Holdings: Integral transforms and their applications

Integral transforms and their applications:

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Bibliographic Details
Main Author:	Davies, Brian (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 2002
Edition:	3. ed.
Series:	Texts in applied mathematics 41
Subjects:	Equações integrais (análise) Métodos matemáticos da física Transformada de fourier (análise matemática) Transformada de laplace (análise) Transformada de mellin (análise) Transformations intégrales Integral transforms Integraltransformation
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 357 - 362
Physical Description:	XVII, 367 S. graph. Darst.
ISBN:	0387953140

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Record in the Search Index

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adam_text	BRIAN DAVIES INTEGRAL TRANSFORMS AND THEIR APPLICATIONS THIRD EDITION WITH 59 ILLUSTRATIONS SPRINGER 2008 AGI-INFORMATION MANAGEMENT CONSULTANTS MAY BE USED FOR PERSONAL PURPORSES ONLY OR BY LIBRARIES ASSOCIATED TO DANDELON.COM NETWORK. CONTENTS PREFACE TO THE THIRD EDITION VII PREFACE TO THE SECOND EDITION IX PREFACE TO THE FIRST EDITION XI 1 FUNCTIONS OF A COMPLEX VARIABLE 1 1.1 ANALYTIC FUNCTIONS 1 1.2 CONTOUR INTEGRATION 6 1.3 ANALYTIC CONTINUATION 9 1.4 RESIDUE THEORY 13 1.5 LOOP INTEGRALS 15 1.6 LIOUVILLE S THEOREM 18 1.7 THE FACTORIAL FUNCTION 19 1.8 RIEMANN S ZETA FUNCTION 23 2 THE LAPLACE TRANSFORM 27 2.1 THE LAPLACE INTEGRAL 27 2.2 IMPORTANT PROPERTIES 28 2.3 SIMPLE APPLICATIONS 32 2.4 ASYMPTOTIC PROPERTIES: WATSON S LEMMA 33 PROBLEMS 36 3 THE INVERSION INTEGRAL 39 3.1 THE RIEMANN-LEBESGUE LEMMA 39 CONTENTS 3.2 DIRICHLET INTEGRALS 41 3.3 THE INVERSION 42 3.4 INVERSION OF RATIONAL FUNCTIONS 44 3.5 TAYLOR SERIES EXPANSION 46 3.6 INVERSION OF MEROMORPHIC FUNCTIONS 47 3.7 INVERSIONS INVOLVING A BRANCH POINT 49 3.8 WATSON S LEMMA FOR LOOP INTEGRALS 50 3.9 ASYMPTOTIC FORMS FOR LARGE T 52 3.10 HEAVISIDE SERIES EXPANSION 53 PROBLEMS 54 ORDINARY DIFFERENTIAL EQUATIONS 57 4.1 ELEMENTARY EXAMPLES 57 4.2 HIGHER-ORDER EQUATIONS 59 4.3 TRANSFER FUNCTIONS AND BLOCK DIAGRAMS 61 4.4 EQUATIONS WITH POLYNOMIAL COEFFICIENTS 65 4.5 SIMULTANEOUS DIFFERENTIAL EQUATIONS 67 4.6 LINEAR CONTROL THEORY 72 4.7 REALIZATION OF TRANSFER FUNCTIONS 79 PROBLEMS 82 PARTIAL DIFFERENTIAL EQUATIONS I 85 5.1 HEAT DIFFUSION: SEMI-INFINITE REGION 86 5.2 FINITE THICKNESS 89 5.3 WAVE PROPAGATION 90 5.4 TRANSMISSION LINE 92 PROBLEMS 94 INTEGRAL EQUATIONS 97 6.1 CONVOLUTION EQUATIONS OF VOLTERRA TYPE 97 6.2 CONVOLUTION EQUATIONS OVER AN INFINITE RANGE 101 6.3 THE PERCUS-YEVICK EQUATION 104 PROBLEMS 107 THE FOURIER TRANSFORM 111 7.1 EXPONENTIAL, SINE, AND COSINE TRANSFORMS ILL 7.2 IMPORTANT PROPERTIES 116 7.3 SPECTRAL ANALYSIS 119 7.4 KRAMERS-KRONIG RELATIONS 121 PROBLEMS 123 PARTIAL DIFFERENTIAL