Fourier series, transforms, and boundary value problems:
Gespeichert in:
| Vorheriger Titel: | Hanna, J. R. Fourier series and integrals of boundary value problems |
|---|---|
| Hauptverfasser: | , |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1990
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 354 S. |
| ISBN: | 0471619833 |
Internformat
MARC
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| 100 | 1 | |a Hanna, J. R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fourier series, transforms, and boundary value problems |c J. Ray Hanna ; John H. Rowland |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1990 | |
| 300 | |a XII, 354 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 650 | 7 | |a Fourier, séries de |2 ram | |
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Fourier series | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fourier-Reihe |0 (DE-588)4155109-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fourier-Reihe |0 (DE-588)4155109-6 |D s |
| 689 | 0 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rowland, John H. |e Verfasser |4 aut | |
| 780 | 0 | 0 | |i 1. Auflage |a Hanna, J. R. |t Fourier series and integrals of boundary value problems |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002687810&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002687810 | ||
Datensatz im Suchindex
| _version_ | 1804118511034826752 |
|---|---|
| adam_text | CONTENTS
1. Linear Differential Equations 1
1.1. Linear Operators, 1
1.2. Ordinary Differential Equations, 2
1.3. Homogeneous Linear ODE with Constant Coefficients, 5
1.4. Euler s ODE, 7
1.5. Series Solutions, 8
1.6. Frobenius Method, 13
1.7. Numerical Solutions, 19
1.8. Linear PDEs, 23
1.9. Classification of a Linear PDE of Second Order, 23
1.10. Boundary Value Problems with PDEs, 24
1.11. Second Order Linear PDEs with Constant Coefficients, 26
1.12. Separation of Variables, 35
2. Orthogonal Sets of Functions 40
2.1. Orthogonality and Vectors, 40
2.2. Orthogonal Functions, 42
2.3. Complex Functions, 46
2.4. Additional Concepts of Orthogonality, 47
2.5. The Sturm Liouville Boundary Value Problem, 50
2.6. Uniform Convergence of Series, 58
2.7. Series of Orthogonal Functions, 61
2.8. Approximation by Least Squares, 64
2.9. Completeness of Sets, 65
3. Fourier Series 68
3.1. Piecewise Continuous Functions, 68
3.2. A Basic Fourier Series, 72
3.3. Even and Odd Functions, 76
ix
x CONTENTS
3.4. Fourier Sine and Cosine Series, 77
3.5. Complex Fourier Series, 80
3.6. Harmonic Analysis, 82
3.7. Uniform Convergence of Fourier Series, 89
3.8. Differentiation of Fourier Series, 92
3.9. Integration of Fourier Series, 94
3.10. Double Fourier Series, 97
4. Fourier Integrals 102
4.1. Uniform Convergence of Integrals, 102
4.2. A Generalization of the Fourier Series, 107
4.3. Fourier Sine and Cosine Integrals, 109
4.4. The Exponential Fourier Integral, 112
5. Bessel Functions 117
5.1. The Gamma Function and the Bessel Function, 117
5.2. Additional Bessel Functions, 120
5.3. Differential Equations Solvable with Bessel Functions, 122
5.4. Special Bessel Functions and Identities, 124
5.5. An Integral Form for /„(*), 130
5.6. Singular SLPs, 133
5.7. Orthogonality of Bessel Functions, 134
5.8. Orthogonal Series of Bessel Functions, 137
5.9. Bessel Functions and Cylindrical Geometry, 140
6. Legendre Polynomials 142
6.1. Solutions to the Legendre Equation, 142
6.2. Rodrigues Formula for Legendre Polynomials, 146
6.3. A Generating Function for Pn{x), 149
6.4. The Legendre Polynomial Pn(cos 6), 151
6.5. Orthogonality and Norms of Pn(x), 152
6.6. Legendre Series, 154
6.7. Legendre Polynomials and Spherical Geometry, 158
6.8. Spherical Harmonics, 161
6.9. The Generalized Legendre Equation, 162
7. Integral Transforms 168
7.1. Laplace Transforms, 168
7.2. Existence of the Transform, 169
7.3. The Gamma Function and Laplace Transforms, 170
7.4. Transforms of Derivatives, 172
7.5. Derivatives of Transforms, 172
7.6. The Inverse Laplace Transform, 173
CONTENTS xi
7.7. Solutions of ODEs and IVPs, 173
7.8. Partial Fractions, 174
7.9. The Unit Step Function, 175
7.10. Shifting Properties, 176
7.11. The Dirac Delta Function, 177
7.12. Convolution, 180
7.13. Laplace Transform Method for PDEs, 186
7.14. Finite Fourier Transforms, 189
7.15. Fourier Transforms, 191
7.16. The Discrete Fourier Transform, 197
7.17. The Fast Fourier Transform, 203
7.18. Fourier Transforms of Functions of Two Variables, 208
7.19. Hankel Transforms, 209
7.20. Legendre Transform, 214
7.21. Mellin Transform, 215
8. Application of BVPs 219
8.1. The Vibrating String, 219
