An Introduction to Complex Analysis

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner.   Key features of this textbook: -Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures - Uses detailed examples...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Agarwal, Ravi P. (Autor), Perera, Kanishka (Autor), Pinelas, Sandra (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer US : Imprint: Springer, 2011.
Edición:1st ed. 2011.
Temas:
Functions of complex variables.
Mathematical analysis.
Functions of a Complex Variable.
Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preface.-Complex Numbers.-Complex Numbers II
  • Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I
  • Elementary Functions II
  • Mappings by Functions
  • Mappings by Functions II
  • Curves, Contours, and Simply Connected Domains
  • Complex Integration
  • Independence of Path
  • Cauchy-Goursat Theorem
  • Deformation Theorem
  • Cauchy's Integral Formula
  • Cauchy's Integral Formula for Derivatives
  • Fundamental Theorem of Algebra
  • Maximum Modulus Principle
  • Sequences and Series of Numbers
  • Sequences and Series of Functions
  • Power Series
  • Taylor's Series
  • Laurent's Series
  • Zeros of Analytic Functions
  • Analytic Continuation
  • Symmetry and Reflection
  • Singularities and Poles I
  • Singularities and Poles II
  • Cauchy's Residue Theorem
  • Evaluation of Real Integrals by Contour Integration I
  • Evaluation of Real Integrals by Contour Integration II
  • Indented Contour Integrals
  • Contour Integrals Involving Multi-valued Functions
  • Summation of Series. Argument Principle and Rouch´e and Hurwitz Theorems
  • Behavior of Analytic Mappings
  • Conformal Mappings
  • Harmonic Functions
  • The Schwarz-Christoffel Transformation
  • Infinite Products
  • Weierstrass's Factorization Theorem
  • Mittag-Leffler's Theorem
  • Periodic Functions
  • The Riemann Zeta Function
  • Bieberbach's Conjecture
  • The Riemann Surface
  • Julia and Mandelbrot Sets
  • History of Complex Numbers
  • References for Further Reading
  • Index.

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