A course in complex analysis in one variable:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
River Edge, NJ [u.a.]
World Scientific
2002
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 149 S. graph. Darst. |
| ISBN: | 981024780X |
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Record in the Search Index
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| adam_text | IMAGE 1
A COURSE IN
COMPLEX ANALYSIS IN ONE VARIABLE
MARTIN A. MOSKOWITZ PROFESSOR OF MATHEMATICS CITY UNIVERSITY OF NEW YORK
GRADUATE CENTER
118* WORLD SCIENTIFIC WL NEW JERSEY LONDON * SINE NEW JERSEY * LONDON *
SINGAPORE * HONG KONG
IMAGE 2
CONTENTS
PREFACE AND ACKNOWLEDGMENTS V
1 FIRST CONCEPTS 1
1.1 FUNDAMENTALS OF THE COMPLEX FIELD 1
1.2 HOLOMORPHIC FUNCTIONS 3
1.3 SOME IMPORTANT EXAMPLES 5
1.4 THE CAUCHY-RIEMANN EQUATIONS 10
1.5 SOME ELEMENTARY DIFFERENTIAL EQUATIONS 14
1.6 CONFORMALITY 16
1.7 POWER SERIES 18
2 INTEGRATION ALONG A CONTOUR 21
2.1 CURVES AND THEIR TRAJECTORIES 21
2.2 CHANGE OF PARAMETER AND A FUNDAMENTAL INEQUALITY . . 24 2.3 SOME
IMPORTANT EXAMPLES OF CONTOUR INTEGRATION . . .. 27
2.4 THE CAUCHY THEOREM IN SIMPLY CONNECTED DOMAINS . .. 29
2.5 SOME IMMEDIATE CONSEQUENCES OF CAUCHY S THEOREM FOR A SIMPLY
CONNECTED DOMAIN 39
3 THE MAIN CONSEQUENCES OF CAUCHY S THEOREM 43
3.1 THE CAUCHY THEOREM IN MULTIPLY CONNECTED DOMAINS AND THE PRE-RESIDUE
THEOREM 43
3.2 THE CAUCHY INTEGRAL FORMULA AND ITS CONSEQUENCES . .. 45
3.3 ANALYTICITY, TAYLOR S THEOREM AND THE IDENTITY THEOREM 53
VN
IMAGE 3
3.4 THE AREA FORMULA AND SOME CONSEQUENCES 61
3.5 APPLICATION TO SPACES OF SQUARE INTEGRABLE HOLOMORPHIC FUNCTIONS 64
3.6 SPACES OF HOLOMORPHIC FUNCTIONS AND MONTEL S THEOREM 67
3.7 THE MAXIMUM MODULUS THEOREM AND SCHWARZ LEMMA . 70
SINGULARITIES 75
4.1 CLASSIFICATION OF ISOLATED SINGULARITIES, THE THEOREMS OF RIEMANN
AND CASORATI-WEIERSTRASS 75
4.2 THE PRINCIPLE OF THE ARGUMENT 80
4.3 ROUCHE S THEOREM AND ITS CONSEQUENCES 86
4.4 THE STUDY OF A TRANSCENDENTAL EQUATION 91
4.5 LAURENT EXPANSION 94
4.6 THE CALCULATION OF RESIDUES AT AN ISOLATED SINGULARITY, THE RESIDUE
THEOREM 99
4.7 APPLICATION TO THE CALCULATION OF REAL INTEGRALS 103
4.8 A MORE GENERAL REMOVABLE SINGULARITIES THEOREM AND THE SCHWARZ
REFLECTION PRINCIPLE 108
CONFORMAL MAPPINGS 113
5.1 LINEAR FRACTIONAL TRANSFORMATIONS, EQUIVALENCE OF THE UNIT DISK AND
THE UPPER HALF PLANE 113
5.2 AUTOMORPHISM GROUPS OF THE DISK, UPPER HALF PLANE AND ENTIRE PLANE
114
5.3 ANNULI 120
5.4 THE RIEMANN MAPPING THEOREM FOR PLANAR DOMAINS . .. 123
APPLICATIONS OF COMPLEX ANALYSIS TO LIE THEORY 131
6.1 APPLICATIONS OF THE IDENTITY THEOREM: COMPLETE REDUCIBILITY OF
REPRESENTATIONS ACCORDING TO HERMANN WEYL AND THE FUNCTIONAL EQUATION
FOR THE EXPONENTIAL MAP OF A REAL LIE GROUP 131
6.2 APPLICATION OF RESIDUES: THE SURJECTIVITY OF THE EXPONENTIAL MAP FOR
U(P,Q) 134
IMAGE 4
CONTENTS
IX
6.3 APPLICATION OF LIOUVILLE S THEOREM AND THE MAXIMUM MODULUS THEOREM:
THE ZARISKI DENSITY OF CONNITE VOLUME SUBGROUPS OF COMPLEX LIE GROUPS .
. .. 138
6.4 APPLICATIONS OF THE IDENTITY THEOREM TO DIFFERENTIAL TOPOLOGY AND
LIE GROUPS 140
BIBLIOGRAPHY 143
INDEX 145
|
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| author | Moskowitz, Martin A. |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T19:04:10Z |
| institution | BVB |
| isbn | 981024780X |
| language | English |
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| physical | IX, 149 S. graph. Darst. |
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| publisher | World Scientific |
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| spelling | Moskowitz, Martin A. Verfasser (DE-588)114556628 aut A course in complex analysis in one variable Martin A. Moskowitz River Edge, NJ [u.a.] World Scientific 2002 IX, 149 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Functions of complex variables Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktionentheorie (DE-588)4018935-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009924680&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moskowitz, Martin A. A course in complex analysis in one variable Functions of complex variables Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4151278-9 |
| title | A course in complex analysis in one variable |
| title_auth | A course in complex analysis in one variable |
| title_exact_search | A course in complex analysis in one variable |
| title_full | A course in complex analysis in one variable Martin A. Moskowitz |
| title_fullStr | A course in complex analysis in one variable Martin A. Moskowitz |
| title_full_unstemmed | A course in complex analysis in one variable Martin A. Moskowitz |
| title_short | A course in complex analysis in one variable |
| title_sort | a course in complex analysis in one variable |
| topic | Functions of complex variables Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Functions of complex variables Mathematical analysis Funktionentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009924680&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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