《華章數學原版精品系列:複變函數及套用(英文版·第9版)》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。這本經典的教材對複變函數的教學影響深遠，被美國史丹福大學、加州理工學院、加州大學伯克利分校、喬治亞理工學院、普度大學、達特茅斯學院、南加州大學等眾多名校採用。
基本介紹
- 書名：華章數學原版精品系列:複變函數及套用
- 作者：布朗 (James Ward Brown)
- 出版日期：2014年7月1日
- 語種：簡體中文, 英語
- ISBN：9787111470878
- 外文名：Complex Variables and Applications
- 出版社：機械工業出版社
- 頁數：461頁
- 開本：16
- 品牌：機械工業出版社
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《華章數學原版精品系列:複變函數及套用(英文版·第9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。
作者簡介
作者：（美國）布朗（James Ward Brown） （美國）邱吉爾（Ruel V.Churchill）
圖書目錄
Preface
Complex Numbers 1
Sums and Products 1
Basic Algebraic Properties 3
Further Algebraic Properties 5
Vectors and Moduli 8
Triangle Inequality 11
Complex Conjugates 14
Exponential Form 17
Products and Powers in Exponential Form 20
Arguments of Products and Quotients 21
Roots of Complex Numbers 25
Examples 28
Regions in the Complex Plane 32
2 Analytic Functions 37
Functions and Mappings 37
The Mapping w = z2 40
Limits 44
Theorems on Limits 47
Limits Involving the Point at Infinity 50
Continuity 52
Derivatives 55
Rules for Differentiation 59
Cauchy-Riemann Equations 62
Examples 64
Sufficient Conditions for Differentiability 65
Polar Coordinates 68
Analytic Functions 72
Further Examples 74
Harmonic Functions 77
Uniquely Determined Analytic Functions 80
Reflection Principle 82
3 Elementary Functions 87
The Exponential Function 87
The Logarithmic Function 90
Examples 92
Branches and Derivatives of Logarithms 93
Some Identities Involving Logarithms 97
The Power Function 100
Examples 101
The Trigonometric Functions sin z and cos z 103
Zeros and Singularities of Trigonometric Functions 105
Hyperbolic Functions 109
Inverse Trigonometric and Hyperbolic Functions 112
4 Integrals 115
Derivatives of Functions w (t) 115
Definite Integrals of Functions w (t) 117
Contours 120
Contour Integrals 125
……
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-Christoffel Transformation
12 Integral Formulas of the Poisson Type
Appenclixes
Index
Complex Numbers 1
Sums and Products 1
Basic Algebraic Properties 3
Further Algebraic Properties 5
Vectors and Moduli 8
Triangle Inequality 11
Complex Conjugates 14
Exponential Form 17
Products and Powers in Exponential Form 20
Arguments of Products and Quotients 21
Roots of Complex Numbers 25
Examples 28
Regions in the Complex Plane 32
2 Analytic Functions 37
Functions and Mappings 37
The Mapping w = z2 40
Limits 44
Theorems on Limits 47
Limits Involving the Point at Infinity 50
Continuity 52
Derivatives 55
Rules for Differentiation 59
Cauchy-Riemann Equations 62
Examples 64
Sufficient Conditions for Differentiability 65
Polar Coordinates 68
Analytic Functions 72
Further Examples 74
Harmonic Functions 77
Uniquely Determined Analytic Functions 80
Reflection Principle 82
3 Elementary Functions 87
The Exponential Function 87
The Logarithmic Function 90
Examples 92
Branches and Derivatives of Logarithms 93
Some Identities Involving Logarithms 97
The Power Function 100
Examples 101
The Trigonometric Functions sin z and cos z 103
Zeros and Singularities of Trigonometric Functions 105
Hyperbolic Functions 109
Inverse Trigonometric and Hyperbolic Functions 112
4 Integrals 115
Derivatives of Functions w (t) 115
Definite Integrals of Functions w (t) 117
Contours 120
Contour Integrals 125
……
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-Christoffel Transformation
12 Integral Formulas of the Poisson Type
Appenclixes
Index
