(英文版·第7版)
复变函数及应用(英文版·第7版)


  在线购买
(美)James Ward Brown,Ruel V.Churchill
7-111-13304-8
42.00
458
2004年01月01日

数学 > 函数论 > 复变函数与积分变换
McGraw-Hill
6042
英语
16开
Complex Variables and Applications
教材
经典原版书库







相关新闻
本书始印于20世纪40年代,是本科数学方面为数不多的几本典范教材之一。James Ward Brown在Ruel V. Churchill原作的基础上加以扩充,编写出了复变函数课程基础教材的最新版本。
  本书的首要目标是阐述复变函数应用方面的一些重要理论;另外,提供有关于残数及共形映射应用方面的介绍。
  与第6版相比,第7版提供了更多的新例子、图片和补充材料;专门为讲解例子增设了许多新的小节;重新绘制了部分插图。
James Ward Brown is Professor of Mathematics at The University of Michigan Dearborn. He earned his A.B. in Physics at Harvard University and his A.M. and Ph.D. in Mathematics at The University of Michigan in Ann Arbor, where he was an Institute of Science and Technology Predoctoral Fellow. He was coauthor with Dr. Churchill of the sixth edition of Fourier Series and Boundary Value Problems. A past director of a research grant from the National Science Foundation, he is the recipient of a Distinguished Teaching Award from his institution, as well as a Distinguished Faculty Award from the Michigan Association of Governing Boards of Colleges and Universities. He is listed in Who's Who in America.
  Ruel V. Churchill is Late Professor of Mathematics at The University of Michigan, where he began teaching in 1922. He received his B.S. in Physics from the University of Chicago and his M.S. in Physics and Ph.D. in Mathematics from The University of Michigan. He was coauthor with Dr. Brown of the recent sixth edition of Fourier Series and Boundary Value Problems, a classic text that he first wrote over sixty years ago. He was also the author of Operational Mathematics, now in its third edition. Throughout his long and productive career, Dr. Churchill held various offices in the Mathematical Association of America and in other mathematical societies and councils.

  James Ward Brown密歇根大学迪尔本分校数学系教授,美国数学学会会员。1964年于密歇根大学获得数学博士学位。他曾经主持研究美国国家自然科学基金项目,获得过密歇根大学杰出教师奖,并被列入美国名人录。
  Ruel V.Churchill 已故密歇根大学知名教授。早在60多年前,就开始编写一系列经典教材。除本书外,还与James Ward Brown合著有《Fourier Series and Boundary Value Problems》、《Selections from Complex Variables,5th ed》等。另外独自著有《Operational Mathematics》一书。他曾在美国数学学会等研究机构担任过多项职务。
This book is a revision of the sixth edition, published in 1996. That edition has served, just as the earlier ones did, as a textbook for a one-term introductory course in the theory and application of functions of a complex variable. This edition preserves the basic content and style of the earlier editions, the first two of which were written by the late Ruel V. Churchill alone.
   In this edition, the main changes appear in the first nine chapters, which make up the core of a one-term course. The remaining three chapters are devoted to physical applications, from which a selection can be made, and are intended mainly for selfstudy or reference.
   Among major improvements, there are thirty new figures; and many of the old ones have been redrawn. Certain sections have been divided up in order to emphasize specific topics, and a number of new sections have been devoted exclusively to examples. Sections that can be skipped or postponed without disruption are more clearly identified in order to make more time for material that is absolutely essential in a first course, or for selected applications later on. Throughout the book, exercise sets occur more often than in earlier editions. As a result, the number of exercises in any given set is generally smaller, thus making it more convenient for an instructor in assigning homework.
   As for other improvements in this edition, we mention that the introductory material on mappings in Chap. 2 has been simplified and now includes mapping properties of the exponential function. There has been some rearrangement of material in Chap. 3 on elementary functions, in order to make the flow of topics more natural. Specifically, the sections on logarithms now directly follow the one on the exponential function; and the sections on trigonometric and hyberbolic functions are now closer to the ones on their inverses. Encouraged by comments from users of the book in the past several years, we have brought some important material out of the exercises and into the text. Examples of this are the treatment of isolated zeros of analytic functions in Chap. 6 and the discussion of integration along indented paths in Chap. 7.
   The first objective of the book is to develop those parts of the theory which are prominent in applications of the subject. The second objective is to furnish an introduction to applications of residues and conformal mapping. Special emphasis is given to the use of conformal mapping in solving boundary value problems that arise in studies of heat conduction, electrostatic potential, and fluid flow. Hence the book may be considered as a companion volume to the authors' "Fourier Series and Boundary Value Problems" and Ruel V. Churchill's "Operational Mathematics," where other classical methods for solving boundary value problems in partial differential equations are developed. The latter book also contains further applications of residues in connection with Laplace transforms.
   This book has been used for many years in a three-hour course given each term at The University of Michigan. The classes have consisted mainly of seniors and graduate students majoring in mathematics, engineering, or one of the physical sciences. Before taking the course, the students have completed at least a three-term calculus sequence, a first course in ordinary differential equations, and sometimes a term of advanced calculus. In order to accommodate as wide a range of readers as possible, there are footnotes referring to texts that give proofs and discussions of the more delicate results from calculus that are occasionally needed. Some of the material in the book need not be covered in lectures and can be left for students to read on their own. If mapping by elementary functions and applications of conformal mapping are desired earlier in the course, one can skip to Chapters 8, 9, and 10 immediately after Chapter 3 on elementary functions.
   Most of the basic results are stated as theorems or corollaries, followed by examples and exercises illustrating those results. A bibliography of other books, many of which are more advanced, is provided in Appendix 1. A table of conformal transformations useful in applications appears in Appendix 2.
   In the preparation of this edition, continual interest and support has been provided by a number of people, mar y of whom are family, colleagues, and students. They include Jacqueline R. Brown Ronald P. Morash, Margret H. Hoft, Sandra M. Weber, Joyce A. Moss, as well as Robert E. Ross and Michelle D. Munn of the editorial staff at McGraw-Hill Higher Education.
   James Ward Brown
Preface
1 Complex Numbers
Sums and Products
Basic Algebraic Properties
Further Properties
Moduli
Complex Conjugates
Exponential Form
Products and Quotients in Exponential Form
Roots of Complex Numbers
Examples
Regions in the Complex Plane

