Title Details: | |
Complex Analysis |
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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.
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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 |
User comments | |
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