Complex analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harrow
Alpha Science Internat.
2006
|
| Ausgabe: | 2. ed., 1. reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 427 S. graph. Darst. |
| ISBN: | 1842651714 |
Internformat
MARC
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| 100 | 1 | |a Karunakaran, Varadhathathachariar |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex analysis |c V. Karunakaran |
| 250 | |a 2. ed., 1. reprint. | ||
| 264 | 1 | |a Harrow |b Alpha Science Internat. |c 2006 | |
| 300 | |a X, 427 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 7 | |a Fonctions d'une variable complexe |2 ram | |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804138090893148160 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
v
Preface to the First Edition
vii
PART I: BASIC COMPLEX ANALYSIS
1.
A Bird s Eye View of the Complex Plane
1
1.1
Introduction
1
12
Mathematical Logic
2
13
Development of the Complex Number System
and Its Algebra
5
1.4
Arithmetic of the Complex Numbers
9
1.5
Geometry of the Complex Plane
11
1.6
Extended Complex Plane and the
Stereographic
Projection
17
1.7
Topology of the Complex Plane
19
1.8
One-Point Compactification and the Riemann Sphere
31
1.9
Analysis in the Complex Domain
35
1.10
Sequences and Series
51
Solved Exercises
56
Exercises
64
Notes
65
References
65
2.
Elementary Properties of Analytic Functions
66
2.1
Introduction to the Concept of an Analytic Function
66
12
Power Series
76
23
Linear Fractional Transformations
81
2.4
Exponential and Trigonometric Functions
87
Solved Exercises
92
Exercises
103
Notes
104
References
104
3.
Conformai
Mappings
105
3.1
Definition and Properties of
Conformai
Mappings
105
32
Elementary
Conformai
Mappings
114
33
Physical Applications of
Conformai
Mappings
125
X
Contents
3.4
Single-Valued Branches for
Multi-
Valued Functions
127
3.5
Elementary Riemann Surfaces
130
Solved Exercises
143
Exercises
148
Notes
149
References
150
PARTII:
COMPLEX INTEGRATION
4.
Complex Integral Calculus
152
4.
1 Basic Definition and Properties of Complex Integration
152
42
Cauchy s Theorems
158
4.3
General form of Cauchy s Theorem
172
4.4
Cauchy s Integral Formula and Its Applications
182
4.5
Singularities
204
4.6
Calculus of Residues
220
4.7
Computation of Integrals
232
4.8
Harmonic Functions
264
Solved Exercises
283
Exercises
322
Notes
326
References
331
PART III: SPECIAL TOPICS IN COMPLEX ANALYSIS
5.
Riemann Mapping Theorem
333
5.1
Riemann Mapping Theorem and Boundary Behaviour
333
52
Schwarz-Christoffel Formula
349
53
Conformai
Mappings of Doubly Connected
Regions and Regions of Finite Connectivity
356
5.4
Simply Connectedness and Equivalent Conditions
365
5.5
Analytic Automorphisms of Regions in the Complex Plane
371
5.6
Univalent
Functions Defined on the Open Unit Disc
383
5.7
A Brief History of the Bieberbach Conjecture and Its Solution
403
Solved Exercises
409
Exercises
416
Notes
417
References
420
Solved Exercises
409
Index
421
|
| adam_txt |
Contents
Preface
to the Second Edition
v
Preface to the First Edition
vii
PART I: BASIC COMPLEX ANALYSIS
1.
A Bird's Eye View of the Complex Plane
1
1.1
Introduction
1
12
Mathematical Logic
2
13
Development of the Complex Number System
and Its Algebra
5
1.4
Arithmetic of the Complex Numbers
9
1.5
Geometry of the Complex Plane
11
1.6
Extended Complex Plane and the
Stereographic
Projection
17
1.7
Topology of the Complex Plane
19
1.8
One-Point Compactification and the Riemann Sphere
31
1.9
Analysis in the Complex Domain
35
1.10
Sequences and Series
51
Solved Exercises
56
Exercises
64
Notes
65
References
65
2.
Elementary Properties of Analytic Functions
66
2.1
Introduction to the Concept of an Analytic Function
66
12
Power Series
76
23
Linear Fractional Transformations
81
2.4
Exponential and Trigonometric Functions
87
Solved Exercises
92
Exercises
103
Notes
104
References
104
3.
Conformai
Mappings
105
3.1
Definition and Properties of
Conformai
Mappings
105
32
Elementary
Conformai
Mappings
114
33
Physical Applications of
Conformai
Mappings
125
X
Contents
3.4
Single-Valued Branches for
Multi-
Valued Functions
127
3.5
Elementary Riemann Surfaces
130
Solved Exercises
143
Exercises
148
Notes
149
References
150
PARTII:
COMPLEX INTEGRATION
4.
Complex Integral Calculus
152
4.
1 Basic Definition and Properties of Complex Integration
152
42
Cauchy's Theorems
158
4.3
General form of Cauchy's Theorem
172
4.4
Cauchy's Integral Formula and Its Applications
182
4.5
Singularities
204
4.6
Calculus of Residues
220
4.7
Computation of Integrals
232
4.8
Harmonic Functions
264
Solved Exercises
283
Exercises
322
Notes
326
References
331
PART III: SPECIAL TOPICS IN COMPLEX ANALYSIS
5.
Riemann Mapping Theorem
333
5.1
Riemann Mapping Theorem and Boundary Behaviour
333
52
Schwarz-Christoffel Formula
349
53
Conformai
Mappings of Doubly Connected
Regions and Regions of Finite Connectivity
356
5.4
Simply Connectedness and Equivalent Conditions
365
5.5
Analytic Automorphisms of Regions in the Complex Plane
371
5.6
Univalent
Functions Defined on the Open Unit Disc
383
5.7
A Brief History of the Bieberbach Conjecture and Its Solution
403
Solved Exercises
409
Exercises
416
Notes
417
References
420
Solved Exercises
409
Index
421 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:19:26Z |
| indexdate | 2024-07-09T21:22:40Z |
| institution | BVB |
| isbn | 1842651714 |
| language | English |
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| spelling | Karunakaran, Varadhathathachariar Verfasser aut Complex analysis V. Karunakaran 2. ed., 1. reprint. Harrow Alpha Science Internat. 2006 X, 427 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fonctions d'une variable complexe ram Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783311&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karunakaran, Varadhathathachariar Complex analysis Fonctions d'une variable complexe ram Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Complex analysis |
| title_auth | Complex analysis |
| title_exact_search | Complex analysis |
| title_exact_search_txtP | Complex analysis |
| title_full | Complex analysis V. Karunakaran |
| title_fullStr | Complex analysis V. Karunakaran |
| title_full_unstemmed | Complex analysis V. Karunakaran |
| title_short | Complex analysis |
| title_sort | complex analysis |
| topic | Fonctions d'une variable complexe ram Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Fonctions d'une variable complexe Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783311&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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