EQUATIONS II 129 8.1 POTENTIAL PROBLEMS 129 8.2 WATER WAVES: BASIC EQUATIONS 132 8.3 WAVES GENERATED BY A SURFACE DISPLACEMENT 135 CONTENTS XV 8.4 WAVES GENERATED BY A PERIODIC DISTURBANCE 137 PROBLEMS 140 9 GENERALIZED FUNCTIONS 143 9.1 THE DELTA FUNCTION 143 9.2 TEST FUNCTIONS AND GENERALIZED FUNCTIONS 144 9.3 ELEMENTARY PROPERTIES 148 9.4 ANALYTIC FUNCTIONALS 153 9.5 FOURIER TRANSFORMS OF GENERALIZED FUNCTIONS 155 PROBLEMS 157 10 GREEN S FUNCTIONS 163 10.1 ONE-DIMENSIONAL GREEN S FUNCTIONS 163 10.2 GREEN S FUNCTIONS AS GENERALIZED FUNCTIONS 167 10.3 POISSON S EQUATION IN TWO DIMENSIONS 169 10.4 HELMHOLTZ S EQUATION IN TWO DIMENSIONS 173 PROBLEMS 176 11 TRANSFORMS IN SEVERAL VARIABLES 181 11.1 BASIC NOTATION AND RESULTS 181 11.2 DIFFRACTION OF SCALAR WAVES 185 11.3 RETARDED POTENTIALS OF ELECTROMAGNETISM 187 PROBLEMS 189 12 THE MELLIN TRANSFORM 195 12.1 DEFINITIONS 195 12.2 SIMPLE EXAMPLES 196 12.3 ELEMENTARY PROPERTIES 200 12.4 POTENTIAL PROBLEMS IN WEDGE-SHAPED REGIONS 202 12.5 TRANSFORMS INVOLVING POLAR COORDINATES 203 12.6 HERMITE FUNCTIONS 205 PROBLEMS 207 13 APPLICATION TO SUMS AND INTEGRALS 211 13.1 MELLIN SUMMATION FORMULA 211 13.2 A PROBLEM OF RAMANUJIN 213 13.3 ASYMPTOTIC BEHAVIOR OF POWER SERIES 215 13.4 INTEGRALS INVOLVING A PARAMETER 218 13.5 ASCENDING EXPANSIONS FOR FOURIER INTEGRALS 221 PROBLEMS 223 14 HANKEL TRANSFORMS 227 14.1 THE HANKEL TRANSFORM PAIR 227 14.2 ELEMENTARY PROPERTIES 230 14.3 SOME EXAMPLES 231 14.4 BOUNDARY-VALUE PROBLEMS 232 XVI CONTENTS 14.5 WEBER S INTEGRAL 234 14.6 THE ELECTRIFIED DISC 236 14.7 DUAL INTEGRAL EQUATIONS OF TITCHMARSH TYPE 237 14.8 ERDELYI-KOBER OPERATORS 239 PROBLEMS 242 15 INTEGRAL TRANSFORMS GENERATED BY GREEN S FUNCTIONS 249 15.1 THE BASIC FORMULA 249 15.2 FINITE INTERVALS 251 15.3 SOME SINGULAR PROBLEMS 253 15.4 KONTOROVICH-LEBEDEV TRANSFORM 256 15.5 BOUNDARY-VALUE PROBLEMS IN A WEDGE 258 15.6 DIFFRACTION OF A PULSE BY A TWO-DIMENSIONAL HALF-PLANE . . 259 PROBLEMS 262 16 THE WIENER-HOPF TECHNIQUE 265 16.1 THE SOMMERFELD DIFFRACTION PROBLEM 265 16.2 WIENER-HOPF PROCEDURE: HALF-PLANE PROBLEMS 273 16.3 INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS 274 PROBLEMS 278 17 METHODS BASED ON CAUCHY INTEGRALS 283 17.1 WIENER-HOPF DECOMPOSITION BY CONTOUR INTEGRATION .... 283 17.2 CAUCHY INTEGRALS 285 17.3 THE RIEMANN-HILBERT PROBLEM 289 17.4 PROBLEMS IN LINEAR TRANSPORT THEORY 291 17.5 THE ALBEDO PROBLEM 295 17.6 A DIFFRACTION PROBLEM 297 PROBLEMS 302 18 LAPLACE S METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS 303 18.1 LAPLACE S METHOD 303 18.2 HERMITE POLYNOMIALS 305 18.3 HERMITE FUNCTIONS 307 18.4 BESSEL FUNCTIONS: INTEGRAL REPRESENTATIONS 310 18.5 BESSEL FUNCTIONS OF THE FIRST KIND 312 18.6 FUNCTIONS OF THE SECOND AND THIRD KIND 314 18.7 POISSON AND RELATED REPRESENTATIONS 319 18.8 MODIFIED BESSEL FUNCTIONS 320 PROBLEMS 321 19 NUMERICAL INVERSION OF LAPLACE TRANSFORMS 327 19.1 GENERAL CONSIDERATIONS 327 19.2 GAVER-STEHFEST METHOD 329 19.3 MOBIUS TRANSFORMATION 331 CONTENTS XVII 19.4 USE OF CBEBYSHEV POLYNOMIALS 335 19.5 USE OF LAGUERRE POLYNOMIALS 338 19.6 REPRESENTATION BY FOURIER SERIES 343 19.7 QUOTIENT-DIFFERENCE ALGORITHM 349 19.8 TALBOT S METHOD 352 BIBLIOGRAPHY 357 INDEX 363
