COMPLEX ANALYSI
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作者Li Na，Ma Lixin[著]
出版社科学技术文献出版社
ISBN9787518955657
出版时间2019-08
装帧平装
开本16开
定价48元
货号1201932930
上书时间2024-09-04
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目录
Chapter 1Complex Numbers and Functions
1Complex Numbers
1.1Complex Number Field
1.2Complex Plane
1.3Modulus，Conjugation，Argument，and Polar Representation
1.4Powers and Roots of Complex Numbers
2Regions in the Complex Plane
2.1Some Basic Concepts
2.2Domain and Jordan Curve
3Functions of a Complex Variable
3.1The Concept of Functions of a Complex Variable
3.2Limits and Continuous
4The Extended Complex Plane and the Point at Infinity
4.1The Spherical Representation，and the Extended
Complex Plane
4.2Some Concepts in the Extended Complex Plane
Chapter 2Analytic Functions
1The Concept of the Analytic Function
1.1The Derivative of Functions of a Complex Variable
1.2Analytic Functions
2Cauchy-Riemann Equations
3Elementary Functions
3.1Exponential Functions
3.2Trigonometric Functions
3.3Hyperbolic Functions
4Multi-valued Functions
4.1Logarithmic Functions
4.2Complex Power Functions
4.3Inverse Trigonometric and Hyperbolic Functions
Chapter 3Complex Integration
1The Concept of Contour Integral
1.1Integral of a Complex Function over a Real Interval
1.2Contour Integrals
2Cauchy-Goursat Theorem
2.1Cauchy-Goursat Theorem
2.2Cauchy Integral Formula
2.3Derivatives of Analytic Functions
2.4Liouville’s Theorem and the Fundamental Theorem of Algebra
3Harmonic Functions
Chapter 4Series
1Basic Properties of Series
1.1Convergence of Sequences
1.2Convergence of Series
1.3Uniform Convergence
2Power Series
3Taylor Series
4Laurent Series
5Zeros of Analytic Functions and Uniquely Determined
Analytic Functions
5.1Zeros of Analytic Functions
5.2Uniquely Determined Analytic Functions
5.3Maximum Modulus Principle
6Three Types of Isolated Singular Points at a Finite Point
7Three Types of Isolated Singular Points at an Infinite Point
Chapter 5Calculus of Residues
1Residues
1.1Residues
1.2Cauchy’s Residue Theorem
1.3The Calculus of Residue
2Applications of Residue
2.1The Type of Definite Integral ∫2π0F(sinθ,cosθ)dθ
2.2The Type of Improper Integral ∫∞－∞p(x)q(x)dx
2.3The Type of Improper Integral ∫+∞－∞p(x)q(x)sinxdx
or ∫+∞－∞p(x)q(x)cosxdx
3Argument Principle
Chapter 6Conformal Mappings
1Analytic Transformation
1.1Preservation of Domains of Analytic Transformation
1.2Conformality of Analytic Transformation
2Rational Functions
2.1Polynomials
2.2Rational Functions
3Fractional Linear Transformations
4Elementary Conformal Mappings
5The Riemann Mapping Theorem
内容摘要
复分析是研究复函数，特别是亚纯函数和复解析函数的数学理论。复分析的应用领域较为广泛，在其它数学分支和物理学中也起着重要的作用。包括数论、应用数学、流体力学、热力学和电动力学。
复分析研究的主要内容包括：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。
复分析研究的函数定义在复平面上，其值为复数，而且可微。研究中常用的理论、公式以及方法包括柯西积分定理、
主编推荐
复分析是研究复函数，特别是亚纯函数和复解析函数的数学理论。复分析的应用领域较为广泛，在其它数学分支和物理学中也起着重要的作用。包括数论、应用数学、流体力学、热力学和电动力学。
媒体评论
复分析是研究复函数，特别是亚纯函数和复解析函数的数学理论。复分析的应用领域较为广泛，在其它数学分支和物理学中也起着重要的作用。包括数论、应用数学、流体力学、热力学和电动力学。
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