A course in complex analysis: from basic results to advanced topics
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wiesbaden
Vieweg & Teubner
2012
|
| Edition: | 1. ed. |
| Series: | Textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Teilausg. von: Fischer, Wolfgang: Einführung in die Komplexe Analysis |
| Physical Description: | VIII, 272 S. graph. Darst. |
| ISBN: | 9783834815767 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
I. ANALYSIS IN THE COMPLEX PLANE 1
0. NOTATIONS AND BASIC CONCEPTS 1
1. HOLOMORPHIC FUNCTIONS 3
2. REAL AND COMPLEX DIFFERENTIABILITY 7
3. UNIFORM CONVERGENCE AND POWER SERIES 13
4. ELEMENTARY FUNCTIONS 18
5. INTEGRATION 24
6. SEVERAL COMPLEX VARIABLES 32
II. THE FUNDAMENTAL THEOREMS OF COMPLEX ANALYSIS 36
1. PRIMITIVE FUNCTIONS 36
2. THE CAUCHY INTEGRAL THEOREM 40
3. THE CAUCHY INTEGRAL FORMULA 44
4. POWER SERIES EXPANSIONS OF HOLOMORPHIC FUNCTIONS 48
5. CONVERGENCE THEOREMS, MAXIMUM MODULUS PRINCIPLE, OPEN MAPPING THEOREM
55
6. ISOLATED SINGULARITIES AND MEROMORPHIC FUNCTIONS 61
7. HOLOMORPHIC FUNCTIONS OF SEVERAL VARIABLES 66
III. FUNCTIONS ON THE PLANE AND ON THE SPHERE 71
1. THE RIEMANN SPHERE 71
2. POLYNOMIALS AND RATIONAL FUNCTIONS 75
3. ENTIRE FUNCTIONS 80
4. MOEBIUS TRANSFORMATIONS 82
5. LOGARITHMS, POWERS, AND ROOTS 87
6. PARTIAL FRACTION DECOMPOSITIONS 95
7. PRODUCT EXPANSIONS 102
IV. INTEGRAL FORMULAS, RESIDUES, AND APPLICATIONS 108
1. THE GENERAL CAUCHY INTEGRAL THEOREM 108
2. THE INHOMOGENEOUS CAUCHY INTEGRAL FORMULA 117
3. LAURENT DECOMPOSITION AND LAURENT EXPANSION 119
4. RESIDUES 123
5. RESIDUE CALCULUS 127
6. COUNTING ZEROS 137
7. THE WEIERSTRASS PREPARATION THEOREM 141
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1015086330
DIGITALISIERT DURCH
IMAGE 2
VM
V. NON-ELEMENTARY FUNCTIONS 148
1. THE T-FUNCTION 148
2. THE -FUNCTION AND THE PRIME NUMBER THEOREM 156
3. THE FUNCTIONAL EQUATION OF THE C-FUNCTION 167
4. ELLIPTIC FUNCTIONS 174
5. ELLIPTIC FUNCTIONS AND PLANE CUBICS 188
VI. MEROMORPHIC FUNCTIONS OF SEVERAL VARIABLES 193
1. ZERO SETS OF HOLOMORPHIC FUNCTIONS 193
2. MEROMORPHIC FUNCTIONS 195
3. THE INHOMOGENEOUS CAUCHY-RIEMANN EQUATION IN DIMENSION 1 197 4. THE
CAUCHY-RIEMANN EQUATIONS WITH COMPACT SUPPORT 199
5. THE CAUCHY-RIEMANN EQUATIONS IN A POLYDISK 201
6. PRINCIPAL PARTS: THE FIRST COUSIN PROBLEM 204
7. DIVISORS: THE SECOND COUSIN PROBLEM 207
8. MEROMORPHIC FUNCTIONS REVISITED 211
VII.HOLOMORPHIC MAPS: GEOMETRIC ASPECTS 214
1. HOLOMORPHIC AUTOMORPHISMS 214
2. THE HYPERBOLIC METRIC 218
3. HYPERBOLIC GEOMETRY 224
4. THE RIEMANN MAPPING THEOREM 236
5. HARMONIC FUNCTIONS 241
6. SCHWARZ S REFLECTION PRINCIPLE 247
7. THE MODULAR MAP A 251
8. THEOREMS OF PICARD AND MONTEL 255
HINTS AND SOLUTIONS OF SELECTED EXERCISES 258
BIBLIOGRAPHY 263
INDEX OF SYMBOLS 265
INDEX 266
|
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| dewey-full | 515.93 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.93 |
| dewey-search | 515.93 |
| dewey-sort | 3515.93 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| institution | BVB |
| isbn | 9783834815767 |
| language | English |
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| physical | VIII, 272 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| spelling | Fischer, Wolfgang 1936- Verfasser (DE-588)124653480 aut A course in complex analysis from basic results to advanced topics Wolfgang Fischer ; Ingo Lieb 1. ed. Wiesbaden Vieweg & Teubner 2012 VIII, 272 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbook Teilausg. von: Fischer, Wolfgang: Einführung in die Komplexe Analysis Funktionentheorie (DE-588)4018935-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionentheorie (DE-588)4018935-1 s DE-604 Lieb, Ingo 1939- Verfasser (DE-588)124653219 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024465987&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fischer, Wolfgang 1936- Lieb, Ingo 1939- A course in complex analysis from basic results to advanced topics Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4123623-3 |
| title | A course in complex analysis from basic results to advanced topics |
| title_auth | A course in complex analysis from basic results to advanced topics |
| title_exact_search | A course in complex analysis from basic results to advanced topics |
| title_full | A course in complex analysis from basic results to advanced topics Wolfgang Fischer ; Ingo Lieb |
| title_fullStr | A course in complex analysis from basic results to advanced topics Wolfgang Fischer ; Ingo Lieb |
| title_full_unstemmed | A course in complex analysis from basic results to advanced topics Wolfgang Fischer ; Ingo Lieb |
| title_short | A course in complex analysis |
| title_sort | a course in complex analysis from basic results to advanced topics |
| title_sub | from basic results to advanced topics |
| topic | Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Funktionentheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024465987&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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