Elementary boundary value problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1993
|
| Schriftenreihe: | Pure and applied mathematics
173 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 248 S. graph. Darst. |
| ISBN: | 0824788990 |
Internformat
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| 100 | 1 | |a Bick, Theodore A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elementary boundary value problems |c T. A. Bick |
| 264 | 1 | |a New York u.a. |b Dekker |c 1993 | |
| 300 | |a VIII, 248 S. |b graph. Darst. | ||
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| 490 | 1 | |a Pure and applied mathematics |v 173 | |
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Datensatz im Suchindex
| _version_ | 1804120919365386240 |
|---|---|
| adam_text | Contents
Preface v
1 Boundary Value Problems As Models 1
1.1 Introduction 1
1.2 One dimensional wave equation 3
1.3 Two dimensional wave equation (optional) 11
1.4 One dimensional diffusion equation 18
1.5 Three dimensional diffusion equation (optional) 23
1.6 Laplace s equation 28
1.7 Auxiliary conditions and classification 32
1.8 Some additional models 42
2 The Method of Characteristics 45
2.1 Introduction 45
2.2 General solutions—first order equations 46
2.3 Second order equations—canonical forms 55
2.4 D Alembert s solution for the vibrating string 63
3 Fourier Series 73
3.1 Introduction 73
3.2 The wave equation and Fourier sine series 74
vii
viii CONTENTS
3.3 The diffusion equation and Fourier cosine series 84
3.4 Full range series 90
3.5 Some remarks on convergence 99
4 Linear Algebra and Sturm Liouville Systems 115
4.1 Introduction 115
4.2 Some ideas from linear algebra 116
4.3 Sturm Liouville systems 123
4.4 Eigenfunction expansions 135
4.5 Bessel s equation and Bessel functions 145
4.6 Legendre s equation and Legendre polynomials 156
5 Fourier Transforms 171
5.1 Introduction 171
5.2 The Fourier transform 172
5.3 Solving BVPs with the Fourier transform 187
5.4 The Laplace and Hankel transforms 199
Appendix I A Fourier Series Theorem 215
Appendix II A Fourier Integral Theorem 225
Appendix III Proof of Theorems 3.5.2 and 3.5.3 231
Appendix IV Uniqueness Theorem for Second Order Linear ODE 235
Appendix V On the Zeros of the Bessel Functions 239
Bibliography 243
Index 245
|
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| id | DE-604.BV006642288 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:49:44Z |
| institution | BVB |
| isbn | 0824788990 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004245733 |
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| physical | VIII, 248 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Bick, Theodore A. Verfasser aut Elementary boundary value problems T. A. Bick New York u.a. Dekker 1993 VIII, 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 173 Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s DE-604 Pure and applied mathematics 173 (DE-604)BV000001885 173 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004245733&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bick, Theodore A. Elementary boundary value problems Pure and applied mathematics Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Elementary boundary value problems |
| title_auth | Elementary boundary value problems |
| title_exact_search | Elementary boundary value problems |
| title_full | Elementary boundary value problems T. A. Bick |
| title_fullStr | Elementary boundary value problems T. A. Bick |
| title_full_unstemmed | Elementary boundary value problems T. A. Bick |
| title_short | Elementary boundary value problems |
| title_sort | elementary boundary value problems |
| topic | Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004245733&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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