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- 原书名：Complex Variables and Applications 8 edition
- 原出版社： McGraw-Hill Science/Engineering/Math
- 作者： (美)James Ward Brown Ruel V. Churchill
- 丛书名： 经典原版书库
- 出版社：机械工业出版社
- ISBN：9787111253631
- 上架时间：2009-3-11
- 出版日期：2009 年3月
- 开本：16开
- 页码：468
- 版次：8-1
- 所属分类：数学 > 函数论 > 复变函数与积分变换
教材
内容简介
目录
Preface .
1 Complex Numbers
Sums and Products
Basic Algebraic Properties
Further Properties
Vectors and Moduli
Complex Conjugates
Exponential Form
Products and Powers in Exponential Form
Arguments of Products and Quotients
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
1 Complex Numbers
Sums and Products
Basic Algebraic Properties
Further Properties
Vectors and Moduli
Complex Conjugates
Exponential Form
Products and Powers in Exponential Form
Arguments of Products and Quotients
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
前言
This book is a revision of the seventh edition, which was published in 2004. 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 new 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. .
The first objective of the book is to develop those parts of the theory that are prominent in applications of the subject. The second objective is to furnish an introduction to applications of residues and conformal mapping. With regard to residues, special emphasis is given to their use in evaluating real improper integrals, finding inverse Laplace transforms, and locating zeros of functions. As for conformal mapping, considerable attention is paid to its use in solving boundary value problems that arise in studies of heat conduction and fluid flow. Hence the book may be considered as a companion volume to the authors' text "Fourier Series and Boundary Value Problems," where another classical method for solving boundary value problems in partial differential equations is developed.
The first nine chapters of this book have for many years formed the basis of a three-hour course given each term at The University of Michigan. The classes have consisted mainly of seniors and graduate students concentrating in mathematics, engineering, or one of the physical sciences. Before taking the course, the students have completed at least a three-term calculus sequence and a first course in ordinary differential equations. Much of the material in the book need not be covered in the lectures and can be left for self-study or used for reference. If mapping by elementary functions is desired earlier in the course, one can skip to Chap. 8 immediately after Chap. 3 on elementary functions.
In order to accommodate as wide a range of readers as possible, there are footnotes referring to other texts that give proofs and discussions of the more delicate results from calculus and advanced calculus that are occasionally needed. A bibliography of other books on complex variables, many of which are more advanced, is provided in Appendix 1. A table of conformal transformations that are useful in applications appears in Appendix 2. ..
The main changes in this edition appear in the first nine chapters. Many of those changes have been suggested by users of the last edition. Some readers have urged that sections which can be skipped or postponed without disruption be more clearly identified. The statements of Taylor's theorem and Laurent's theorem, for example, now appear in sections that are separate from the sections containing their proofs. Another significant change involves the extended form of the Cauchy integral formula for derivatives. The treatment of that extension has been completely rewritten, and its immediate consequences are now more focused and appear together in a single section.
Other improvements that seemed necessary include more details in arguments involving mathematical induction, a greater emphasis on rules for using complex exponents, some discussion of residues at infinity, and a clearer exposition of real improper integrals and their Cauchy principal values. In addition, some rearrangement of material was called for. For instance, the discussion of upper bounds of. moduli of integrals is now entirely in one section, and there is a separate section devoted to the definition and illustration of isolated singular points. Exercise sets occur more frequently than in earlier editions and, as a result, concentrate more directly on the material at hand.
Finally, there is an Instructor's Solutions Manual (ISBN: 978-0-07-333730-2; MHID: 0-07-333730-7) that is available upon request to instructors who adopt the book. It contains solutions of selected exercises in Chapters 1 through 7, covering the material through residues.
In the preparation of this edition, continual interest and support has been provided by a variety of people, especially the staff at McGraw-Hill and my wife Jacqueline Read Brown. ...
James Ward Brown
The first objective of the book is to develop those parts of the theory that are prominent in applications of the subject. The second objective is to furnish an introduction to applications of residues and conformal mapping. With regard to residues, special emphasis is given to their use in evaluating real improper integrals, finding inverse Laplace transforms, and locating zeros of functions. As for conformal mapping, considerable attention is paid to its use in solving boundary value problems that arise in studies of heat conduction and fluid flow. Hence the book may be considered as a companion volume to the authors' text "Fourier Series and Boundary Value Problems," where another classical method for solving boundary value problems in partial differential equations is developed.
The first nine chapters of this book have for many years formed the basis of a three-hour course given each term at The University of Michigan. The classes have consisted mainly of seniors and graduate students concentrating in mathematics, engineering, or one of the physical sciences. Before taking the course, the students have completed at least a three-term calculus sequence and a first course in ordinary differential equations. Much of the material in the book need not be covered in the lectures and can be left for self-study or used for reference. If mapping by elementary functions is desired earlier in the course, one can skip to Chap. 8 immediately after Chap. 3 on elementary functions.
In order to accommodate as wide a range of readers as possible, there are footnotes referring to other texts that give proofs and discussions of the more delicate results from calculus and advanced calculus that are occasionally needed. A bibliography of other books on complex variables, many of which are more advanced, is provided in Appendix 1. A table of conformal transformations that are useful in applications appears in Appendix 2. ..
The main changes in this edition appear in the first nine chapters. Many of those changes have been suggested by users of the last edition. Some readers have urged that sections which can be skipped or postponed without disruption be more clearly identified. The statements of Taylor's theorem and Laurent's theorem, for example, now appear in sections that are separate from the sections containing their proofs. Another significant change involves the extended form of the Cauchy integral formula for derivatives. The treatment of that extension has been completely rewritten, and its immediate consequences are now more focused and appear together in a single section.
Other improvements that seemed necessary include more details in arguments involving mathematical induction, a greater emphasis on rules for using complex exponents, some discussion of residues at infinity, and a clearer exposition of real improper integrals and their Cauchy principal values. In addition, some rearrangement of material was called for. For instance, the discussion of upper bounds of. moduli of integrals is now entirely in one section, and there is a separate section devoted to the definition and illustration of isolated singular points. Exercise sets occur more frequently than in earlier editions and, as a result, concentrate more directly on the material at hand.
Finally, there is an Instructor's Solutions Manual (ISBN: 978-0-07-333730-2; MHID: 0-07-333730-7) that is available upon request to instructors who adopt the book. It contains solutions of selected exercises in Chapters 1 through 7, covering the material through residues.
In the preparation of this edition, continual interest and support has been provided by a variety of people, especially the staff at McGraw-Hill and my wife Jacqueline Read Brown. ...
James Ward Brown
