Boundary value problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Press
1979
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 351 S. graph. Darst. |
| ISBN: | 0125637608 |
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MARC
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| 100 | 1 | |a Powers, David Leusch |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boundary value problems |c David L. Powers |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1979 | |
| 300 | |a XI, 351 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Mathematics | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 0 ORDINARY DIFFERENTIAL EQUATIONS
1. Ordinary differential equations 1
2. Variation of parameters 7
3. Boundary value problems 11
4. Singular boundary value problems 21
Miscellaneous exercises 26
Chapter 1 FOURIER SERIES AND INTEGRALS
1. Periodic functions and Fourier series 30
2. Arbitrary period and half-range expansions 35
3. Convergence of Fourier series 43
4. Uniform convergence 47
5. Operations on Fourier series 52
6. Mean error and convergence in mean 57
7. Numerical determination of Fourier coefficients 61
v
vi / Contents
8. Fourier integral 66
9. Complex methods 71
10. Applications of Fourier series and integrals 74
11. Comments and references 78
Miscellaneous exercises 79
Chapter 2 THE HEAT EQUATION
1. Derivation and boundary conditions 86
2. Steady-state temperatures 92
3. Example: Fixed end temperatures 98
4. Example: Insulated bar 104
5. Example: Different boundary conditions 108
6. Example: Convection 113
7. Sturm-Liouville problems 117
8. Expansion in series of eigenfunctions 123
9. Generalities on the heat conduction problem 126
10. Semi-infinite rod 130
11. Infinite rod 133
12. Comments and references 136
Miscellaneous exercises 138
Chapter 3 THE WAVE EQUATION
1. The vibrating string 143
2. Solution of the vibrating string problem 146
3. D Alembert s solution 152
4. Generalities on the one-dimensional wave equation 157
5. Estimation of eigenvalues 160
6. Wave equation in unbounded regions 163
7. References 168
Miscellaneous exercises 170
Chapter4 THE POTENTIAL EQUATION
1. Potential equation 176
2. Potential in a rectangle 179
3. Potential in a slot 184
4. Potential in a disk 188
5. Classification of partial differential equations and 192
limitations of the product method
6. Comments and references 195
Miscellaneous exercises 195
Contents / vii
Chapter 5 PROBLEMS IN SEVERAL DIMENSIONS
1. Derivation of the two-dimensional wave equation 200
2. Derivation of the two-dimensional heat equation 203
3. Solution of the two-dimensional heat equation 205
4. Problems in polar coordinates 210
5. Bessel s equation 213
6. Temperature in a cylinder 218
7. Vibrations of a circular membrane 222
8. Some applications of Bessel functions 229
9. Spherical coordinates. Legendre polynomials 234
10. References 241
Miscellaneous exercises 242
Chapter 6 LAPLACE TRANSFORM
1. Definition and elementary properties 246
2. Elementary applications. Partial fractions and 252
convolutions
3. Applications to partial differential equations 258
4. More difficult examples 265
5. Comments and references 271
Miscellaneous exercises 272
Chapter 7 NUMERICAL METHODS
1. Boundary value problems 276
2. The heat equation 283
3. Two-dimensional heat equation 287
4. Potential equation 291
5. Wave equation 296
6. References 302
Bibliography 304
Answers to Odd-Numbered Exercises 306
Index 345
|
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| id | DE-604.BV001944971 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:40Z |
| institution | BVB |
| isbn | 0125637608 |
| language | English |
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| physical | XI, 351 S. graph. Darst. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Acad. Press |
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| spelling | Powers, David Leusch Verfasser aut Boundary value problems David L. Powers 2. ed. New York [u.a.] Acad. Press 1979 XI, 351 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Problèmes aux limites Équations aux dérivées partielles Mathematik Boundary value problems Differential equations, Partial Mathematics Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001267765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Powers, David Leusch Boundary value problems Problèmes aux limites Équations aux dérivées partielles Mathematik Boundary value problems Differential equations, Partial Mathematics Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Boundary value problems |
| title_auth | Boundary value problems |
| title_exact_search | Boundary value problems |
| title_full | Boundary value problems David L. Powers |
| title_fullStr | Boundary value problems David L. Powers |
| title_full_unstemmed | Boundary value problems David L. Powers |
| title_short | Boundary value problems |
| title_sort | boundary value problems |
| topic | Problèmes aux limites Équations aux dérivées partielles Mathematik Boundary value problems Differential equations, Partial Mathematics Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Problèmes aux limites Équations aux dérivées partielles Mathematik Boundary value problems Differential equations, Partial Mathematics Randwertproblem |
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