具體描述
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
Preface1 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.
用戶評價
購買這本《復變函數及應用》（英文版）（第8版）主要是因為我的工作需要，我是一傢科技公司的工程師，工作中經常會涉及到一些復雜的信號分析和係統設計問題，而復變函數理論正是解決這些問題的關鍵工具之一。我選擇英文原版，是希望能夠最直接地接觸到作者的思想，並且在一些專業術語的理解上更加精確。我之前也接觸過一些國內齣版的復變函數書籍，但總覺得在應用案例的深度和廣度上，以及在數學工具的描述上，與國際前沿相比還有一定差距。我特彆希望能在這本書中找到一些關於復變函數在現代通信、圖像處理、甚至人工智能等領域中的具體實現和優化方法。我希望它能夠提供清晰的算法描述和代碼示例，方便我將其應用到實際工作中。這本書的厚重感也讓我相信，它能夠提供非常詳盡的知識體係，幫助我解決工作中遇到的各種挑戰。我期待它能夠成為我解決實際工程問題的寶庫。
評分我對復變函數的研究興趣由來已久，這次購入《復變函數及應用》（英文版）（第8版），是希望能通過一本權威的教材，係統地梳理和深化我對這一領域的理解。我一直認為，復變函數不僅僅是一門獨立的數學分支，更是連接瞭代數、分析、幾何等多個數學領域的重要橋梁，並且在物理學的許多分支中扮演著至關重要的角色。從這本書的題目就可以看齣，它不僅涵蓋瞭純粹的數學理論，還強調瞭其“應用”的重要性，這一點對我來說尤為吸引人。我期待這本書能夠提供對解析函數、留數定理、保形映射等核心概念的深刻闡釋，並且能夠展示這些概念在解決實際問題中的強大威力。我希望書中能夠包含一些經典的物理問題（如穩態熱傳導、電勢分布等）的復變函數解法，以及一些更現代的工程應用案例。如果書中還能對一些較少被提及的高級主題有所涉獵，例如黎曼麯麵、復積分在統計物理學中的應用等，那將是對我研究視野的極大拓展。這本書的齣版，本身就是對復變函數理論及其廣泛應用價值的有力證明。
評分我是一位有一定復變函數基礎的研究生，這次選擇的是《復變函數及應用》（英文版）（第8版），主要是想更新一下知識庫，並且深入瞭解一些高級的應用。在我看來，一本好的數學教材，不僅在於其理論的嚴謹性，更在於其理論的實用性和啓發性。從初步翻閱的經驗來看，這本書似乎在保持傳統復變函數理論核心內容的同時，融入瞭更多現代研究的前沿視角。我尤其關注的是書中對一些復雜函數的處理，以及在數值計算和科學計算中的最新進展。如果書中能包含一些關於復變函數在機器學習、數據科學或現代物理學（如量子場論）中應用的新案例，那就再好不過瞭。我希望這本書能夠提供更深入的證明技巧，以及一些不常見的定理和性質的闡釋，從而幫助我拓寬研究思路。同時，對於作者在數學建模方麵的指導，以及如何將復變函數理論轉化為實際問題的解決方案，我也非常期待。這本書的存在，本身就證明瞭復變函數理論的生命力，而它的每一次更新，都是對這一生命力的注入。
評分作為一名剛剛接觸復變函數領域的初學者，我選擇這本書純粹是聽從瞭許多前輩的推薦，據說這是“入門必看”的經典之作。拿到實體書的時候，首先吸引我的是它封麵設計的那種經典而又不失現代感的風格，預示著內容會既紮實又富有啓發性。雖然我還沒有深入學習，但僅憑初步的瀏覽，就能感受到作者在組織內容上的精心安排，從最基礎的概念引入，逐步深入到各種定理和證明，再到最後的應用部分，結構清晰，邏輯性強。我特彆看重的是它是否能夠提供豐富的例題和習題，因為我知道理解抽象的數學概念最有效的方式就是通過大量的練習來加深印象。這本書的篇幅看上去不小，這意味著它很可能包含瞭相當全麵的知識點，並且會對每一個知識點進行詳盡的解釋。我希望這本書能夠幫助我打下堅實的復變函數基礎，為我後續在電子工程、控製理論等領域的學習鋪平道路。目前來看，它的齣版質量和內容編排都讓我充滿瞭信心，相信它會成為我學習道路上的一位得力助手。
評分終於拿到這本《復變函數及應用》（英文版）（第8版）瞭，這本書在我心中一直占有很重要的位置，盡管我還沒有真正開始閱讀正文，但僅僅是翻閱目錄和前言，就已經能感受到它厚重的學術分量和作者嚴謹的治學態度。我購買這本書主要是齣於對數學學科的熱愛，尤其是對那些看似抽象卻又貫穿於物理、工程等多個領域的理論工具的探索。我一直對傅裏葉變換、拉普拉斯變換等在信號處理和係統分析中的應用很感興趣，也聽說復變函數是理解這些工具背後深層原理的關鍵。這次換瞭新版本，自然希望能看到是否有在數學錶述、證明方法上有所更新，或者在應用案例方麵有更貼近當今技術發展的例子。書的裝幀也很精美，紙張的觸感和印刷的清晰度都讓人賞心悅目，這對於一個需要長時間與書為伴的學習者來說，無疑是一種額外的享受。我期待著能夠通過這本書，建立起對復變函數理論體係的完整認知，並最終能夠將其靈活運用到我感興趣的數學建模和算法設計問題中。這本書的齣版，本身就是對數學知識傳承和發展的一種貢獻，能夠成為其中的一份子，我感到非常榮幸。
評分《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。
評分國外關於復變函數的經典著作。印刷質量不錯。
評分大概翻瞭下，內容還行，紙張不是很好，感覺優惠後價格纔是實價
評分為復變函數論的創建做瞭最早期工作的是歐拉、達朗貝爾，法國的拉普拉斯也隨後研究過復變函數的積分，他們都是創建這門學科的先驅。
評分幫老師買的
評分不錯，是正版！
評分經典原版書庫 (共54冊), 這套叢書還有《數學分析原理》,《抽象代數基礎教程》,《復分析》,《搜索引擎》,《逼近論教程》 等
評分非常好的圖書 物有所值
評分內容偏專業，價格貴，剛開始看
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