Introduction to complex analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2003
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 328 S. graph. Darst. |
| ISBN: | 0198525613 0198525621 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | INTRODUCTION TO COMPLEX ANALYSIS SECOND EDITION H. A. PRIESTLEY OXPORD
UNIVERSITY PRESS CONTENTS NOTATION AND TERMINOLOGY XIII 1. THE COMPLEX
PLANE 1 COMPLEX NUMBERS 1 ALGEBRA IN THE COMPLEX PLANE 3 CONJUGATION,
MODULUS, AND INEQUALITIES 7 EXERCISES 9 2. GEOMETRY IN THE COMPLEX PLANE
12 LINES AND CIRCLES 12 THE EXTENDED COMPLEX PLANE AND THE RIEMANN
SPHERE 17 MOBIUS TRANSFORMATIONS 22 EXERCISES 26 3. TOPOLOGY AND
ANALYSIS IN THE COMPLEX PLANE 30 OPEN SETS AND CLOSED SETS IN THE
COMPLEX PLANE 30 CONVEXITY AND CONNECTEDNESS 35 LIMITS AND CONTINUITY 39
EXERCISES 43 4. PATHS 47 INTRODUCING CURVES AND PATHS 47 PROPERTIES OF
PATHS AND CONTOURS 51 EXERCISES 54 5. HOLOMORPHIC FUNCTIONS 56
DIFFERENTIATION AND THE CAUCHY-RIEMANN EQUATIONS 56 HOLOMORPHIC
FUNCTIONS 59 EXERCISES 64 X CONTENTS 6. COMPLEX SERIES AND POWER SERIES
67 COMPLEX SERIES 68 POWER SERIES 71 A PROOF OF THE DIFFERENTIATION
THEOREM FOR POWER SERIES 74 EXERCISES 76 7. A CORNUCOPIA OF HOLOMORPHIC
FUNCTIONS 78 THE EXPONENTIAL FUNCTION 78 COMPLEX TRIGONOMETRIC AND
HYPERBOLIC FUNCTIONS 80 ZEROS AND PERIODICITY 83 ARGUMENT, LOGARITHMS,
AND POWERS 84 HOLOMORPHIC BRANCHES OF SOME SIMPLE MULTIFUNCTIONS 86
EXERCISES 88 8. CONFORMAL MAPPING 91 CONFORMAL MAPPING 91 SOME STANDARD
CONFORMAL MAPPINGS 95 MAPPINGS OF REGIONS BY STANDARD MAPPINGS 97
BUILDING CONFORMAL MAPPINGS 102 EXERCISES 104 9. MULTIFUNCTIONS 107
BRANCH POINTS AND MULTIBRANCHES 107 CUTS AND HOLOMORPHIC BRANCHES 112
EXERCISES 118 10. INTEGRATION IN THE COMPLEX PLANE 119 INTEGRATION ALONG
PATHS 119 THE FUNDAMENTAL THEOREM OF CALCULUS 124 EXERCISES 126 11.
CAUCHY S THEOREM: BASIC TRACK 128 CAUCHY S THEOREM 129 DEFORMATION 134
LOGARITHMS AGAIN 137 EXERCISES 140 12. CAUCHY S THEOREM: ADVANCED TRACK
142 DEFORMATION AND HOMOTOPY 142 HOLOMORPHIC FUNCTIONS IN SIMPLY
CONNECTED REGIONS 145 ARGUMENT AND INDEX 146 CAUCHY S THEOREM REVISITED
149 EXERCISES J 150 CONTENTS XI 13. CAUCHY S FORMULAE 151 CAUCHY S
INTEGRAL FORMULA 151 HIGHER-ORDER DERIVATIVES 154 EXERCISES 159 14.
POWER SERIES REPRESENTATION 161 INTEGRATION OF SERIES IN GENERAL AND
POWER SERIES IN PARTICULAR 161 TAYLOR S THEOREM 163 MULTIPLICATION OF
POWER SERIES 167 A PRIMER ON UNIFORM CONVERGENCE 168 EXERCISES 174 15.
