Partial differential equations and boundary value problems with Maple V:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Diego [u.a.]
Acad. Press
1998
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 628 S. graph. Darst. + 1 CD-ROM (12 cm) |
| ISBN: | 0120644754 |
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Datensatz im Suchindex
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| adam_text | PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS WITH MAPLE V
GEORGE A. ARTICOLO DEPARTMENT OF MATHEMATICAL SCIENCES RUTGERS
UNIVERSITY ACADEMIC PRESS SAN DIEGO LONDON BOSTON NEW YORK SYDNEY TOKYO
TORONTO CONTENTS PREFACE XI CHAPTER 0 BASIC REVIEW 0.1 PREPARATION FOR
MAPLE V WORKSHEETS 0.2 PREPARATION FOR LINEAR ALGEBRA 0.3 PREPARATION
FOR ORDINARY DIFFERENTIAL EQUATIONS 0.4 PREPARATION FOR PARTIAL
DIFFERENTIAL EQUATIONS 1 4 7 9 CHAPTER I ORDINARY LINEAR DIFFERENTIAL
EQUATIONS 1.1 INTRODUCTION 1.2 FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS
1.3 FIRST-ORDER INITIAL VALUE PROBLEM 1.4 SECOND-ORDER LINEAR
DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 1.5 SECOND-ORDER
LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS 1.6 FINDING A
SECOND BASIS VECTOR BY THE METHOD OF REDUCTION OF ORDER 1.7 THE
PARTICULAR SOLUTION BY THE METHOD OF VARIATION OF PARAMETERS 1.8 INITIAL
VALUE PROBLEM FOR SECOND-ORDER DIFFERENTIAL EQUATIONS 1.9 FROBENIUS
METHOD OF SERIES SOLUTIONS TO ORDINARY DIFFERENTIAL EQUATIONS 1.10
SERIES SINE AND COSINE SOLUTIONS TO THE EULER DIFFERENTIAL EQUATION 1.11
FROBENIUS SERIES SOLUTION TO THE BESSEL DIFFERENTIAL EQUATION CHAPTER
SUMMARY EXERCISES II 11 12 17 19 24 27 31 38 41 43 48 56 58 CHAPTER 2
STURM-LIOUVILLE EIGENVALUE PROBLEMS AND GENERALIZED FOURIER SERIES 65
2.1 INTRODUCTION 65 2.2 THE REGULAER STURM-LIOUVILLE EIGENVALUE PROBLEM
65 2.3 GREEN S FORMULA AND THE STATEMENT OF ORTHONORMALITY 67 2.4 THE
GENERALIZED FOURIER SERIES EXPANSION 72 2.5 EXAMPLES OF REGULAER
STURM-LIOUVILLE EIGENVALUE PROBLEMS 76 VII VIII CONTENTS 2.6 NONREGULAR
OR SINGULAR STURM-LIOUVILLE EIGENVALUE PROBLEMS 115 CHAPTER SUMMARY 130
EXERCISES 131 CHAPTER 3 THE DIFFUSION OR HEAT PARTIAL DIFFERENTIAL
EQUATION 143 3.1 INTRODUCTION 143 3.2 ONE-DIMENSIONAL DIFFUSION OPERATOR
IN RECTANGULAR COORDINATES 143 3.3 METHOD OF SEPARATION OF VARIABLES FOR
THE DIFFUSION EQUATION 145 3.4 STURM-LIOUVILLE PROBLEM FOR THE DIFFUSION
EQUATION 146 3.5 INITIAL CONDITIONS FOR THE DIFFUSION EQUATION IN
RECTANGULAR COORDINATES 149 3.6 EXAMPLE DIFFUSION PROBLEMS IN
RECTANGULAR COORDINATES 151 3.7 VERIFICATION OF SOLUTIONS * THREE-STEP
VERIFICATION PROCEDURE 165 3.8 DIFFUSION EQUATION IN THE CYLINDRICAL
COORDINATE SYSTEM 169 3.9 INITIAL CONDITIONS FOR THE DIFFUSION EQUATION
IN CYLINDRICAL COORDINATES 173 3.10 EXAMPLE DIFFUSION PROBLEMS IN
CYLINDRICAL COORDINATES 174 CHAPTER SUMMARY 182 EXERCISES 183 CHAPTER 4
THE WAVE PARTIAL DIFFERENTIAL EQUATION 193 4.1 INTRODUCTION 193 4.2
ONE-DIMENSIONAL WAVE OPERATOR IN RECTANGULAR COORDINATES 193 4.3 METHOD
OF SEPARATION OF VARIABLES FOR THE WAVE EQUATION 195 4.4 STURM-LIOUVILLE
PROBLEM FOR THE WAVE EQUATION 197 4.5 INITIAL CONDITIONS FOR THE WAVE
EQUATION IN RECTANGULAR COORDINATES 200 4.6 EXAMPLE WAVE EQUATION
