| 000 | 03724nam a22004455i 4500 | ||
|---|---|---|---|
| 001 | 978-3-540-30823-2 | ||
| 003 | DE-He213 | ||
| 005 | 20161121230934.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2005 gw | s |||| 0|eng d | ||
| 020 |
_a9783540308232 _9978-3-540-30823-2 |
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| 024 | 7 |
_a10.1007/3-540-30823-7 _2doi |
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| 050 | 4 | _aQA331-355 | |
| 072 | 7 |
_aPBKD _2bicssc |
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| 072 | 7 |
_aMAT034000 _2bisacsh |
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| 082 | 0 | 4 |
_a515.9 _223 |
| 100 | 1 |
_aFreitag, Eberhard. _eauthor. |
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| 245 | 1 | 0 |
_aComplex Analysis _h[electronic resource] / _cby Eberhard Freitag, Rolf Busam. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2005. |
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| 300 |
_aX, 552p. 112 illus., 2 illus. in color. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 | _aUniversitext | |
| 505 | 0 | _aDifferential Calculus in the Complex Plane ? -- Integral Calculus in the Complex Plane ? -- Sequences and Series of Analytic Functions, the Residue Theorem -- Construction of Analytic Functions -- Elliptic Functions -- Elliptic Modular Forms -- Analytic Number Theory -- Solutions to the Exercises. | |
| 520 | _aThe guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. The first four chapters cover the essential core of complex analysis: - differentiation in C (including elementary facts about conformal mappings) - integration in C (including complex line integrals, Cauchy's Integral Theorem, and the Integral Formulas) - sequences and series of analytic functions, (isolated) singularities, Laurent series, calculus of residues - construction of analytic functions: the gamma function, Weierstrass' Factorization Theorem, Mittag-Leffler Partial Fraction Decomposition, and -as a particular highlight- the Riemann Mapping Theorem, which characterizes the simply connected domains in C. Further topics included are: - the theory of elliptic functions based on the model of K. Weierstrass (with an excursions to older approaches due to N.H. Abel and C.G.J. Jacobi using theta series) - an introduction to the theory of elliptic modular functions and elliptic modular forms - the use of complex analysis to obtain number theoretical results - a proof of the Prime Number Theorem with a weak form of the error term. The book is especially suited for graduated students in mathematics and advanced undergraduated students in mathematics and other sciences. Motivating introductions, more than four hundred exercises of all levels of difficulty with hints or solutions, historical annotations, and over 120 figures make the overall presentation very attractive. The structure of the text, including abstracts beginning each chapter and highlighting of the main results, makes this book very appropriate for self-guided study and an indispensable aid in preparing for tests. This English edition is based on the fourth forthcoming German edition. | ||
| 650 | 0 | _aMathematics. | |
| 650 | 0 | _aFunctions of complex variables. | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aFunctions of a Complex Variable. |
| 700 | 1 |
_aBusam, Rolf. _eauthor. |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783540257240 |
| 830 | 0 | _aUniversitext | |
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/3-540-30823-7 |
| 912 | _aZDB-2-SMA | ||
| 950 | _aMathematics and Statistics (Springer-11649) | ||
| 999 |
_c506178 _d506178 |
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