Complex analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Erg. bildet: Complex Analysis 2 / Eberhard Freitag |
| Physical Description: | X, 532 S. Ill., graph. Darst. |
| ISBN: | 9783540939825 |
Staff View
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Record in the Search Index
| _version_ | 1805092138280550400 |
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| adam_text |
Titel: Complex analysis
Autor: Freitag, Eberhard
Jahr: 2009
Contents
I Differential Calculus in the Complex Plane C. 9
1.1 Complex Numbers. 9
1.2 Convergent Sequences and Series. 24
1.3 Continuity. 36
1.4 Complex Derivatives . 42
1.5 The Cauchy-Riemann Differential Equations. 47
II Integral Calculus in the Complex Plane C. 69
II. 1 Complex Line Integrals. 70
11.2 The Cauchy Integral Theorem. 77
11.3 The CAUCHY Integral Formulas. 92
III Sequences and Series of Analytic Functions, the Residue
Theorem.103
111.1 Uniform Approximation .104
111.2 Power Series.109
111.3 Mapping Properties of Analytic Functions.124
111.4 Singularities of Analytic Functions.133
111.5 Laurent Decomposition.142
A Appendix to III.4 and III.5.155
111.6 The Residue Theorem.162
111.7 Applications of the Residue Theorem.170
IV Construction of Analytic Functions.191
IV.l The Gamma Function.192
IV.2 The Weierstrass Product Formula.210
IV.3 The Mittag-Leffler Partial Fraction Decomposition . 218
IV.4 The Riemann Mapping Theorem.223
A Appendix : The Homotopical Version of the Cauchy
Integral Theorem.233
B Appendix : A Homological Version of the Cauchy
Integral Theorem.239
X Contents
C Appendix : Characterizations of Elementary Domains . 244
V Elliptic Functions.251
V.I Liouville's Theorems .252
A Appendix to the Definition of the Period Lattice.259
V.2 The Weierstrass p-function.261
V.3 The Field of Elliptic Functions.267
A Appendix to Sect. V.3 : The Torus as an Algebraic Curve . 271
V.4 The Addition Theorem.278
V.5 Elliptic Integrals.284
V.6 Abel's Theorem.291
V.7 The Elliptic Modular Group.301
V.8 The Modular Function j.309
VI Elliptic Modular Forms.317
VI. 1 The Modular Group and Its Fundamental Region.318
VI.2 The fc/12-formula and the Injectivity
of the j-function.326
VI.3 The Algebra of Modular Forms.334
VI.4 Modular Forms and Theta Series.338
VI.5 Modular Forms for Congruence Groups.352
A Appendix to VI.5 : The Theta Group.363
VI.6 A Ring of Theta Functions.370
VII Analytic Number Theory.381
VII.l Sums of Four and Eight Squares.382
VII.2 Dirichlet Series.399
VII.3 Dirichlet Series with Functional Equations.408
VII.4 The Riemann Ç-function and Prime Numbers.421
VII.5 The Analytic Continuation of the ^-function.429
VII.6 A TAUBERian Theorem.436
VIII Solutions to the Exercises.449
VIII. 1 Solutions to the Exercises of Chapter 1.449
VIII.2 Solutions to the Exercises of Chapter II.459
VIII.3 Solutions to the Exercises of Chapter III.464
VIII.4 Solutions to the Exercises of Chapter IV.475
VIII.5 Solutions to the Exercises of Chapter V.482
VIII.6 Solutions to the Exercises of Chapter VI.490
VIII.7 Solutions to the Exercises of Chapter VII.498
References.^09
Symbolic Notations.519 |
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| author | Freitag, Eberhard 1942- Busam, Rolf |
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Freitag, Eberhard 1942- Verfasser (DE-588)142950017 aut Funktionentheorie Complex analysis Eberhard Freitag ; Rolf Busam 2. ed. Berlin [u.a.] Springer 2009 X, 532 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Erg. bildet: Complex Analysis 2 / Eberhard Freitag Funktionentheorie - Lehrbuch Functions of complex variables Functions of complex variables Problems, exercises, etc Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Funktionstheorie (DE-588)4301988-2 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Abelsche Funktion (DE-588)4140987-5 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionentheorie (DE-588)4018935-1 s DE-604 Riemannsche Fläche (DE-588)4049991-1 s Abelsche Funktion (DE-588)4140987-5 s Modulform (DE-588)4128299-1 s 1\p DE-604 Funktionstheorie (DE-588)4301988-2 s 2\p DE-604 Busam, Rolf Verfasser (DE-588)106822195 aut Erscheint auch als Online-Ausgabe 978-3-540-93983-2 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3253836&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017325994&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Freitag, Eberhard 1942- Busam, Rolf Complex analysis Funktionentheorie - Lehrbuch Functions of complex variables Functions of complex variables Problems, exercises, etc Riemannsche Fläche (DE-588)4049991-1 gnd Funktionstheorie (DE-588)4301988-2 gnd Modulform (DE-588)4128299-1 gnd Abelsche Funktion (DE-588)4140987-5 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4301988-2 (DE-588)4128299-1 (DE-588)4140987-5 (DE-588)4018935-1 (DE-588)4123623-3 |
| title | Complex analysis |
| title_alt | Funktionentheorie |
| title_auth | Complex analysis |
| title_exact_search | Complex analysis |
| title_full | Complex analysis Eberhard Freitag ; Rolf Busam |
| title_fullStr | Complex analysis Eberhard Freitag ; Rolf Busam |
| title_full_unstemmed | Complex analysis Eberhard Freitag ; Rolf Busam |
| title_short | Complex analysis |
| title_sort | complex analysis |
| topic | Funktionentheorie - Lehrbuch Functions of complex variables Functions of complex variables Problems, exercises, etc Riemannsche Fläche (DE-588)4049991-1 gnd Funktionstheorie (DE-588)4301988-2 gnd Modulform (DE-588)4128299-1 gnd Abelsche Funktion (DE-588)4140987-5 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Funktionentheorie - Lehrbuch Functions of complex variables Functions of complex variables Problems, exercises, etc Riemannsche Fläche Funktionstheorie Modulform Abelsche Funktion Funktionentheorie Lehrbuch |
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