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isbn	0387953140
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spelling	Davies, Brian Verfasser aut Integral transforms and their applications Brian Davies 3. ed. New York [u.a.] Springer 2002 XVII, 367 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 41 Literaturverz. S. 357 - 362 Equações integrais (análise) larpcal Métodos matemáticos da física larpcal Transformada de fourier (análise matemática) larpcal Transformada de laplace (análise) larpcal Transformada de mellin (análise) larpcal Transformations intégrales Integral transforms Integraltransformation (DE-588)4027235-7 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s DE-604 Texts in applied mathematics 41 (DE-604)BV002476038 41 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Davies, Brian Integral transforms and their applications Texts in applied mathematics Equações integrais (análise) larpcal Métodos matemáticos da física larpcal Transformada de fourier (análise matemática) larpcal Transformada de laplace (análise) larpcal Transformada de mellin (análise) larpcal Transformations intégrales Integral transforms Integraltransformation (DE-588)4027235-7 gnd
subject_GND	(DE-588)4027235-7
title	Integral transforms and their applications
title_auth	Integral transforms and their applications
title_exact_search	Integral transforms and their applications
title_full	Integral transforms and their applications Brian Davies
title_fullStr	Integral transforms and their applications Brian Davies
title_full_unstemmed	Integral transforms and their applications Brian Davies
title_short	Integral transforms and their applications
title_sort	integral transforms and their applications
topic	Equações integrais (análise) larpcal Métodos matemáticos da física larpcal Transformada de fourier (análise matemática) larpcal Transformada de laplace (análise) larpcal Transformada de mellin (análise) larpcal Transformations intégrales Integral transforms Integraltransformation (DE-588)4027235-7 gnd
topic_facet	Equações integrais (análise) Métodos matemáticos da física Transformada de fourier (análise matemática) Transformada de laplace (análise) Transformada de mellin (análise) Transformations intégrales Integral transforms Integraltransformation
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV002476038
work_keys_str_mv	AT daviesbrian integraltransformsandtheirapplications

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