Holdings: Green's functions with applications

Green's functions with applications:

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Bibliographic Details
Main Author:	Duffy, Dean G. (Author)
Format:	Book
Language:	English
Published:	Boca Raton, Fla. Chapman & Hall/CRC 2001
Series:	Studies in advanced mathematics
Subjects:	Green, Fonctions de Green's functions Mathematische Physik Randwertproblem Green-Funktion
Online Access:	Inhaltsverzeichnis
Physical Description:	443 S. Ill., graph. Darst.
ISBN:	1584881100

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MARC


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adam_text	GREEN S FUNCTIONS WITH APPLICATIONS DEAN G. DUFFY CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS INTRODUCTION DEFINITIONS OF THE MOST COMMONLY USED FUNCTIONS 1 SOME BACKGROUND MATERIAL 1 1.1 HISTORICAL DEVELOPMENT 1 1.2 THE DIRAC DELTA FUNCTION 5 1.3 GREEN S FORMULAS 14 1.4 WHAT IS A GREEN S FUNCTION? 18 2 GREEN S FUNCTIONS FOR ORDINARY DIFFERENTIAL EQUATIONS 27 2.1 INITIAL-VALUE PROBLEMS 27 2.2 THE SUPERPOSITION INTEGRAL 33 2.3 REGULAR BOUNDARY-VALUE PROBLEMS 35 2.4 EIGENFUNCTION EXPANSION FOR REGULAR BOUNDARY-VALUE PROBLEMS 44 2.5 SINGULAR BOUNDARY-VALUE PROBLEMS 51 2.6 MAXWELL S RECIPROCITY 59 3 GREEN S FUNCTIONS FOR THE WAVE EQUATION 75 3.1 ONE-DIMENSIONAL WAVE EQUATION IN AN UNLIMITED DOMAIN 79 3.2 ONE-DIMENSIONAL WAVE EQUATION ON THE INTERVAL 0 X L 90 3.3 AXISYMMETRIC VIBRATIONS OF A CIRCULAR MEMBRANE 96 3.4 TWO-DIMENSIONAL WAVE EQUATION IN AN UNLIMITED DOMAIN 97 3.5 THREE-DIMENSIONAL WAVE EQUATION IN AN UNLIMITED DOMAIN 99 3.6 ASYMMETRIC VIBRATIONS OF A CIRCULAR MEMBRANE 108 3.7 THERMAL WAVES 113 3.8 DISCRETE WAVENUMBER REPRESENTATION 115 3.9 LEAKY MODES 117 3.10 WATER WAVES 136 4 GREEN S FUNCTION FOR THE HEAT EQUATION 177 4.1 HEAT EQUATION OVER INFINITE OR SEMI-INFINITE DOMAINS 181 4.2 HEAT EQUATION WITHIN A FINITE CARTESIAN DOMAIN 197 4.3 HEAT EQUATION WITHIN A CYLINDER 209 4.4 HEAT EQUATION WITHIN A SPHERE 222 4.5 PRODUCT SOLUTION 226 4.6 ABSOLUTE AND CONVECTIVE INSTABILITY 231 5 GREEN S FUNCTION FOR THE HELMHOLTZ EQUATION 269 5.1 FREE-SPACE GREEN S FUNCTIONS FOR HELMHOLTZ S AND POISSON S EQUATIONS 273 5.2 TWO-DIMENSIONAL POISSON S EQUATION OVER RECTANGULAR AND CIRCULAR DOMAINS 291 5.3 TWO-DIMENSIONAL HELMHOLTZ EQUATION OVER RECTANGULAR AND CIRCULAR DOMAINS 305 5.4 POISSON S AND HELMHOLTZ S EQUATIONS ON A RECTANGULAR STRIP 321 5.5 THREE-DIMENSIONAL PROBLEMS IN A HALF-SPACE 330 5.6 THREE-DIMENSIONAL POISSON S EQUATION IN A CYLINDRICAL DOMAIN 336 5.7 POISSON S EQUATION FOR A SPHERICAL DOMAIN 338 5.8 IMPROVING THE CONVERGENCE RATE OF GREEN S FUNCTIONS 344 APPENDIX A: THE FOURIER TRANSFORM 391 A.I DEFINITION AND PROPERTIES OF FOURIER TRANSFORMS 391 A.2 INVERSION OF FOURIER TRANSFORMS 393 A.3 SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS 396 A.3 SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS 398 APPENDIX B: THE LAPLACE TRANSFORM 401 B.I DEFINITION AND ELEMENTARY PROPERTIES 401 B.2 THE SHIFTING THEOREMS 404 B.3 CONVOLUTION 406 B.4 SOLUTION OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 407 B.5 INVERSION BY CONTOUR INTEGRATION 409 B.6 SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS 413 APPENDIX C: BESSEL FUNCTIONS 417 C.I BESSEL FUNCTIONS AND THEIR PROPERTIES 417 C.2 HANKEL FUNCTIONS 421 C.3 FOURIER-BESSEL SERIES 423 APPENDIX D: RELATIONSHIP BETWEEN SOLUTIONS OF HELMHOLTZ S AND LAPLACE S EQUATIONS IN CYLINDRICAL AND SPHERICAL COORDINATES 429 ANSWERS TO SOME OF THE PROBLEMS 433 INDEX 441
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illustrated	Illustrated
indexdate	2024-07-09T18:53:07Z
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isbn	1584881100
language	English
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spelling	Duffy, Dean G. Verfasser aut Green's functions with applications Dean G. Duffy Boca Raton, Fla. Chapman & Hall/CRC 2001 443 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics Green, Fonctions de Green's functions Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Green-Funktion (DE-588)4158123-4 gnd rswk-swf Green-Funktion (DE-588)4158123-4 s Randwertproblem (DE-588)4048395-2 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009472189&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	Duffy, Dean G. Green's functions with applications Green, Fonctions de Green's functions Mathematische Physik (DE-588)4037952-8 gnd Randwertproblem (DE-588)4048395-2 gnd Green-Funktion (DE-588)4158123-4 gnd
subject_GND	(DE-588)4037952-8 (DE-588)4048395-2 (DE-588)4158123-4
title	Green's functions with applications
title_auth	Green's functions with applications
title_exact_search	Green's functions with applications
title_full	Green's functions with applications Dean G. Duffy
title_fullStr	Green's functions with applications Dean G. Duffy
title_full_unstemmed	Green's functions with applications Dean G. Duffy
title_short	Green's functions with applications
title_sort	green s functions with applications
topic	Green, Fonctions de Green's functions Mathematische Physik (DE-588)4037952-8 gnd Randwertproblem (DE-588)4048395-2 gnd Green-Funktion (DE-588)4158123-4 gnd
topic_facet	Green, Fonctions de Green's functions Mathematische Physik Randwertproblem Green-Funktion
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009472189&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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