Complex variables: introduction and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Cambridge texts in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Table of contents Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 637-639) and index |
| Beschreibung: | xii, 647 p. graph. Darst. |
| ISBN: | 0521534291 |
Internformat
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| 245 | 1 | 0 | |a Complex variables |b introduction and applications |c Mark J. Ablowitz ; Athanassios S. Fokas |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge, UK [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a xii, 647 p. |b graph. Darst. | ||
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| 650 | 7 | |a Matemática |2 larpcal | |
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Datensatz im Suchindex
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| adam_text | CONTENTS SECTIONS DENOTED WITH AN ASTERISK (*) CAN BE EITHER OMITTED OR
READ INDEPENDENTLY. PREFACE PAGE XI PART I FUNDAMENTALS AND TECHNIQUES
OF COMPLEX FUNCTION THEORY 1 1 1.1 1.2 1.3 1.4 2 2.1 2.2 2.3 2.4 2.5 2.6
COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS COMPLEX NUMBERS AND THEIR
PROPERTIES ELEMENTARY FUNCTIONS AND STEREOGRAPHIC PROJECTIONS 1.2.1
ELEMENTARY FUNCTIONS 1.2.2 STEREOGRAPHIC PROJECTIONS LIMITS, CONTINUITY,
AND COMPLEX DIFFERENTIATION ELEMENTARY APPLICATIONS TO ORDINARY
DIFFERENTIAL EQUATIONS ANALYTIC FUNCTIONS AND INTEGRATION ANALYTIC
FUNCTIONS 2.1.1 THE CAUCHY-RIEMANN EQUATIONS 2.1.2 IDEAL FLUID FLOW
MULTIVALUED FUNCTIONS MORE COMPLICATED MULTIVALUED FUNCTIONS AND RIEMANN
SURFACES COMPLEX INTEGRATION CAUCHY S THEOREM CAUCHY S INTEGRAL FORMULA,
ITS 9 GENERALIZATION AND CONSEQUENCES 3 3 8 8 15 20 26 32 32 32 40 46 61
70 81 91 VLL VIII CONTENTS 2.6.1 CAUCHY S INTEGRAL FORMULA AND ITS
DERIVATIVES 91 *2.6.2 LIOUVILLE, MORERA, AND MAXIMUM-MODULUS THEOREMS 95
*2.6.3 GENERALIZED CAUCHY FORMULA AND 3 DERIVATIVES 98 *2.7 THEORETICAL
DEVELOPMENTS 105 3 SEQUENCES, SERIES, AND SINGULARITIES OF COMPLEX
FUNCTIONS 109 3.1 DEFINITIONS AND BASIC PROPERTIES OF COMPLEX SEQUENCES,
SERIES 109 3.2 TAYLOR SERIES 114 3.3 LAURENT SERIES 127 *3.4 THEORETICAL
RESULTS FOR SEQUENCES AND SERIES 137 3.5 SINGULARITIES OF COMPLEX
FUNCTIONS 144 3.5.1 ANALYTIC CONTINUATION AND NATURAL BARRIERS 152 *3.6
INFINITE PRODUCTS AND MITTAG-LEFFLER EXPANSIONS 158 *3.7 DIFFERENTIAL
EQUATIONS IN THE COMPLEX PLANE: PAINLEVE EQUATIONS 174 *3.8
COMPUTATIONAL METHODS 196 *3.8.1 LAURENT SERIES 196 *3.8.2 DIFFERENTIAL
EQUATIONS 198 4 RESIDUE CALCULUS AND APPLICATIONS OF CONTOUR INTEGRATION
206 4.1 CAUCHY RESIDUE THEOREM 206 4.2 EVALUATION OF CERTAIN DEFINITE
INTEGRALS 217 4.3 PRINCIPAL VALUE INTEGRALS AND INTEGRALS WITH BRANCH
POINTS 237 4.3.1 PRINCIPAL VALUE INTEGRALS 237 4.3.2 INTEGRALS WITH
BRANCH POINTS 245 4.4 THE ARGUMENT PRINCIPLE, ROUCHE S THEOREM 259 *4.5
FOURIER AND LAPLACE TRANSFORMS 267 *4.6 APPLICATIONS OF TRANSFORMS TO
DIFFERENTIAL EQUATIONS 285 PART II APPLICATIONS OF COMPLEX FUNCTION
THEORY 309 5 CONFORMAL MAPPINGS AND APPLICATIONS 311 5.1 INTRODUCTION
311 5.2 CONFORMAL TRANSFORMATIONS 312 5.3 CRITICAL POINTS AND INVERSE
MAPPINGS 317 5.4 PHYSICAL APPLICATIONS 322 *5.5 THEORETICAL
CONSIDERATIONS - MAPPING THEOREMS 341 CONTENTS IX 5.6 THE
SCHWARZ-CHRISTOFFEL TRANSFORMATION 345 5.7 BILINEAR TRANSFORMATIONS 366
*5.8 MAPPINGS INVOLVING CIRCULAR ARCS 382 5.9 OTHER CONSIDERATIONS 400
5.9.1 RATIONAL FUNCTIONS OF THE SECOND DEGREE 400 5.9.2 THE MODULUS OF A
QUADRILATERAL 405 *5.9.3 COMPUTATIONAL ISSUES 408 6 ASYMPTOTIC
EVALUATION OF INTEGRALS 411 6.1 INTRODUCTION 411 6.1.1 FUNDAMENTAL
CONCEPTS 412 6.1.2 ELEMENTARY EXAMPLES 418 6.2 LAPLACE TYPE INTEGRALS
422 6.2.1 INTEGRATION BY PARTS 423 6.2.2 WATSON S LEMMA 426 6.2.3
LAPLACE S METHOD 430 6.3 FOURIER TYPE INTEGRALS 439 6.3.1 INTEGRATION BY
PARTS 440 6.3.2 ANALOG OF WATSON S LEMMA 441 6.3.3 THE STATIONARY PHASE
