具体描述
内容简介
《复变函数及应用（英文版）（第8版）》初版于20世纪40年代，是经典的本科数学教材之一，对复变函数的教学影响深远，被美国加州理工学院、加州大学伯克利分校、佐治亚理工学院、普度大学、达特茅斯学院、南加州大学等众多名校采用。《复变函数及应用（英文版）（第8版）》阐述了复变函数的理论及应用，还介绍了留数及保形映射理论在物理、流体及热传导等边值问题中的应用。
新版对原有内容进行了重新组织，增加了更现代的示例和应用，更加方便教学。
作者简介
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《Fourier Series and Boundary Value Problems》。
目录
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
精彩书摘
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.
用户评价
作为一名刚刚接触复变函数领域的初学者，我选择这本书纯粹是听从了许多前辈的推荐，据说这是“入门必看”的经典之作。拿到实体书的时候，首先吸引我的是它封面设计的那种经典而又不失现代感的风格，预示着内容会既扎实又富有启发性。虽然我还没有深入学习，但仅凭初步的浏览，就能感受到作者在组织内容上的精心安排，从最基础的概念引入，逐步深入到各种定理和证明，再到最后的应用部分，结构清晰，逻辑性强。我特别看重的是它是否能够提供丰富的例题和习题，因为我知道理解抽象的数学概念最有效的方式就是通过大量的练习来加深印象。这本书的篇幅看上去不小，这意味着它很可能包含了相当全面的知识点，并且会对每一个知识点进行详尽的解释。我希望这本书能够帮助我打下坚实的复变函数基础，为我后续在电子工程、控制理论等领域的学习铺平道路。目前来看，它的出版质量和内容编排都让我充满了信心，相信它会成为我学习道路上的一位得力助手。
评分终于拿到这本《复变函数及应用》（英文版）（第8版）了，这本书在我心中一直占有很重要的位置，尽管我还没有真正开始阅读正文，但仅仅是翻阅目录和前言，就已经能感受到它厚重的学术分量和作者严谨的治学态度。我购买这本书主要是出于对数学学科的热爱，尤其是对那些看似抽象却又贯穿于物理、工程等多个领域的理论工具的探索。我一直对傅里叶变换、拉普拉斯变换等在信号处理和系统分析中的应用很感兴趣，也听说复变函数是理解这些工具背后深层原理的关键。这次换了新版本，自然希望能看到是否有在数学表述、证明方法上有所更新，或者在应用案例方面有更贴近当今技术发展的例子。书的装帧也很精美，纸张的触感和印刷的清晰度都让人赏心悦目，这对于一个需要长时间与书为伴的学习者来说，无疑是一种额外的享受。我期待着能够通过这本书，建立起对复变函数理论体系的完整认知，并最终能够将其灵活运用到我感兴趣的数学建模和算法设计问题中。这本书的出版，本身就是对数学知识传承和发展的一种贡献，能够成为其中的一份子，我感到非常荣幸。
评分我对复变函数的研究兴趣由来已久，这次购入《复变函数及应用》（英文版）（第8版），是希望能通过一本权威的教材，系统地梳理和深化我对这一领域的理解。我一直认为，复变函数不仅仅是一门独立的数学分支，更是连接了代数、分析、几何等多个数学领域的重要桥梁，并且在物理学的许多分支中扮演着至关重要的角色。从这本书的题目就可以看出，它不仅涵盖了纯粹的数学理论，还强调了其“应用”的重要性，这一点对我来说尤为吸引人。我期待这本书能够提供对解析函数、留数定理、保形映射等核心概念的深刻阐释，并且能够展示这些概念在解决实际问题中的强大威力。我希望书中能够包含一些经典的物理问题（如稳态热传导、电势分布等）的复变函数解法，以及一些更现代的工程应用案例。如果书中还能对一些较少被提及的高级主题有所涉猎，例如黎曼曲面、复积分在统计物理学中的应用等，那将是对我研究视野的极大拓展。这本书的出版，本身就是对复变函数理论及其广泛应用价值的有力证明。
评分我是一位有一定复变函数基础的研究生，这次选择的是《复变函数及应用》（英文版）（第8版），主要是想更新一下知识库，并且深入了解一些高级的应用。在我看来，一本好的数学教材，不仅在于其理论的严谨性，更在于其理论的实用性和启发性。从初步翻阅的经验来看，这本书似乎在保持传统复变函数理论核心内容的同时，融入了更多现代研究的前沿视角。我尤其关注的是书中对一些复杂函数的处理，以及在数值计算和科学计算中的最新进展。如果书中能包含一些关于复变函数在机器学习、数据科学或现代物理学（如量子场论）中应用的新案例，那就再好不过了。我希望这本书能够提供更深入的证明技巧，以及一些不常见的定理和性质的阐释，从而帮助我拓宽研究思路。同时，对于作者在数学建模方面的指导，以及如何将复变函数理论转化为实际问题的解决方案，我也非常期待。这本书的存在，本身就证明了复变函数理论的生命力，而它的每一次更新，都是对这一生命力的注入。
评分购买这本《复变函数及应用》（英文版）（第8版）主要是因为我的工作需要，我是一家科技公司的工程师，工作中经常会涉及到一些复杂的信号分析和系统设计问题，而复变函数理论正是解决这些问题的关键工具之一。我选择英文原版，是希望能够最直接地接触到作者的思想，并且在一些专业术语的理解上更加精确。我之前也接触过一些国内出版的复变函数书籍，但总觉得在应用案例的深度和广度上，以及在数学工具的描述上，与国际前沿相比还有一定差距。我特别希望能在这本书中找到一些关于复变函数在现代通信、图像处理、甚至人工智能等领域中的具体实现和优化方法。我希望它能够提供清晰的算法描述和代码示例，方便我将其应用到实际工作中。这本书的厚重感也让我相信，它能够提供非常详尽的知识体系，帮助我解决工作中遇到的各种挑战。我期待它能够成为我解决实际工程问题的宝库。
评分可以
评分复变函数必备教材。就是不好记忆。
评分国外关于复变函数的经典著作。印刷质量不错。
评分内容偏专业，价格贵，刚开始看
评分《复变函数及应用(英文版)(第8版)》阐述了复变函数的理论及应用，还介绍了留数及保形映射理论在物理、流体及热传导等边值问题中的应用。
评分内容偏专业，价格贵，刚开始看
评分帮老师买的
评分不错，是正版！
评分恕我直言，手纸也能印书？？
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