Complex analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
2005
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 547 S. graph. Darst. 24 cm |
| ISBN: | 9783540257240 3540257241 |
Staff View
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Record in the Search Index
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| adam_text | Contents
I Differential Calculus in the Complex Plane C
1.1 Complex Numbers
1.2
1.3
1.4
1.5
II Integral Calculus in the Complex Plane C
ILI
II.2 The Cauchy Integral Theorem
113
III Sequences and Series of Analytic Functions, the Residue
Theorem
III.
111.2 Power Series
111.3 Mapping Properties for Analytic Functions
111.4 Singularities of Analytic Functions
111.5 Laurent Decomposition
A Appendix to III.4 and III.5
111.6 The Residue Theorem
III.
IV Construction of Analytic Functions
IV.l The Gamma Function
IV.2 The Wbierstrass Product Formula
IV.3 The Mittag-Leffler Partial Fraction Decomposition
IV.4 The RlEMANN Mapping Theorem
A Appendix
Integral Theorem
B Appendix
Integral Theorem
X
C Appendix :
V Elliptic Functions
V.I The LlOUVlLLB Theorems
A Appendix to the Definition of the Periods Lattice
V.2 The Weierstrass p-function
V.3 The Field of Elliptic Functions
A Appendix to Sect. V.3
V.4 The Addition Theorem
V.5 Elliptic Integrals
V.6 Abel s Theorem
V.7 The Elliptic Modular Group
V.8 The Modular Function j
VI Elliptic Modular Forms
VT.l The Modular Group and Its Fundamental Region
VI.2 The fc/12-formula and the Injectivity
of the j-function
VI.3 The Algebra of Modular Forms
VI.4 Modular Forms and Theta Series
VI.5 Modular Forms for Congruence Groups
A Appendix to VI.5
VI.6 A Ring of Theta Functions
VII
VILI
VII.2 DlRICHLET Series
VII.3 Dirichlet Series with Functional Equations
VII.4 The Riemann
VII.5 The Analytic Continuation of the C-function
VII.6 A TAUBERian Theorem
VIII Solutions to the Exercises
VIII.
VIII.2 Solutions to the Exercises of Chapter II
VIII.3 Solutions to the Exercises of Chapter III
VIII.4 Solutions to the Exercises of Chapter IV
VIII.5 Solutions to the Exercises of Chapter V
VIII.6 Solutions to the Exercises of Chapter VI
VIII.7 Solutions to the Exercises of Chapter
References
Symbolic Notations
Index
The book is especially suited for graduated students in mathematics and ad¬
vanced undergraduated students in mathematics and other sciences.
Motivating introductions, more than four hundred exercises of all levels of diffi¬
culty with hints or solutions, historical annotations, and over
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.
|
| adam_txt |
Contents
I Differential Calculus in the Complex Plane C
1.1 Complex Numbers
1.2
1.3
1.4
1.5
II Integral Calculus in the Complex Plane C
ILI
II.2 The Cauchy Integral Theorem
113
III Sequences and Series of Analytic Functions, the Residue
Theorem
III.
111.2 Power Series
111.3 Mapping Properties for Analytic Functions
111.4 Singularities of Analytic Functions
111.5 Laurent Decomposition
A Appendix to III.4 and III.5
111.6 The Residue Theorem
III.
IV Construction of Analytic Functions
IV.l The Gamma Function
IV.2 The Wbierstrass Product Formula
IV.3 The Mittag-Leffler Partial Fraction Decomposition
IV.4 The RlEMANN Mapping Theorem
A Appendix
Integral Theorem
B Appendix
Integral Theorem
X
C Appendix :
V Elliptic Functions
V.I The LlOUVlLLB Theorems
A Appendix to the Definition of the Periods Lattice
V.2 The Weierstrass p-function
V.3 The Field of Elliptic Functions
A Appendix to Sect. V.3
V.4 The Addition Theorem
V.5 Elliptic Integrals
V.6 Abel's Theorem
V.7 The Elliptic Modular Group
V.8 The Modular Function j
VI Elliptic Modular Forms
VT.l The Modular Group and Its Fundamental Region
VI.2 The fc/12-formula and the Injectivity
of the j-function
VI.3 The Algebra of Modular Forms
VI.4 Modular Forms and Theta Series
VI.5 Modular Forms for Congruence Groups
A Appendix to VI.5
VI.6 A Ring of Theta Functions
VII
VILI
VII.2 DlRICHLET Series
VII.3 Dirichlet Series with Functional Equations
VII.4 The Riemann
VII.5 The Analytic Continuation of the C-function
VII.6 A TAUBERian Theorem
VIII Solutions to the Exercises
VIII.
VIII.2 Solutions to the Exercises of Chapter II
VIII.3 Solutions to the Exercises of Chapter III
VIII.4 Solutions to the Exercises of Chapter IV
VIII.5 Solutions to the Exercises of Chapter V
VIII.6 Solutions to the Exercises of Chapter VI
VIII.7 Solutions to the Exercises of Chapter
References
Symbolic Notations
Index
The book is especially suited for graduated students in mathematics and ad¬
vanced undergraduated students in mathematics and other sciences.
Motivating introductions, more than four hundred exercises of all levels of diffi¬
culty with hints or solutions, historical annotations, and over
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. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV021300283 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:52:22Z |
| indexdate | 2024-07-09T20:35:06Z |
| institution | BVB |
| isbn | 9783540257240 3540257241 |
| language | English |
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| physical | X, 547 S. graph. Darst. 24 cm |
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| spelling | Freitag, Eberhard 1942- Verfasser (DE-588)142950017 aut Complex analysis Eberhard Freitag ; Rolf Busam Berlin ; Heidelberg ; New York Springer 2005 X, 547 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Universitext Functions of complex variables Functions of complex variables Problems, exercises, etc Funktionstheorie (DE-588)4301988-2 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Abelsche Funktion (DE-588)4140987-5 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Modulform (DE-588)4128299-1 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 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2668405&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UBRegensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014620992&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014620992&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 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 Functions of complex variables Functions of complex variables Problems, exercises, etc Funktionstheorie (DE-588)4301988-2 gnd Funktionentheorie (DE-588)4018935-1 gnd Abelsche Funktion (DE-588)4140987-5 gnd Riemannsche Fläche (DE-588)4049991-1 gnd Modulform (DE-588)4128299-1 gnd |
| subject_GND | (DE-588)4301988-2 (DE-588)4018935-1 (DE-588)4140987-5 (DE-588)4049991-1 (DE-588)4128299-1 (DE-588)4123623-3 |
| title | Complex analysis |
| title_auth | Complex analysis |
| title_exact_search | Complex analysis |
| title_exact_search_txtP | 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 | Functions of complex variables Functions of complex variables Problems, exercises, etc Funktionstheorie (DE-588)4301988-2 gnd Funktionentheorie (DE-588)4018935-1 gnd Abelsche Funktion (DE-588)4140987-5 gnd Riemannsche Fläche (DE-588)4049991-1 gnd Modulform (DE-588)4128299-1 gnd |
| topic_facet | Functions of complex variables Functions of complex variables Problems, exercises, etc Funktionstheorie Funktionentheorie Abelsche Funktion Riemannsche Fläche Modulform Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2668405&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014620992&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014620992&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT freitageberhard complexanalysis AT busamrolf complexanalysis |