2 Analytic Functions
Functions of a Complex Variable
Mappings
Mappings by the Exponential Function
Limits
Theorems on Limits
Limits Involving the Point at Infinity
Continuity
Derivatives
Differentiation Formulas
Cauchy-Riemann Equations
Sufficient Conditions for Differentiability
Polar Coordinates
Analytic Functions
Examples
Harmonic Functions
Uniquely Determined Analytic Functions
Reflection Principle

3 Elementary Functions
The Exponential Function
The Logarithmic Function
Branches mid Derivatives of Logarithms
Some Identities Involving Logarithms
Complex Exponents
Trigonometric Functions
Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions

4 Integrals
Derivatives of Functions w(t)
Definite Integrals of Functions w(t)
Contours
Contour Integrals
Examples
Upper Bounds for Moduli of Contour Integrals
Antiderivatives
Examples
Cauchy-Goursat Theorem
Proof of the Theorem
Simply and Multiply Connected Domains
Cauchy Integral Formula
Derivatives of Analytic Functions
Liouville's Theorem and the Fundamental Theorem of Algebra
Maximum Modulus Principle

5 Series
Convergence of Sequences
Convergence of Series
Taylor Series
Examples
Laurent Series
Examples
Absolute and Uniform Convergence of Power Series
Continuity of Sums of Power Series
Integration and Differentiation of Power Series
Uniqueness of Series Representations
Multiplication and Division of Power Series6 Residues and Poles

6 Residues
Cauchy's Residue Theorem
Using a Single Residue
The Three Types of Isolated Singular Points
Residues at Poles
Examples
Zeros of Analytic Functions
Zeros and Poles
Behavior of f Near Isolated Singular Points

7 Applications of Residues
Evaluation of Improper Integrals
Example
Improper Integrals from Fourier Analysis
Jordan's Lemma
Indented Paths
An Indentation Around a Branch Point
Integration Along a Branch Cut
Definite Integrals involving Sines and Cosines
Argument Principle
Rouche's Theorem
Inverse Laplace Transforms
Examples

8 Mapping by Elementary Functions
Linear Transformations
The Transformation w=1/z
Mappings by 1/z
Linear Fractional Transformations
An Implicit Form
Mappings of the Upper Half Plane
The Transformation w=sin z
Mappings by z2 and Branches of z1/2
Square Roots of Polynomials
Riemann Surfaces
Surfaces for Related Functions

9 Conformal Mapping
Preservation of Angles
Scale Factors
Local Inverses
Harmonic Conjugates
Transformations of Harmonic Functions
Transformations of Boundary Conditions

10 Applications of Conformal Mapping
Steady Temperatures
Steady Temperatures in a Half Plane
A Related Problem
Temperatures in a Quadrant
Electrostatic Potential
Potential in a Cylindrical Space
Two-Dimensional Fluid Flow
The Stream Function
Flows Around a Corner and Around a Cylinder

11 The Schwarz-Christoffel Transformation
Mapping the Real Axis onto a Polygon
Schwarz-Christoffel Transformation
Triangles and Rectangles
Degenerate Polygons
Fluid Flow in a Channel Through a Slit
Flow in a Channel with an Offset
Electrostatic Potential about an Edge of a Conducting Plate

12 Integral Formulas of the Poisson Type
Poisson Integral Formula
Dirichlet Problem for a Disk
Related Boundary Value Problems
Schwarz Integral Formula
Dirichlet Problem for a Half Plane
Neumann Problems
Appendixes
Bibliography
Table of Transformations of Regions
Index
读者书评
发表评论



高级搜索
复变函数及应用(英文版·第9版)
复变函数及应用(英文版·第8版)
复变函数及其应用(原书第7版)


版权所有© 2017  北京华章图文信息有限公司 京ICP备08102525号 京公网安备110102004606号
通信地址:北京市百万庄南街1号 邮编:100037
电话:(010)68318309, 88378998 传真:(010)68311602, 68995260
高校教师服务
华章教育微信
诚聘英才
诚聘英才