ZEROS OF HOLOMORPHIC FUNCTIONS 176 CHARACTERIZING ZEROS 176 THE IDENTITY
THEOREM AND THE UNIQUENESS THEOREM 178 COUNTING ZEROS 183 EXERCISES 185
16. HOLOMORPHIC FUNCTIONS: FURTHER THEORY 188 THE MAXIMUM MODULUS
THEOREM 188 HOLOMORPHIC MAPPINGS 189 EXERCISES 192 17. SINGULARITIES 194
LAURENT S THEOREM 194 SINGULARITIES 200 MEROMORPHIC FUNCTIONS 205
EXERCISES 207 18. CAUCHY S RESIDUE THEOREM 211 RESIDUES AND CAUCHY S
RESIDUE THEOREM 211 CALCULATION OF RESIDUES 213 EXERCISES 219 19. A
TECHNICAL TOOLKIT FOR CONTOUR INTEGRATION 221 EVALUATING REAL INTEGRALS
BY CONTOUR INTEGRATION 221 INEQUALITIES AND LIMITS 223 ESTIMATION
TECHNIQUES 225 IMPROPER AND PRINCIPAL-VALUE INTEGRALS 229 EXERCISES 232
20. APPLICATIONS OF CONTOUR INTEGRATION 234 INTEGRALS OF RATIONAL
FUNCTIONS 234 INTEGRALS OF OTHER FUNCTIONS WITH A FINITE NUMBER OF POLES
237 XII CONTENTS INTEGRALS INVOLVING FUNCTIONS WITH INFINITELY MANY
POLES 241 INTEGRALS INVOLVING MULTIFUNCTIONS 243 EVALUATION OF DEFINITE
INTEGRALS: OVERVIEW (BASIC TRACK) 245 SUMMATION OF SERIES 247 FURTHER
TECHNIQUES 248 EXERCISES 251 21. THE LAPLACE TRANSFORM 256 BASIC
PROPERTIES AND EVALUATION OF LAPLACE TRANSFORMS 256 INVERSION OF LAPLACE
TRANSFORMS 259 APPLICATIONS 267 EXERCISES 274 22. THE FOURIER TRANSFORM
278 INTRODUCING THE FOURIER TRANSFORM 278 EVALUATION AND INVERSION 280
APPLICATIONS 282 EXERCISES 287 23. HARMONIC FUNCTIONS AND CONFORMAL
MAPPING 289 HARMONIC FUNCTIONS 289 THE DIRICHLET PROBLEM AND ITS
SOLUTION BY CONFORMAL MAPPING 296 FURTHER EXAMPLES OF CONFORMAL MAPPING
299 EXERCISES 306 APPENDIX: NEW PERSPECTIVES 309 THE PRIME NUMBER
THEOREM 309 THE BIEBERBACH CONJECTURE 313 JULIA SETS AND THE MANDELBROT
SET 314 BIBLIOGRAPHY 319 NOTATION INDEX 321 INDEX 323
|
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 700 |
| ctrlnum | (OCoLC)51965018 (DE-599)BVBBV016460453 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T19:10:46Z |
| institution | BVB |
| isbn | 0198525613 0198525621 |
| language | English |
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| physical | XII, 328 S. graph. Darst. |
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| spelling | Priestley, Hilary A. Verfasser aut Introduction to complex analysis H. A. Priestley 2. ed. Oxford [u.a.] Oxford Univ. Press 2003 XII, 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Functions of complex variables Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010177404&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Priestley, Hilary A. Introduction to complex analysis Functions of complex variables Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Introduction to complex analysis |
| title_auth | Introduction to complex analysis |
| title_exact_search | Introduction to complex analysis |
| title_full | Introduction to complex analysis H. A. Priestley |
| title_fullStr | Introduction to complex analysis H. A. Priestley |
| title_full_unstemmed | Introduction to complex analysis H. A. Priestley |
| title_short | Introduction to complex analysis |
| title_sort | introduction to complex analysis |
| topic | Functions of complex variables Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Functions of complex variables Mathematical analysis Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010177404&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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