Introduction to analytic functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley Publishing Company
1966
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| Series: | Addison-Wesley Series in Mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 212 Seiten graph. Darst. |
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| 245 | 1 | 0 | |a Introduction to analytic functions |c Wilfred Kaplan, University of Michigan |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley Publishing Company |c 1966 | |
| 300 | |a IX, 212 Seiten |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Chapter 1 D Complex Numbers
1 1 The complex number system 1
1 2 Polar form of complex numbers 4
1 3 The exponential function 6
1 4 Sequences and series of complex numbers 8
Chapter 2 D Functions of a Complex Variable
2 1 Concept of complex function 14
2 2 Limits and continuity 16
2 3 Sequences and series of functions 19
2 4 Derivatives and differentials 22
2 5 Integrals 28
Chapter 3 D Analytic Functions
3 1 Analytic functions. Cauchy Riemann equations ... 35
3 2 Integrals of analytic functions. Cauchy
integral theorem 42
3 3 Change of variable in complex integrals 45
3 4 Elementary analytic functions 48
Chapter 4 D The Logarithm and Related Functions
4 1 Inverse functions 53
4 2 The function log z 55
4 3 The functions a , z , sin z, cos Iz 58
Chapter 5 ? Power Series
5 1 Power series as analytic functions 62
5 2 Cauchy s theorem for multiply connected domains . . 69
vii
Viii CONTENTS
5 3 Cauchy s integral formula 70
5 4 Power series expansion of general analytic function . . 72
5 5 Properties of real and imaginary parts
of analytic functions 78
5 6 Poisson integral formula 80
Chapter 6 D Laurent Series and Residues
6 1 Power series in positive and negative powers.
Laurent expansion 88
6 2 Isolated singularities of an analytic function.
Zeros and poles 91
6 3 The complex number °o 94
6 4 Residues 101
6 5 Residue at infinity 107
6 6 Logarithmic residues argument principle 110
6 7 Application of residues to evaluation of real integrals . . 116
Chapter 7 ? Conformal Mapping
7 1 Definition of conformal mapping 122
7 2 Examples of conformal mapping 125
7 3 Applications of conformal mapping.
The Dirichlet problem 135
7 4 Dirichlet problem for the half plane 137
7 5 Conformal mapping in hydrodynamics 146
7 6 Applications of conformal mapping in the
theory of elasticity 148
7 7 Further applications of conformal mapping 150
7 8 General formulas for one to one mapping.
Schwarz Christoffel transformation 152
CONTENTS ix
Chapter 8 D Analytic Continuation and Riemann Surfaces
8 1 Analytic continuation 159
8 2 Riemann surfaces 162
Chapter 9 D Analytic Functions of Several Complex Variables
9 1 Introduction 165
9 2 Basic definitions 166
9 3 Cauchy integral formula. Power series expansion . . . 170
9 4 Convergence region for power series 176
9 5 Laurent expansion 184
9 6 Analytic continuation 189
9 7 Zeros of analytic functions 195
9 8 Singularities of analytic functions 200
Bibliography 205
Index 209
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| any_adam_object | 1 |
| author | Kaplan, Wilfred 1915- |
| author_GND | (DE-588)1145433146 |
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| author_sort | Kaplan, Wilfred 1915- |
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| dewey-full | 517.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.8 |
| dewey-search | 517.8 |
| dewey-sort | 3517.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003713059 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:15Z |
| institution | BVB |
| language | English |
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| physical | IX, 212 Seiten graph. Darst. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Addison-Wesley Publishing Company |
| record_format | marc |
| series2 | Addison-Wesley Series in Mathematics |
| spelling | Kaplan, Wilfred 1915- Verfasser (DE-588)1145433146 aut Introduction to analytic functions Wilfred Kaplan, University of Michigan Reading, Mass. [u.a.] Addison-Wesley Publishing Company 1966 IX, 212 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley Series in Mathematics Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002363394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaplan, Wilfred 1915- Introduction to analytic functions Analytische Funktion (DE-588)4142348-3 gnd |
| subject_GND | (DE-588)4142348-3 |
| title | Introduction to analytic functions |
| title_auth | Introduction to analytic functions |
| title_exact_search | Introduction to analytic functions |
| title_full | Introduction to analytic functions Wilfred Kaplan, University of Michigan |
| title_fullStr | Introduction to analytic functions Wilfred Kaplan, University of Michigan |
| title_full_unstemmed | Introduction to analytic functions Wilfred Kaplan, University of Michigan |
| title_short | Introduction to analytic functions |
| title_sort | introduction to analytic functions |
| topic | Analytische Funktion (DE-588)4142348-3 gnd |
| topic_facet | Analytische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002363394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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