Complex analysis: the argument principle in analysis and topology
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
John Wiley & Sons
1979
|
| Series: | A Wiley-Interscience Publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 239 Seiten graph. Darst. |
| ISBN: | 0471996718 0471996726 |
Staff View
MARC
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| 245 | 1 | 0 | |a Complex analysis |b the argument principle in analysis and topology |c A. F. Beardon, University of Cambridge |
| 264 | 1 | |a Chichester [u.a.] |b John Wiley & Sons |c 1979 | |
| 300 | |a XIII, 239 Seiten |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
PARTI ANGLES
Chapter 1 3
1.1 Sets 3
1.2 Complex numbers 6
1.3 Upper bounds 9
1.4 Square roots 12
1.5 Distance 13
Chapter 2 17
2.1 Infinite series 17
2.2 Tests for convergence 19
2.3 The Cauchy product 24
Chapter 3 28
3.1 Continuity 28
3.2 Real continuous functions. . 31
Chapter 4 35
4.1 The exponential function 35
4.2 The trigonometric functions 38
4.3 Periodicity 40
4.4 The hyperbolic functions 44
Chapters 46
5.1 The argument of a complex number 46
5.2 Logarithms 52
5.3 Exponents 55
5.4 Continuity of the logarithm 58
xii
PART II BASIC COMPLEX ANALYSIS
Chapter 6 65
6.1 Open and closed sets 65
6.2 Connected sets 69
6.3 Limits 72
6.4 Compact sets 77
6.5 Homeomorphisms 81
6.6 Uniform convergence 83
Chapter 7 87
7.1 Plane curves 87
7.2 The index of a curve 89
7.3 Properties of the index 95
Chapter 8 102
8.1 Polynomials 102
8.2 Power series Ill
8.3 Analytic functions 114
8.4 Inequalities 118
8.5 The zeros of analytic functions 124
Chapter 9 133
9.1 Derivatives 133
9.2 Line integrals 138
9.3 Inequalities 141
9.4 Chains and cycles 145
9.5 Evaluation of integrals 148
9.6 Cauchy s Theorem 159
9.7 Applications 166
Chapter 10 180
10.1 Conformal mapping 180
10.2 Stereographic projection 185
10.3 Mobius transformations 190
PART III INTERACTIONS WITH PLANE TOPOLOGY
Chapter 11 201
11.1 Simply connected domains 201
11.2 The Riemann Mapping Theorem 206
11.3 Branches of the argument 212
xiii
11.4 The Jordan Curve Theorem 218
11.5 Conformal mapping of a Jordan domain 226
Appendix 232
Bibliography 235
Index 237
|
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| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002257931 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:54Z |
| institution | BVB |
| isbn | 0471996718 0471996726 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001483826 |
| oclc_num | 3893610 |
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| physical | XIII, 239 Seiten graph. Darst. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | John Wiley & Sons |
| record_format | marc |
| series2 | A Wiley-Interscience Publication |
| spelling | Beardon, Alan F. Verfasser (DE-588)110704886 aut Complex analysis the argument principle in analysis and topology A. F. Beardon, University of Cambridge Chichester [u.a.] John Wiley & Sons 1979 XIII, 239 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience Publication Analyse (wiskunde) gtt Complexe variabelen gtt Fonctions d'une variable complexe Nombres complexes Topologie gtt Functions of complex variables Numbers, Complex Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001483826&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beardon, Alan F. Complex analysis the argument principle in analysis and topology Analyse (wiskunde) gtt Complexe variabelen gtt Fonctions d'une variable complexe Nombres complexes Topologie gtt Functions of complex variables Numbers, Complex Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Complex analysis the argument principle in analysis and topology |
| title_auth | Complex analysis the argument principle in analysis and topology |
| title_exact_search | Complex analysis the argument principle in analysis and topology |
| title_full | Complex analysis the argument principle in analysis and topology A. F. Beardon, University of Cambridge |
| title_fullStr | Complex analysis the argument principle in analysis and topology A. F. Beardon, University of Cambridge |
| title_full_unstemmed | Complex analysis the argument principle in analysis and topology A. F. Beardon, University of Cambridge |
| title_short | Complex analysis |
| title_sort | complex analysis the argument principle in analysis and topology |
| title_sub | the argument principle in analysis and topology |
| topic | Analyse (wiskunde) gtt Complexe variabelen gtt Fonctions d'une variable complexe Nombres complexes Topologie gtt Functions of complex variables Numbers, Complex Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Analyse (wiskunde) Complexe variabelen Fonctions d'une variable complexe Nombres complexes Topologie Functions of complex variables Numbers, Complex Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001483826&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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