Partial differential equations through examples and exercises:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1997
|
| Schriftenreihe: | Kluwer texts in the mathematical sciences
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 404 S. graph Darst. |
| ISBN: | 0792347242 |
Internformat
MARC
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| 245 | 1 | 0 | |a Partial differential equations through examples and exercises |c by Endre Pap, Arpad Takači, and Djurdjica Takači |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
List of symbols xi
1 Introduction 1
1.1 Basic Notions 1
1.1.1 Preliminaries 1
1.1.2 Examples and Exercises 3
1.2 The Cauchy Kowalevskaya Theorem 12
1.2.1 Preliminaries 12
1.2.2 Examples and Exercises 13
1.3 Equations of Mathematical Physics 15
2 First Order PDEs 17
2.1 Quasi linear PDEs 17
2.1.1 Preliminaries 17
2.1.2 Examples and Exercises 18
2.2 Pfaff s Equations 32
2.2.1 Preliminaries 32
2.2.2 Examples and Exercises 33
2.3 Nonlinear First Order PDEs 35
2.3.1 Preliminaries 35
2.3.2 Examples and Exercises 38
3 Classification of the Second Order PDEs 49
3.1 Two Independent Variables 49
3.1.1 Preliminaries 49
3.1.2 Examples and Exercises 53
3.2 n Independent Variables 64
3.2.1 Preliminaries 64
3.2.2 Examples and Exercises 66
v
vi CONTENTS
3.3 Wave, Potential and Heat Equation 69
4 Hyperbolic Equations 71
4.1 Cauchy Problem for the One dimensional Wave Equation 71
4.1.1 Preliminaries 71
4.1.2 Examples and Exercises 72
4.2 Cauchy Problem for the n dimensional Wave Equation 80
4.2.1 Preliminaries 80
4.2.2 Examples and Exercises 82
4.3 The Fourier Method of Separation Variables 89
4.3.1 Preliminaries 89
4.3.2 Examples and Exercises 93
4.4 The Sturm Liouville Problem 106
4.4.1 Preliminaries 106
4.4.2 Examples and Exercises 109
4.5 Miscellaneous Problems 129
4.6 The Vibrating String 141
5 Elliptic Equations 143
5.1 Dirichlet Problem 143
5.1.1 Preliminaries 143
5.1.2 Examples and Exercises 144
5.2 The Maximum Principle 163
5.2.1 Preliminaries 163
5.2.2 Examples and Exercises 163
5.3 The Green Function 167
5.3.1 Preliminaries 167
5.3.2 Examples and Exercises 168
5.4 The Harmonic Functions 173
5.4.1 Examples and Exercises 173
5.5 Gravitational Potential 182
6 Parabolic Equations 183
6.1 Cauchy Problem 183
6.1.1 Preliminaries 183
6.1.2 Examples and Exercise 184
6.2 Mixed Type Problem 193
6.2.1 Preliminaries 193
6.2.2 Examples and Exercises 194
6.3 Heat conduction 223
CONTENTS vii
7 Numerical Methods 227
7.0.1 Preliminaries 227
7.0.2 Examples and Exercises 230
8 Lebesgue s Integral, Fourier Transform 249
8.1 Lebesgue s Integral and the L2(Q) Space 249
8.1.1 Preliminaries 249
8.1.2 Examples and Exercises 252
8.2 Delta Nets 256
8.2.1 Preliminaries 256
8.2.2 Examples and Exercises 257
8.3 The Surface Integrals 260
8.3.1 Preliminaries 260
8.3.2 Examples and Exercises 261
8.4 The Fourier Transform 267
8.4.1 Preliminaries 267
8.4.2 Examples and Exercises 269
9 Generalized Derivative and Sobolev Spaces 279
9.1 Generalized Derivative 279
9.1.1 Preliminaries 279
9.1.2 Examples and Exercises 279
9.2 Sobolev Spaces 285
9.2.1 Preliminaries 285
9.2.2 Examples and Exercises 286
10 Some Elements from Functional Analysis 303
10.1 Hilbert Space 303
10.1.1 Preliminaries 303
10.1.2 Examples and Exercises 305
10.2 The Fredholm Alternatives 313
10.2.1 Preliminaries 313
10.2.2 Examples and Exercises 314
10.3 Normed Vector Spaces 321
10.3.1 Preliminaries 321
10.3.2 Examples and Exercises 323
11 Functional Analysis Methods in PDEs 329
11.1 Generalized Dirichlet Problem 329
11.1.1 Preliminaries 329
11.1.2 Examples and Exercises 330
11.2 The Generalized Mixed Problems 355
11.2.1 Examples and Exercises 355
viii CONTENTS
1 1.3 Numerical Solutions 366
11.3.1 Preliminaries 366
11.3.2 Examples and Exercises 367
11.4 Miscellaneous 368
11.4.1 Preliminaries 368
11.4.2 Examples and Exercises 369
12 Distributions in the theory of PDEs 373
12.1 Basic Properties 373
12.1.1 Preliminaries 373
12.1.2 Examples and Exercises 376
12.2 Fundamental Solutions 390
12.2.1 Preliminaries 390
12.2.2 Examples and Exercises 390
Bibliography 397
Index 401
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:21:16Z |
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| isbn | 0792347242 |
| language | English |
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| physical | XII, 404 S. graph Darst. |
| publishDate | 1997 |
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| spelling | Pap, Endre Verfasser (DE-588)125398549 aut Partial differential equations through examples and exercises by Endre Pap, Arpad Takači, and Djurdjica Takači Dordrecht [u.a.] Kluwer Acad. Publ. 1997 XII, 404 S. graph Darst. txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 18 Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Takači, Arpad Verfasser aut Takači, Djurdjica Verfasser aut Kluwer texts in the mathematical sciences 18 (DE-604)BV005450041 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008176008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pap, Endre Takači, Arpad Takači, Djurdjica Partial differential equations through examples and exercises Kluwer texts in the mathematical sciences Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Partial differential equations through examples and exercises |
| title_auth | Partial differential equations through examples and exercises |
| title_exact_search | Partial differential equations through examples and exercises |
| title_full | Partial differential equations through examples and exercises by Endre Pap, Arpad Takači, and Djurdjica Takači |
| title_fullStr | Partial differential equations through examples and exercises by Endre Pap, Arpad Takači, and Djurdjica Takači |
| title_full_unstemmed | Partial differential equations through examples and exercises by Endre Pap, Arpad Takači, and Djurdjica Takači |
| title_short | Partial differential equations through examples and exercises |
| title_sort | partial differential equations through examples and exercises |
| topic | Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Partial Partielle Differentialgleichung |
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