复变函数论【正版新书】
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作者马立新 编
出版社中国农业出版社
ISBN9787109197268
出版时间2014-12
装帧平装
开本16开
定价35元
货号1201049521
上书时间2024-06-25
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目录
前言
Chapter 1 Complex Numbers and Functions
1 Complex Numbers
1.1 Complex Number Field
1.2 Complex Plane
1.3 Modulus， Conjugation， Argument， Polar Representation
1.4 Powers and Roots of Complex Numbers
Exercises
2 Regions in the Complex Plane
2.1 Some Basic Concept
2.2 Domain and Jordan Curve
Exercises
3 Functions of a Complex Variable
3.1 The Concept of Functions of a Complex Variable
3.2 Limits and Continuous
Exercises
4 The Extended Complex Plane and the Point at Infinity
4.1 The Spherical Representation， the Extended Complex Plane
4.2 Some Concepts in the Extended Complex Plane
Exercises
Chapter 2 Analytic Functions
1 The Concept of the Analytic Function
1.1 The Derivative of the Functions of a Complex Variable
1.2 Analytic Functions
Exercises
2 Cauchy—Riemann Equations
Exercises
3 Elementary Functions
3.1 The Exponential Function
3.2 Trigonometric Functions
3.3 Hyperbolic Functions
Exercises
4 Multi—Valued Functions
4.1 The Logarithmic Function
4.2 Complex Power Functions
4.3 Inverse Trigonometric and Hyperbolic Functions
Exercises
Chapter 3 Complex Integration
1 The Concept of Contour Integrals
1.1 Integral of a Complex Function over a Real Interval
1.2 Contour Integrals
Exercises
Cauchy—Goursat Theorem
2.1 Cauchy Theorem
2.2 Cauchy Integral Formula
2.3 Derivatives of Analytic Functions
2.4 Liouvilles Theorem and the Fundamental Theorem of Algebra
Exercises
Harmonic Functions
Exercises
Chapter 4 Series
1 Basic Properties of Series
1.1 Convergence of Sequences
1.2 Convergence of Series
1.3 Uniform convergence
Exercises
2 Power Series
Exercises
3 Taylor Series
Exercises
4 Laurent Series
Exercises
5 Zeros of an Analytic Functions and Uniquely Determined Analytic
Functions
5.1 Zeros of Analytic Functions
5.2 Uniquely Determined Analytic Functions
5.3 Maximum Modulus Principle
Exercises
6 The Three Types of Isolated Singular Points at a Finite Point
Exercises
7 The Three Types of Isolated Singular Points at a Infinite Point
Exercises
Chapter 5 Calculus of Residues
1 Residues
1.1 Residues
1.2 Cauchys Residue Theorem
1.3 The Calculus of Residue
Exercises
2 Applications of Residue
Exercises
3 Argument Principle
Exercises
Chapter 6 Conformal Mappings
1 Analytic Transformation
1.1 Preservation of Domains of Analytic Transformation
1.2 Conformality of Analytic Transformation
Exercises
2 Rational Functions
2.1 Polynomials
2.2 Rational Functions
Exercises
3 Fractional Linear Transformations
Exercises
4 Elementary Conformal Mappings
Exercises
5 The Riemann Mapping Theorem
Exercises
Appendix
Appendix 1
Appendix 2
Answers
Bibliography
内容摘要
本书为山东省省级双语示范课程，省级精品课程教材，较全面、系统地介绍了复变函数的基础知识。全书共6章，主要内容包括：复数与复变函数、解析函数、复变函数的积分、级数、留数及其应用和共形映射等。内容处理上重点突出，叙述简明，每节末附有适量习题供读者选用。适合高等师范院校数学系及普通综合性大学数学系高年级学生使用。
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