Foundations of analysis in the complex plane:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Holt, Rinehart & Winston
1973
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 287 Seiten graph. Darst. |
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| 245 | 1 | 0 | |a Foundations of analysis in the complex plane |c Thomas MacCullough, California State University, Keith Phillips, New Mexico State University |
| 264 | 1 | |a New York, NY [u.a.] |b Holt, Rinehart & Winston |c 1973 | |
| 300 | |a X, 287 Seiten |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804120489189179392 |
|---|---|
| adam_text | Contents
PREFACE V
chapter ZERO REVIEW 1
0.1 0.9 Complex numbers 1 9
0.10 0.12 Sequences 13 16
0.13 Convergence tests for infinite series 18
0.14 Sequence of functions 25
chapter ONE INTRODUCTION TO FUNCTIONS
OF A COMPLEX VARIABLE 30
1.1 Functions on C 31
1.2 1.3 Continuity 35 36
1.4 1.5 Uniform convergence 38 40
1.6 1.15 Topological considerations 40 44
1.16 1.21 Complex differentiation 47 50
chapter TWO POWER SERIES AND THE
EXPONENTIAL FUNCTION 55
2.1 2.10 Introduction (radius of convergence,
derivatives, multiplication) 55 62
2.11 2.17 Exponential, trigonometric, and other
special functions 65 75
2.18 Convergence on the boundary 78
ix
x Contents
chapter THREE INTEGRATION 82
3.1 3.14 Integration with respect to complex
weight functions and line integrals 83 99
3.15 3.16 Examples; winding number (or index) 106 107
3.18 3.20 Fourier series 109 111
3.21 3.23 Fejer s theorem and some of its con¬
sequences 113 118
chapter FOUR CAUCHY S THEOREM 122
4.1 4.13 Cauchy s theorem for triangles and
convex regions; consequences 123 137
4.14 The Cauchy kernel and integral 143
4.15 4.22 Connectedness 146 151
4.23 4.33 Simple connectedness 153 168
chapter FIVE SINGULARITIES AND RESIDUES 174
5.1 5.3 Laurent series 174 179
5.4 5.8 Residue theorem 185 188
5.9 5.15 Argument principle and related topics 189 192
5.16 5.22 Evaluation of integrals and Fourier
transforms 193 202
5.23 Classification of isolated singularities
by growth conditions 203
chapter SIX HARMONIC FUNCTIONS 206
6.1 6.8 Harmonic conjugate and related topics 206 209
6.9 6.17 Poisson kernel and integral 215 223
6.18 6.24 Mean value property and related topics 225 228
chapter SEVEN CONFORMAL AND UNIVALENT
MAPPINGS 229
7.1 7.7 Conformal mappings—general pro¬
perties and examples 229 233
7.8 7.15 Linear fractional transformations 238 243
7.16 The Dirichlet problem for a half plane 246
7.17 7.18 Schwarz Christoffel formula 250 259
appendix A NOTATION 267
appendix B RATIONAL AND REAL NUMBERS 272
INDEX 283
|
| any_adam_object | 1 |
| author | MacCullough, Thomas A. 1975- Phillips, Keith |
| author_GND | (DE-588)1106409957 |
| author_facet | MacCullough, Thomas A. 1975- Phillips, Keith |
| author_role | aut aut |
| author_sort | MacCullough, Thomas A. 1975- |
| author_variant | t a m ta tam k p kp |
| building | Verbundindex |
| bvnumber | BV006273917 |
| classification_rvk | SK 700 |
| ctrlnum | (OCoLC)251359034 (DE-599)BVBBV006273917 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:42:54Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003964333 |
| oclc_num | 251359034 |
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| owner_facet | DE-739 DE-355 DE-BY-UBR DE-83 DE-188 |
| physical | X, 287 Seiten graph. Darst. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Holt, Rinehart & Winston |
| record_format | marc |
| spelling | MacCullough, Thomas A. 1975- Verfasser (DE-588)1106409957 aut Foundations of analysis in the complex plane Thomas MacCullough, California State University, Keith Phillips, New Mexico State University New York, NY [u.a.] Holt, Rinehart & Winston 1973 X, 287 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Phillips, Keith Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003964333&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | MacCullough, Thomas A. 1975- Phillips, Keith Foundations of analysis in the complex plane Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Foundations of analysis in the complex plane |
| title_auth | Foundations of analysis in the complex plane |
| title_exact_search | Foundations of analysis in the complex plane |
| title_full | Foundations of analysis in the complex plane Thomas MacCullough, California State University, Keith Phillips, New Mexico State University |
| title_fullStr | Foundations of analysis in the complex plane Thomas MacCullough, California State University, Keith Phillips, New Mexico State University |
| title_full_unstemmed | Foundations of analysis in the complex plane Thomas MacCullough, California State University, Keith Phillips, New Mexico State University |
| title_short | Foundations of analysis in the complex plane |
| title_sort | foundations of analysis in the complex plane |
| topic | Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003964333&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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