METHOD 443 6.4 THE METHOD OF STEEPEST DESCENT 448 6.4.1 LAPLACE S METHOD
FOR COMPLEX CONTOURS 453 6.5 APPLICATIONS 474 6.6 THE STOKES PHENOMENON
488 *6.6.1 SMOOTHING OF STOKES DISCONTINUITIES 494 6.7 RELATED
TECHNIQUES 500 *6.7.1 WKB METHOD 500 *6.7.2 THE MELLIN TRANSFORM METHOD
504 7 RIEMANN-HILBERT PROBLEMS 514 7.1 INTRODUCTION 514 7.2 CAUCHY TYPE
INTEGRALS 518 7.3 SCALAR RIEMANN-HILBERT PROBLEMS 527 7.3.1 CLOSED
CONTOURS 529 7.3.2 OPEN CONTOURS 533 7.3.3 SINGULAR INTEGRAL EQUATIONS
538 7.4 APPLICATIONS OF SCALAR RIEMANN-HILBERT PROBLEMS 546 7.4.1
RIEMANN-HILBERT PROBLEMS ON THE REAL AXIS 558 7.4.2 THE FOURIER
TRANSFORM 566 7.4.3 THE RADON TRANSFORM 567 X CONTENTS *7.5 MATRIX
RIEMANN-HILBERT PROBLEMS 579 7.5.1 THE RIEMANN-HILBERT PROBLEM FOR
RATIONAL MATRICES 584 7.5.2 INHOMOGENEOUS RIEMANN*HILBERT PROBLEMS AND
SINGULAR EQUATIONS 586 7.5.3 THE RIEMANN-HILBERT PROBLEM FOR TRIANGULAR
MATRICES 587 7.5.4 SOME RESULTS ON ZERO INDICES 589 7.6 THE DBAR PROBLEM
598 7.6.1 GENERALIZED ANALYTIC FUNCTIONS 601 *7.7 APPLICATIONS OF MATRIX
RIEMANN-HILBERT PROBLEMS AND 9 PROBLEMS 604 APPENDIX A ANSWERS TO
ODD-NUMBERED EXERCISES 627 BIBLIOGRAPHY 637 INDEX 640
|
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| author | Ablowitz, Mark J. 1945- |
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| callnumber-subject | QA - Mathematics |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
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| isbn | 0521534291 |
| language | English |
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| spelling | Ablowitz, Mark J. 1945- Verfasser (DE-588)143611844 aut Complex variables introduction and applications Mark J. Ablowitz ; Athanassios S. Fokas 2. ed. Cambridge, UK [u.a.] Cambridge Univ. Press 2003 xii, 647 p. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge texts in applied mathematics Includes bibliographical references (p. 637-639) and index Fonctions d'une variable complexe Funções de várias variáveis complexas larpcal Matemática larpcal Functions of complex variables Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Mehrere komplexe Variable (DE-588)4169285-8 s 1\p DE-604 Fokas, Athanassios S. 1952- Sonstige (DE-588)113194471 oth http://www.loc.gov/catdir/toc/cam031/2002041247.html Table of contents http://www.loc.gov/catdir/description/cam031/2002041247.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013217854&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ablowitz, Mark J. 1945- Complex variables introduction and applications Fonctions d'une variable complexe Funções de várias variáveis complexas larpcal Matemática larpcal Functions of complex variables Komplexe Variable (DE-588)4164905-9 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4164905-9 (DE-588)4071510-3 (DE-588)4169285-8 |
| title | Complex variables introduction and applications |
| title_auth | Complex variables introduction and applications |
| title_exact_search | Complex variables introduction and applications |
| title_full | Complex variables introduction and applications Mark J. Ablowitz ; Athanassios S. Fokas |
| title_fullStr | Complex variables introduction and applications Mark J. Ablowitz ; Athanassios S. Fokas |
| title_full_unstemmed | Complex variables introduction and applications Mark J. Ablowitz ; Athanassios S. Fokas |
| title_short | Complex variables |
| title_sort | complex variables introduction and applications |
| title_sub | introduction and applications |
| topic | Fonctions d'une variable complexe Funções de várias variáveis complexas larpcal Matemática larpcal Functions of complex variables Komplexe Variable (DE-588)4164905-9 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Fonctions d'une variable complexe Funções de várias variáveis complexas Matemática Functions of complex variables Komplexe Variable Funktion Mathematik Mehrere komplexe Variable |
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