PROBLEMS IN RECTANGULAR COORDINATES 203 4.7 WAVE EQUATION IN THE
CYLINDRICAL COORDINATE SYSTEM 217 4.8 INITIAL CONDITIONS FOR THE WAVE
EQUATION IN CYLINDRICAL COORDINATES 222 4.9 EXAMPLE WAVE EQUATION
PROBLEMS IN CYLINDRICAL COORDINATES 224 CHAPTER SUMMARY 233 EXERCISES
234 CHAPTER 5 THE LAPLACE PARTIAL DIFFERENTIAL EQUATION 247 5.1
INTRODUCTION 247 5.2 LAPLACE EQUATION IN THE RECTANGULAR COORDINATE
SYSTEM 248 5.3 STURM-LIOUVILLE PROBLEM FOR THE LAPLACE EQUATION IN
RECTANGULAR COORDINATES 249 5.4 EXAMPLE LAPLACE PROBLEMS IN THE
RECTANGULAR COORDINATE SYSTEM 255 5.5 LAPLACE EQUATION IN CYLINDRICAL
COORDINATES 268 CONTENTS IX 5.6 STURM-LIOUVILLE PROBLEM FOR THE LAPLACE
EQUATION IN CYLINDRICAL COORDINATES 269 5.7 EXAMPLE LAPLACE PROBLEMS IN
THE CYLINDRICAL COORDINATE SYSTEM 274 CHAPTER SUMMARY 289 EXERCISES 290
CHAPTER 6 THE DIFFUSION EQUATION IN TWO SPATIAL DIMENSIONS 301 6.1
INTRODUCTION 301 6.2 TWO-DIMENSIONAL DIFFUSION OPERATOR IN RECTANGULAR
COORDINATES 301 6.3 METHOD OF SEPARATION OF VARIABLES FOR THE DIFFUSION
EQUATION IN TWO DIMENSIONS 303 6.4 STURM-LIOUVILLE PROBLEM FOR THE
DIFFUSION EQUATION IN TWO DIMENSIONS 304 6.5 INITIAL CONDITIONS FOR THE
DIFFUSION EQUATION IN RECTANGULAR COORDINATES 308 6.6 EXAMPLE DIFFUSION
PROBLEMS IN RECTANGULAR COORDINATES 311 6.7 DIFFUSION EQUATION IN THE
CYLINDRICAL COORDINATE SYSTEM 324 6.8 INITIAL CONDITIONS FOR THE
DIFFUSION EQUATION IN CYCLINDRICAL COORDINATES 329 6.9 EXAMPLE DIFFUSION
PROBLEMS IN CYLINDRICAL COORDINATES 332 CHAPTER SUMMARY 348 EXERCISES
350 CHAPTER 7 THE WAVE EQUATION IN TWO SPATIAL DIMENSIONS 361 7.1
INTRODUCTION 361 7.2 TWO-DIMENSIONAL WAVE OPERATOR IN RECTANGULAR
COORDINATES 361 7.3 METHOD OF SEPARATION OF VARIABLES FOR THE WAVE
EQUATION 363 7.4 STURM-LIOUVILLE PROBLEM FOR THE WAVE EQUATION IN TWO
DIMENSIONS 364 7.5 INITIAL CONDITIONS FOR THE WAVE EQUATION IN
RECTANGULAR COOORDINATES 369 7.6 EXAMPLE WAVE EQUATION PROBLEMS IN
RECTANGULAR COORDINATES 371 7.7 WAVE EQUATION IN THE CYLINDRICAL
COORDINATE SYSTEM 384 7.8 INITIAL CONDITIONS FOR THE WAVE EQUATION IN
CYLINDRICAL COORDINATES 390 7.9 EXAMPLE WAVE EQUATION PROBLEMS IN
CYLINDRICAL COORDINATES 393 CHAPTER SUMMARY 408 EXERCISES 410 CHAPTER 8
NONHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS 419 8.1 INTRODUCTION 419
8.2 NONHOMOGENEOUS DIFFUSION OR HEAT EQUATION 419 8.3 INITIAL CONDITION
CONSIDERATIONS FOR THE NONHOMOGENEOUS HEAT EQUATION 428 8.4 EXAMPLE
NONHOMOGENEOUS PROBLEMS FOR THE DIFFUSION EQUATION 430 8.5
NONHOMOGENEOUS WAVE EQUATION 447 CONTENTS 8.6 INITIAL CONDITION
CONSIDERATIONS FOR THE NONHOMOGENEOUS WAVE EQUATION 456 8.7 EXAMPLE
NONHOMOGENEOUS PROBLEMS FOR THE WAVE EQUATION 458 CHAPTER SUMMARY 478
EXERCISES 480 CHAPTER 9 INFINITE AND SEMI-INFINITE SPATIAL DOMAINS 489
9.1 INTRODUCTION 489 9.2 FOURIER INTEGRAL 489 9.3 FOURIER SINE AND
COSINE INTEGRALS 492 9.4 NONHOMOGENEOUS DIFFUSION EQUATION OVER INFINITE
DOMAINS 495 9.5 CONVOLUTION INTEGRAL SOLUTION FOR THE DIFFUSION EQUATION
498 9.6 NONHOMOGENEOUS DIFFUSION EQUATION OVER SEMI-INFINITE DOMAINS 500
9.7 EXAMPLE DIFFUSION PROBLEMS OVER INFINITE AND SEMI-INFINITE DOMAINS
503 9.8 NONHOMOGENEOUS WAVE EQUATION OVER INFINITE DOMAINS 514 9.9 WAVE
EQUATION OVER SEMI-INFINITE DOMAINS 516 9.10 EXAMPLE WAVE EQUATION
