Partial differential equations: analytical solution techniques
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London
Springer
2000
|
| Edition: | 2. ed. |
| Series: | Texts in applied mathematics
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 617 - 619 |
| Physical Description: | XI, 636 S. graph. Darst. 24 cm |
| ISBN: | 0387986057 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface vii
1. The Diffusion Equation 1
1.1. Heat Conduction 1
1.2. The Fundamental Solution 5
Problems 12
1.3. Initial Value Problem in the Infinite Domain; Superposition ... 13
Problems 16
1.4. Problems in the Semi infinite Domain; Green s Functions .... 16
1.5. Problems in the Finite Domain; Green s Functions 32
Problems 41
1.6. Higher Dimensional Problems 44
Problems 51
1.7. Burgers Equation 54
Problems 58
2. Laplace s Equation 61
2.1. Applications 61
2.2. The Two Dimensional Problem; Conformal Mapping 65
Problems 71
2.3. Fundamental Solution; Dipole Potential 74
Problems 82
2.4. Volume, Surface, and Line Distributions of Sources and Dipoles 89
Problems 101
2.5. Green s Formula and Applications 105
Problems 113
2.6. Green s and Neumann s Functions 114
Problems 126
2.7. Solutions in Terms of Integral Equations 132
x Contents
Problems 137
3. The Wave Equation 141
3.1. The Vibrating String 141
3.2. Shallow Water Waves 146
Problem 157
3.3. Compressible Flow 160
Problems 171
3.4. The One Dimensional Problem on —oo x oo 173
Problems 184
3.5. Initial and Boundary Value Problems on 0 x oo 185
Problems 201
3.6. Initial and Boundary Value Problems on 0 x 1 203
Problems 208
3.7. Effect of Lower Derivative Terms 210
Problems 214
3.8. Dispersive Waves on —oo jc oo 215
Problems 224
3.9. The Three Dimensional Wave Equation; Acoustics 227
Problems 239
4. Linear Second Order Equations with Two Independent Variables 245
4.1. Classification and Transformation to Canonical Form 245
Problems 253
4.2. The General Hyperbolic Equation 254
Problems 273
4.3. Hyperbolic Systems of Two First Order Equations 277
Problems 303
5. The Scalar Quasilinear First Order Equation 311
5.1. Conservation Laws in Two Independent Variables 311
5.2. Strict Solutions in Two Independent Variables 315
Problems 325
5.3. Weak Solutions; Shocks, Fans, and Interfaces 328
Problems 361
5.4. The Scalar Quasilinear Equation in n Independent Variables . . . 369
Problem 376
6. Nonlinear First Order Equations 377
6.1. Geometrical Optics: A Nonlinear Equation 377
6.2. Applications Leading to the Hamilton Jacobi Equation 382
Problems 412
6.3. The Nonlinear Equation 416
Contents xi
Problems 426
6.4. The Complete Integral; Solutions by Envelope Formation .... 427
Problems 438
7. Quasilinear Hyperbolic Systems 441
7.1. The Quasilinear Second Order Hyperbolic Equation 441
Problems 448
7.2. Systems of n First Order Equations 448
Problems 458
7.3. Systems of Two First Order Hyperbolic Equations 459
Problem 476
7.4. Shallow Water Waves 476
Problems 496
7.5. Compressible Flow Problems 498
Problems 510
8. Approximate Solutions by Perturbation Methods 513
8.1. Regular Perturbations 513
Problems 523
8.2. Matched Asymptotic Expansions 525
Problems 549
8.3. Multiple Scale Expansions 553
Problems 572
Appendix 577
A.I. Review of Green s Function for ODEs Using the Dirac Delta
Function 577
A.2. Review of Fourier and Laplace Transforms 588
A.3. Review of Asymptotic Expansions 601
References 617
Index 621
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013062832 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:29Z |
| institution | BVB |
| isbn | 0387986057 |
| language | English |
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| physical | XI, 636 S. graph. Darst. 24 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Kevorkian, Jirayr 1933- Verfasser (DE-588)10978068X aut Partial differential equations analytical solution techniques J. Kevorkian 2. ed. New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London Springer 2000 XI, 636 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 35 Literaturverz. S. 617 - 619 Equações diferenciais parciais larpcal Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Analytische Lösung (DE-588)4313842-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Analytische Lösung (DE-588)4313842-1 s Texts in applied mathematics 35 (DE-604)BV002476038 35 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008900609&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kevorkian, Jirayr 1933- Partial differential equations analytical solution techniques Texts in applied mathematics Equações diferenciais parciais larpcal Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Analytische Lösung (DE-588)4313842-1 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4313842-1 |
| title | Partial differential equations analytical solution techniques |
| title_auth | Partial differential equations analytical solution techniques |
| title_exact_search | Partial differential equations analytical solution techniques |
| title_full | Partial differential equations analytical solution techniques J. Kevorkian |
| title_fullStr | Partial differential equations analytical solution techniques J. Kevorkian |
| title_full_unstemmed | Partial differential equations analytical solution techniques J. Kevorkian |
| title_short | Partial differential equations |
| title_sort | partial differential equations analytical solution techniques |
| title_sub | analytical solution techniques |
| topic | Equações diferenciais parciais larpcal Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Analytische Lösung (DE-588)4313842-1 gnd |
| topic_facet | Equações diferenciais parciais Differential equations, Partial Numerical solutions Partielle Differentialgleichung Analytische Lösung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008900609&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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