8.2. Verification and Uniqueness of the Solution of the
Vibrating String Problem, 225
8.3. The Vibrating String with Two Nonhomogeneous
Conditions, 228
8.4. Longitudinal Vibrations along an Elastic Rod, 230
8.5. Heat Conduction, 236
8.6. Numerical Solution of the Heat Equation, 241
8.7. Verification and Uniqueness of the Solution for the
Heat Problem, 242
8.8. Gravitational Potential, 246
8.9. Laplace s Equation, 247
8.10. Numerical Solution of the Laplace Equation, 251
8.11. Temperature in a Circular Disk with Insulated Faces, 254
8.12. Steady State Temperature in a Right Semicircular Cylinder, 256
8.13. Harmonic Interior of a Right Circular Cylinder, 260
8.14. Steady State Temperature Distribution in a Sphere, 264
8.15. Potential for a Sphere, 267
9. Additional Applications 270
9.1. Mechanical and Electrical Oscillations, 270
9.2. The Vibrating Membrane, 273
9.3. Vibrations of a Circular Membrane Dependent on Distance
from Center, 280
9.4. The Vibrating String with an External Force, 283
9.5. Nonhomogeneous End Temperatures in a Rod, 289
9.6. A Rod with Insulated Ends, 291
xii CONTENTS
9.7. A Semi Infinite Bar, 295
9.8. An Infinite Bar, 297
9.9. Discrete Fourier Transform Solutions, 305
9.10. A Semi Infinite String, 307
9.11. A Semi Infinite String with Initial Velocity, 310
References 315
Answers to Exercises 317
Appendix 1 Selected Integrals 340
Appendix 2 Table of Laplace Transforms 342
Appendix 3 Tables of Finite Fourier Transforms 344
Appendix 4 Tables of Fourier Transforms 346
Index 349
|
| any_adam_object | 1 |
| author | Hanna, J. R. Rowland, John H. |
| author_facet | Hanna, J. R. Rowland, John H. |
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| author_sort | Hanna, J. R. |
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| bvnumber | BV004322295 |
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| callnumber-label | QA379 |
| callnumber-raw | QA379 |
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| ctrlnum | (OCoLC)20670941 (DE-599)BVBBV004322295 |
| dewey-full | 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV004322295 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:11:27Z |
| institution | BVB |
| isbn | 0471619833 |
| language | English |
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| oclc_num | 20670941 |
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| physical | XII, 354 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Hanna, J. R. Verfasser aut Fourier series, transforms, and boundary value problems J. Ray Hanna ; John H. Rowland 2. ed. New York [u.a.] Wiley 1990 XII, 354 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Fourier, séries de ram Problèmes aux limites ram Boundary value problems Fourier series Randwertproblem (DE-588)4048395-2 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s Randwertproblem (DE-588)4048395-2 s DE-604 Rowland, John H. Verfasser aut 1. Auflage Hanna, J. R. Fourier series and integrals of boundary value problems HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002687810&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hanna, J. R. Rowland, John H. Fourier series, transforms, and boundary value problems Fourier, séries de ram Problèmes aux limites ram Boundary value problems Fourier series Randwertproblem (DE-588)4048395-2 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4155109-6 |
| title | Fourier series, transforms, and boundary value problems |
| title_auth | Fourier series, transforms, and boundary value problems |
| title_exact_search | Fourier series, transforms, and boundary value problems |
| title_full | Fourier series, transforms, and boundary value problems J. Ray Hanna ; John H. Rowland |
| title_fullStr | Fourier series, transforms, and boundary value problems J. Ray Hanna ; John H. Rowland |
| title_full_unstemmed | Fourier series, transforms, and boundary value problems J. Ray Hanna ; John H. Rowland |
| title_old | Hanna, J. R. Fourier series and integrals of boundary value problems |
| title_short | Fourier series, transforms, and boundary value problems |
| title_sort | fourier series transforms and boundary value problems |
| topic | Fourier, séries de ram Problèmes aux limites ram Boundary value problems Fourier series Randwertproblem (DE-588)4048395-2 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Fourier, séries de Problèmes aux limites Boundary value problems Fourier series Randwertproblem Fourier-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002687810&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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