Boundary value problems of applied mathematics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
PWS Publ.
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 470, 21 S. graph. Darst. |
| ISBN: | 0534191169 |
Internformat
MARC
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| 100 | 1 | |a Troutman, John L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boundary value problems of applied mathematics |c John L. Troutman with Maurino Bautista |
| 264 | 1 | |a Boston |b PWS Publ. |c 1994 | |
| 300 | |a XI, 470, 21 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 4 | |a Boundary value problems | |
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| 700 | 1 | |a Bautista, Maurino |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006588164 | ||
Datensatz im Suchindex
| _version_ | 1804124311916642304 |
|---|---|
| adam_text | Contents
Preface ix
ijjijjj Foundations 1
0.1 Terminology and Related Properties 1
0.2 The Divergence Theorem 8
0.3 Limit Interchange: Uniform Convergence 10
Part I: Basic Theory
Jjjljj Fourier Series of Periodic Functions 17
1.1 Periodicity 17
1.2 Finite Representation; Orthogonality 20
1.3 Fourier Series 25
1.4 Symmetry Considerations 29
1.5 Convergence Results and Applications 36
1.6 Scale Change and Translation 44
1.7 Numerical Approximation 47
1.8 Convergence Theorems for Fourier Series 54
1.9 Additional Topics 67
|H| Linear Boundary Value Problems 74
2.1 Linear Operators and Equations 75
2.2 Harmonic Preview 77
7»
vi Contents
2.3 Linear Differential and Boundary Operators 85
2.4 Separation Methods 91
2.5 Scale Changes and Dimensional Considerations 104
¦9| Diffusion Problems: The Heat Equation 107
3.1 Heat Conduction 107
3.2 Auxiliary Conditions and Uniqueness 116
3.3 One Dimensional Problems 122
3.4 Nonhomogeneous Problems 135
3.5 Continuous Dependence of Solution on Auxiliary Data 142
|j||§| Steady State Problems: The Potential Equation 148
4.1 Introduction 148
4.2 Static Equilibrium of Membranes 151
4.3 Simple Two Dimensional Problems 156
4.4* Complex Methods of Solution 166
4.5 Poisson s Equation and Green Functions 177
4.6* Static Equilibrium of Elastic Solids 185
||§f§ Propagation Problems: The Wave Equation 191
5.1 Membrane Dynamics 192
5.2 Auxiliary Conditions: Uniqueness 197
5.3 Natural Vibrations 199
5.4 Forced Vibrations and Damped Vibrations; Resonance 205
5.5 Traveling Waves 211
5.6 d Alembert s Formula 215
5.7* Simple Waves and Related Nonlinear Equations 222
Part II: Extensions
HHH General Second Order Linear Equations; Systems 233
6.1 The Cauchy Problem 234
6.2 Classification 239
6.3 Applications to Electrodynamics 243
6.4 Applications to Fluid Mechanics 248
6.5* Linear and Quasilinear Systems of First Order
Equations 258
Contents vii
HII Series Methods 269
7.1 Introduction to Sturm Liouville Problems 269
7.2 Modified Fourier Series 277
7.3 Multiple Fourier Series 284
7.4 Bessel Functions and Related Series 290
7.5 Legendre Polynomials and Related Series 300
7.6 Spherical Problems 307
7.7* Finite S L Transforms 375
^9 Integral Transform Methods 322
8.1 Sine and Cosine Transforms 322
8.2 Applications 330
8.3 The Fourier Transform and Applications 340
8.4* Other Integral Transforms 349
8.5 Uniqueness of Solutions in Unbounded Regions 358
8.6* Bessel s Integral Formula and Asymptotic
Developments 363
jttEjl Sturm—Liouville Problems 371
9.1 Positive S L Problems 372
9.2 Completeness and S L Series 378
9.3 The Rayleigh Principle 387
9.4 Asymptotic Considerations 399
9.5* Representation of Discontinuous Functions 409
9.6 Multidimensional Problems 416
Appendices
A Existence and Compactness 427
B Ordinary Linear Differential Equations 431
C* Pointwise Behavior of Bessel Series 443
Answers to Selected Problems 447
Bibliography 462
Index 466
Boundary Value Problems and MAPLE
|
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009943069 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:43:39Z |
| institution | BVB |
| isbn | 0534191169 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006588164 |
| oclc_num | 29357100 |
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| owner | DE-91G DE-BY-TUM DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-11 DE-188 |
| physical | XI, 470, 21 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | PWS Publ. |
| record_format | marc |
| spelling | Troutman, John L. Verfasser aut Boundary value problems of applied mathematics John L. Troutman with Maurino Bautista Boston PWS Publ. 1994 XI, 470, 21 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physique mathématique ram Problèmes aux limites ram Boundary value problems Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s DE-188 Bautista, Maurino Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006588164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Troutman, John L. Bautista, Maurino Boundary value problems of applied mathematics Physique mathématique ram Problèmes aux limites ram Boundary value problems Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Boundary value problems of applied mathematics |
| title_auth | Boundary value problems of applied mathematics |
| title_exact_search | Boundary value problems of applied mathematics |
| title_full | Boundary value problems of applied mathematics John L. Troutman with Maurino Bautista |
| title_fullStr | Boundary value problems of applied mathematics John L. Troutman with Maurino Bautista |
| title_full_unstemmed | Boundary value problems of applied mathematics John L. Troutman with Maurino Bautista |
| title_short | Boundary value problems of applied mathematics |
| title_sort | boundary value problems of applied mathematics |
| topic | Physique mathématique ram Problèmes aux limites ram Boundary value problems Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Physique mathématique Problèmes aux limites Boundary value problems Randwertproblem |
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