Cargando…
Complex variables
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York,
Academic Press
[1971]
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Complex Variables; Copyright Page; Table of Contents; Preface; Chapter0. PREREQUISITES; 0.1 Basic Definitions; 0.2 The Extended Plane; 0.3 Analytic Functions; 0.4 Cauchy-RiemannEquations and Applications; 0.5 The Elementary Functions; 0.6 Logarithms and Roots; Remarks on Notation; References; Chapter1. THE ELEMENTARY THEORY ; 1.1 Integration on Paths; 1.2 Power Series; 1.3 Applications; Problems; Chapter2. THE GENERAL CAUCHY THEOREM; 2.1 Logarithms and Arguments; 2.2 The Index of a Point with Respect to a Closed Curve; 2.3 Cauchy's Theorem; Problems
- Chapter3. APPLICATIONS OF THE CAUCHY THEORY3.1 Singularities; 3.2 Residue Theory; 3.3 Inverse Functions; 3.4 Analytic Mappings of One Disk into Another; 3.5 Extension of Cauchy's Theorem and Integral Formula; 3.6 The Poisson Integral Formula and Its Applications; 3.7 The Jensen and Poisson-JensenFormulas; 3.8 Analytic Continuation; Problems; Chapter4. ENTIRE FUNCTIONS; 4.1 Infinite Products; 4.2 Canonical Products and the Weierstrass Factorization Theorem; 4.3 Order of an Entire Function; 4.4 The Hadamard Factorization Theorem; Problems; Chapter5. FAMILIES OF ANALYTIC FUNCTIONS
- 5.1 The Spaces A(U) and C(U)5.2 Riemann Mapping Theorem; 5.3 The Homotopic Version of Cauchy'sTheorem; Problems; Chapter6. THE PRIME NUMBER THEOREM; 6.1 The Gamma Function; 6.2 The Riemann Zeta Function; 6.3 Proof of the Prime Number Theorem; Solutions To Problems; Subject Index