Verfügbarkeit: Complex variables | Technische Universität München

Complex variables: introduction and applications

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Bibliographische Detailangaben
Beteilige Person:	Ablowitz, Mark J. 1945- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge, UK [u.a.] Cambridge Univ. Press 2003
Ausgabe:	2. ed.
Schriftenreihe:	Cambridge texts in applied mathematics
Schlagwörter:	Fonctions d'une variable complexe Funções de várias variáveis complexas Matemática Functions of complex variables Komplexe Variable Funktion > Mathematik Mehrere komplexe Variable
Links:	http://www.loc.gov/catdir/toc/cam031/2002041247.html http://www.loc.gov/catdir/description/cam031/2002041247.html 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
Beschreibung:	Includes bibliographical references (p. 637-639) and index
Umfang:	xii, 647 p. graph. Darst.
ISBN:	0521534291

Internformat

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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 RIEMANNHILBERT 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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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
url	http://www.loc.gov/catdir/toc/cam031/2002041247.html http://www.loc.gov/catdir/description/cam031/2002041247.html 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
work_keys_str_mv	AT ablowitzmarkj complexvariablesintroductionandapplications AT fokasathanassioss complexvariablesintroductionandapplications

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