《複變函數及套用》，是2009年機械工業出版社出版的圖書。本書介紹了複變函數的理論及套用和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套用。
基本介紹
- 書名：複變函數及套用
- 作者：（美）布朗
- ISBN：9787111253631
- 出版時間： 2009-3-1
圖書信息,內容簡介,圖書目錄,
圖書信息
書 名: 複變函數及套用（英文版） 作 者：（美）布朗
出版時間： 2009-3-1
ISBN: 9787111253631
開本： 16開
定價: 65.00元
內容簡介
本書闡述了複變函數的理論及套用，還介紹了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套用。
新版對原有內容進行了重新組織，增加了更現代的示例和套用，更加方便教學。
圖書目錄
Preface
1 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
5 Series
6 Residues and Poles
7 Applications of Residues
8 Mapping by Elementary Functions
9 Conformal Mapping
10 Applications of Conformal Mapping
11 The Schwarz-Chrstoffer Transformation
12 Integral Formulas of the Poisson Type
Appendixes
Index
