An Introduction to Complex Analysis

• Κύριοι συγγραφείς: Agarwal, Ravi P. (Συγγραφέας), Perera, Kanishka (Συγγραφέας), Pinelas, Sandra (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Springer US, 2011.
• Έκδοση: 1.
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functions of complex variables.; Functions of a Complex Variable.; 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...

Πίνακας περιεχομένων:

• 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.