《複分析及其套用初級教程（第3版）》是2018年世界圖書出版公司出版的著作，作者是[美] D.G.齊爾，[美] P.D.沙納漢。
基本介紹
- 中文名：《複分析及其套用初級教程（第3版）》
- 作者：[美] D.G.齊爾，[美] P.D.沙納漢
- 出版社：世界圖書出版公司
- 出版時間：2018年10月01日
- ISBN：9787519250577
內容簡介,作者簡介,目錄,
內容簡介
本書主要面向有微積分基礎的本科生，是一部全面介紹複分析的基本理論和套用的入門性教材，其中也以學生易於接受的方式討論了許多相關數學論題。本書語言簡單明了，以大量的例題、圖表和套用實例清晰地闡明複分析概念。各章的大量習題和複分析在科學和工程領域中的套用實例，將有助於學生領會和掌握複分析的理論精髓。
作者簡介
本書的第1作者Dennis G. Zill，愛荷華州立大學套用數學博士，洛杉磯Loyola Marymount大學數學教授，其研究領域包括套用數學、特殊函式及積分變換。
目錄
Preface
Chapter 1． Complex Numbers and the Complex Plane
1．1 Complex Numbers and Their Properties
1．2 ComplexPlane
1．3 Polar Form of Complex Numbers
1．4 Powers and Roots
1．5 Sets of Points in the Complex Plane
1．6 Applications
Chapter 1 Review Quiz
Chapter 2． Complex Functions and Mappings
2．1 ComplexFunctions
2．2 Complex Functions as Mappings
2．3 LinearMappings
2．4 Special Power Functions
2．4．1 The Power Function Zn
2．4．2 The Power Function zl
2．5 ReciprocalFunction
2．6 Applications
Chapter 2 Review Quiz
Chapter 3． Analytic Functions
3．1 Limits and Continuity
3．1．1 Limits
3．1．2 Continuity
3．2 Differentiability and Analyticity
3．3 Cauchy-RiemannEquations
3．4 Harmonic Functions
3．5 Applications
Chapter 3 Review Quiz
Chapter 4． Elementary Functions
4．1 Exponential and Logarithmic Functions
4．1．1 Complex Exponential Function
4．1．2 Complex Logarithmic Function
4．2 Complex Powers
4．3 Trigonometric and Hyperbolic Functions
4．3．1 Complex Trigonometric Functions
4．3．2 Complex Hyperbolic Functions
4．4 Inverse Trigonometric and Hyperbolic Functions
4．5 Applications
Chapter4 Review Quiz
Chapter 5． Integration in the Complex Plane
5．1 Reallntegrals
5．2 Complexlntegrals
5．3 Cauchy-GoursatTheorem
5．4 Independence of Path
5．5 Cauchy's Integral Formulas and Their
Consequences
5．5．1 Cauchy's Twolntegral Formulas
5．5．2 Some Consequences of the Integral
Formulas
5．6 Applications
Chapter 5 Review Quiz
Chapter 6． Series and esidues
6．1 Sequences and Series
6．2 TaylorSeries
6．3 Laurent Series
6．4 Zeros and Poles
6．5 Residues and Residue Theorem
6．6 Some Consequences of the Residue Theorem
6．6．1 Evaluation of Real Trigonometric
Integrals
6．6．2 Evaluation of Reallmproperlntegrals
6．6．3 Integration along a Branch Cut
6．6．4 The Argument Principle and Rouche's
Theorem
6．6．5 Summing Infinite Series
6．7 Applications
Chapter 6 Review Quiz
Chapter 7． ConformaIMappings
7．1 ConformaIMapping
7．2 Linear Fractional Transformations
7．3 Schwarz-ChristoffeITransformations
7．4 Poisson Integral Formulas
7．5 Applications
7．5．1 Boundary-ValueProblems
7．5．2 Fluid Flow
Chapter 7 Review Quiz
Appendixes： I ProofofTheorem 3．1．1 APP
Ⅱ Proof of the Cauchy-Goursat Theorem APP
ni Table ofConformal Mappings APP
Answers to Selected Odd-Numbered Problems ANS
Symbollndex IND
Wordlndex IND
