Partial differential equations of applied mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1989
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
A Wiley-interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 779 S. graph. Darst. |
| ISBN: | 0471612987 |
Staff View
MARC
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| 245 | 1 | 0 | |a Partial differential equations of applied mathematics |
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Record in the Search Index
| _version_ | 1804120666240188416 |
|---|---|
| adam_text | CONTENTS
1. Random Walks and Partial Differential Equations 1
1.1. The Diffusion Equation and Brownian Motion, 2
1.2. The Telegrapher s Equation and Diffusion, 15
1.3. Laplace s Equation and Green s Function, 27
Exercises for Chapter 1, 34
2. First Order Partial Differential Equations 46
2.1. Introduction, 46
2.2. Linear First Order Partial Differential Equations, 48
2.3. Quasilinear First Order Partial Differential Equations, 63
2.4. Nonlinear First Order Partial Differential Equations, 81
Appendix: Envelopes of Curves and Surfaces, 93
Exercises for Chapter 2, 96
3. Classification of Equations and Characteristics 109
3.1. Linear Second Order Partial Differential Equations, 109
3.2. Characteristic Curves, 117
3.3. Classification of Equations in General and Their
Characteristics, 121
3.4. Formulation of Initial and Boundary Value Problems, 136
3.5. Stability Theory, Energy Conservation, and Dispersion, 139
3.6. Adjoint Differential Operators, 146
Exercises for Chapter 3, 150
4. Initial and Boundary Value Problems in Bounded Regions 163
4.1. Introduction, 163
4.2. Separation of Variables, 168
4.3. The Sturm-Liouville Problem and Fourier Series, 178
4.4. Series Solutions of Initial and Boundary Value Problems, 193
4.5. Inhomogeneous Equations: Duhamel s Principle, 201
xi
xii CONTENTS
4.6. Eigenfunction Expansions: Finite Fourier Transforms, 207
4.7. Nonlinear Stability Theory: Eigenfunction Expansions, 218
Exercises for Chapter 4, 225
5. Integral Transforms 244
5.1. Introduction, 244
5.2. One-Dimensional Fourier Transforms, 246
5.3. Fourier Sine and Cosine Transforms, 260
5.4. Higher Dimensional Fourier Transforms, 271
5.5. Hankel Transforms, 280
5.6. Laplace Transforms, 287
5.7. Asymptotic Approximation Methods for Fourier Integrals, 295
Exercises for Chapter 5, 308
6. Integral Relations 324
6.1. Integral Relations, 325
6.2. Composite Media: Discontinuous Coefficients, 329
6.3. Solutions with Discontinuous First Derivatives, 338
6.4. Weak Solutions, 342
6.5. The Integral Wave Equation, 349
6.6. Concentrated Source or Force Terms, 363
6.7. Point Sources and Fundamental Solutions, 370
6.8. Energy Integrals, 390
Exercises for Chapter 6, 396 !
7. Green s Functions 412
7.1. Integral Theorems and Green s Functions, 412
7.2. Generalized Functions, 426
7.3. Green s Functions for Bounded Regions:
Eigenfunction Expansions, 446
7.4. Green s Functions for Unbounded Regions, 467
7.5. The Method of Images, 484
Exercises for Chapter 7, 497
8. Variational and Other Methods 516
8.1. Variational Properties of Eigenvalues and Eigenfunctions, 516
8.2. The Rayleigh-Ritz Method, 536
8.3. Riemann s Method, 549
8.4. Maximum and Minimum Principles, 556
8.5. Solution Methods for Higher Order Equations and Systems, 563 i
Exercises for Chapter 8, 596
CONTENTS xiii
9. Perturbation Methods 616
9.1. Introduction, 616
9.2. Regular Perturbation Methods, 619
9.3. Singular Perturbations and Boundary Layer Theory, 647
Exercises for Chapter 9, 688
10. Asymptotic Methods 700
10.1. Equations with a Large Parameter, 700
10.2. The Propagation of Discontinuities and Singularities for
Hyperbolic Equations, 778
10.3. Asymptotic Simplification of Equations, 808
Exercises for Chapter 10, 832
Bibliography 840
Solutions to Selected Exercises 845
Index 883
|
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| id | DE-604.BV006417267 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:45:43Z |
| institution | BVB |
| isbn | 0471612987 |
| language | English |
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| physical | XIII, 779 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics A Wiley-interscience publication |
| spelling | Zauderer, Erich Verfasser aut Partial differential equations of applied mathematics 2. ed. New York u.a. Wiley 1989 XIII, 779 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics A Wiley-interscience publication Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Angewandte Mathematik (DE-588)4142443-8 s 1\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004064705&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zauderer, Erich Partial differential equations of applied mathematics Numerische Mathematik (DE-588)4042805-9 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4142443-8 (DE-588)4044779-0 |
| title | Partial differential equations of applied mathematics |
| title_auth | Partial differential equations of applied mathematics |
| title_exact_search | Partial differential equations of applied mathematics |
| title_full | Partial differential equations of applied mathematics |
| title_fullStr | Partial differential equations of applied mathematics |
| title_full_unstemmed | Partial differential equations of applied mathematics |
| title_short | Partial differential equations of applied mathematics |
| title_sort | partial differential equations of applied mathematics |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Numerische Mathematik Angewandte Mathematik Partielle Differentialgleichung |
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