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內容簡介

《復變函數及應用（英文版）（第8版）》初版於20世紀40年代，是經典的本科數學教材之一，對復變函數的教學影響深遠，被美國加州理工學院、加州大學伯剋利分校、佐治亞理工學院、普度大學、達特茅斯學院、南加州大學等眾多名校采用。
《復變函數及應用（英文版）（第8版）》闡述瞭復變函數的理論及應用，還介紹瞭留數及保形映射理論在物理、流體及熱傳導等邊值問題中的應用。
新版對原有內容進行瞭重新組織，增加瞭更現代的示例和應用，更加方便教學。

作者簡介

James Ward Brown密歇根大學迪爾本分校數學係教授，美國數學學會會員。1964年於密歇根大學獲得數學博士學位。他曾經主持研究美國國傢自然科學基金項目，獲得過密歇根大學傑齣教師奬，並被列入美國名人錄。
Ruel V.Churchill已故密歇根大學知名教授。早在60多年前，就開始編寫一係列經典教材。除本書外，還與James Ward Brown閤著《Fourier Series and Boundary Value Problems》。

目錄

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
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 and 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
Some Examples
Examples with Branch Cuts
Upper Bounds for Moduli of Contour Integrals
Antiderivatives
Proof of the Theorem
Cauchy-Goursat Theorem
Proof of-the Theorem
Simply Connected Domains
Multiply Connected Domains
Cauchy Integral Formula
An Extension of the Cauchy Integral Formula
Some Consequences of the Extension
Liouvilles Theorem and the Fundamental Theorem of Algebra
Maximum Modulus Principle

5 Series
Convergence of Sequences
Convergence of Series
Taylor Series
ProofofTaylors Theorem
Examples
Laurent Series
ProofofLaurents 111eorem
Examples
Absolute and Uniform Convergence of Power Series
Continuity of Sums of Power Series
Integration and Differentiation ofPower Series
Uniqueness of Series Representations
Multiplication and Division of Power Series

6 Residues and Poles
Isolated Singular Poims
Residues
Cauchys Residue Theorem
Residue at Infinity
The Three Types of Isolated Singular Points
ResiduCS at POles
Examples
Zeros of Analytic Functions
Zeros and Poles
Behavior of Functions Near Isolated Singular Points

7 Applications of Residues
Evaluation of Improper Integrals
Example
Improper Integrals from Fourier Analysis
Jordans Lemma
Indented Paths
An Indentation Around a Branch P0int
Integration Along a Branch Cut
Definite Integrals Involving Sines and Cosines
Argument Principle
Rouch6s Theorem
Inverse Laplace Transforms
Examples

8 Mapping by Elementary Functions
Linear Transformations
The TransfoITnation w=1／Z
Mappings by 1／Z
Linear Fractional Transformations
An Implicit Form
Mappings ofthe Upper HalfPlane
The Transformation w=sinZ
Mappings by z2 and Branches of z1／2
Square Roots of Polynomials
Riemann Surfaces
Surfaces forRelatedFuncfions
9 Conformal Mapping
10 Applications of Conformal Mapping
11 The Schwarz-Chrstoffer Transformation
12 Integral Formulas of the Poisson Type
Appendixes
Index

精彩書摘

The first objective of.the book is to develop those parts of the theory that areprominent in applications of the subject. The second objective is to furnish an intro-duction to applications of residues and conformal mapping. With regard to residues，special emphasis is given to their use in evaluating real improper integrals, findinginverse Laplace transforms, and locating zeros of functions. As for conformal map-ping, considerable attention is paid to its use in solving boundary value problemsthat arise in studies of heat conduction and fluid flow. Hence the book may beconsidered as a companion volume to the authors text "Fourier Series and Bound-ary Value Problems," where another classical method for solving boundary valueproblems in partial differential equations is developed.
The first nine chapters of this book have for many years formed the basis of athree-hour course given each term at The University of Michigan. The classes haveconsisted mainly of seniors and graduate students concentrating in mathematics,engineering, or one of the physical sciences. Before taking the course, the studentshave completed at least a three-term calculus sequence and a first course in ordinarydifferential equations. Much of the material in the book need not be covered in thelectures and can be left for self-study or used for reference.

前言/序言

　　This book is a revision of the seventh edition， which was published in 2004. Thatedition has served, just as the earlier ones did, as a textbook for a oneterm 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, thefirst 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 areprominent 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, findinginverse Laplace transforms, and locating zeros of functions. As for conformal mapping, considerable attention is paid to its use in solving boundary value problemsthat arise in studies of heat conduction and fluid flow. Hence the book may beconsidered as a companion volume to the authors text "Fourier Series and Boundary Value Problems," where another classical method for solving boundary valueproblems in partial differential equations is developed.
　　The first nine chapters of this book have for many years formed the basis of athreehour course given each term at The University of Michigan. The classes haveconsisted mainly of seniors and graduate students concentrating in mathematics,engineering, or one of the physical sciences. Before taking the course, the studentshave completed at least a threeterm calculus sequence and a first course in ordinarydifferential equations. Much of the material in the book need not be covered in thelectures and can be left for selfstudy or used for reference. If mapping by elementaryfunctions is desired earlier in the course, one can skip to Chap. 8 immediately afterChap. 3 on elementary functions.
復變函數及應用（英文版）（第8版） 下載 mobi epub pdf txt 電子書

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《復變函數及應用(英文版)(第8版)》初版於20世紀40年代，是經典的本科數學教材之一，對復變函數的教學影響深遠，被美國加州理工學院、加州大學伯剋利分校、佐治亞理工學院、普度大學、達特茅斯學院、南加州大學等眾多名校采用。

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