PROBLEMS OVER INFINITE AND SEMI-INFINITE DOMAINS 520 9.11 LAPLACE
EQUATION OVER INFINITE AND SEMI-INFINITE DOMAINS 530 9.12 EXAMPLE
LAPLACE EQUATION OVER INFINITE AND SEMI-INFINITE DOMAINS 535 CHAPTER
SUMMARY 541 EXERCISES 542 CHAPTER 10 LAPLACE TRANSFORM METHODS FOR
PARTIAL DIFFERENTIAL EQUATIONS 557 10.1 INTRODUCTION 557 10.2 LAPLACE
TRANSFORM OPERATOR 557 10.3 INVERSE TRANSFORM AND CONVOLUTION INTEGRAL
559 10.4 LAPLACE TRANSFORM PROCEDURES ON THE DIFFUSION EQUATION 560 10.5
EXAMPLE LAPLACE TRANSFORM PROBLEMS FOR THE DIFFUSION EQUATION 564 10.6
LAPLACE TRANSFORM PROCEDURES ON THE WAVE EQUATION 582 10.7 EXAMPLE
LAPLACE TRANSFORM PROBLEMS FOR THE WAVE EQUATION 586 CHAPTER SUMMARY 606
EXERCISES 608 SELECTED REFERENCES ON PARTIAL DIFFERENTIAL EQUATIONS 621
SELECTED REFERENCES ON MAPLE V 623 INDEX 625
|
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| indexdate | 2024-07-09T18:21:18Z |
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| isbn | 0120644754 |
| language | English |
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| spelling | Articolo, George A. Verfasser aut Partial differential equations and boundary value problems with Maple V George A. Articolo San Diego [u.a.] Acad. Press 1998 XII, 628 S. graph. Darst. + 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Problèmes aux limites - Informatique Équations aux dérivées partielles - Informatique Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Maple V (DE-588)4276266-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s Maple V (DE-588)4276266-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008177544&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Articolo, George A. Partial differential equations and boundary value problems with Maple V Problèmes aux limites - Informatique Équations aux dérivées partielles - Informatique Partielle Differentialgleichung (DE-588)4044779-0 gnd Randwertproblem (DE-588)4048395-2 gnd Maple V (DE-588)4276266-2 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4048395-2 (DE-588)4276266-2 |
| title | Partial differential equations and boundary value problems with Maple V |
| title_auth | Partial differential equations and boundary value problems with Maple V |
| title_exact_search | Partial differential equations and boundary value problems with Maple V |
| title_full | Partial differential equations and boundary value problems with Maple V George A. Articolo |
| title_fullStr | Partial differential equations and boundary value problems with Maple V George A. Articolo |
| title_full_unstemmed | Partial differential equations and boundary value problems with Maple V George A. Articolo |
| title_short | Partial differential equations and boundary value problems with Maple V |
| title_sort | partial differential equations and boundary value problems with maple v |
| topic | Problèmes aux limites - Informatique Équations aux dérivées partielles - Informatique Partielle Differentialgleichung (DE-588)4044779-0 gnd Randwertproblem (DE-588)4048395-2 gnd Maple V (DE-588)4276266-2 gnd |
| topic_facet | Problèmes aux limites - Informatique Équations aux dérivées partielles - Informatique Partielle Differentialgleichung Randwertproblem Maple V |
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