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Title Details:
Complex Analysis
Authors: Papadimitrakis, Michael
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE > GENERAL PROPERTIES
Keywords:
Complex number
Complex function
Region
Stereographic projection
Contour integral
Analytic function
Cauchy-Riemman equations
Cauchy’s theorems
Power series (Taylor, Laurent)
Rotation index
Residue
Harmonic function
Dirichlet problem
Conformal mapping
Riemann’s Theorem
Simple connectivity
Description:
Abstract:
The following topics are presented in this book: complex numbers, arguments, powers, roots, exponential, logarithms, the topology of the plane, compact sets, regions, stereographic projection, contour integrals, analytic functions, Cauchy-Riemann equations, examples of analytic functions (exponential function, analytic branches of roots and of the logarithm), Cauchy’s theorems and formulas, infinite differentiability of an analytic function, Liouville’s Theorem, Maximum Principle, Morera’s Theorem, Schwarz Reflection Principle, series of numbers and functions, power series, Taylor and Laurent series, Identity Principle, Open Mapping Theorem, local behavior of an analytic function, isolated singularities, rotation index, Residue Theorem, Argument Principle, evaluation of integrals, harmonic functions, Poisson formulas, the Dirichlet problem for discs and halfplanes, the Global Cauchy’s Theorem, simply connected regions, Riemann’s Τheorem and examples of conformal mappings.
Linguistic Editors: Skordalaki, Eleftheria
Technical Editors: Papadimitrakis, Michael
Type: Undergraduate textbook
Creation Date: 11-06-2024
Item Details:
ISBN 978-618-228-258-8
License: Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0)
DOI http://dx.doi.org/10.57713/kallipos-1005
Handle http://hdl.handle.net/11419/13544
Bibliographic Reference: Papadimitrakis, M. (2024). Complex Analysis [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-1005
Language: Greek
Consists of:
1. Complex numbers
2. Basic topology of C
3. Limits and continuity of functions
4. Contour integrals
5. Analytic functions
6. Cauchy’s Theorem for closed contours in star-shaped regions
7. Series of numbers and functions, power series, Taylor series and Laurent series
8. Residues
9. Harmonic functions
10. The global Cauchy’s Theorem and simply connected regions
Number of pages 414
Publication Origin: Kallipos, Open Academic Editions
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