Fourier series and integrals of boundary value problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1982
|
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 2. Aufl. u.d.T.: Hanna, J. R.: Fourier series, transforms, and boundary value problems. 1990 |
| Beschreibung: | XI, 271 S. |
| ISBN: | 0471081299 |
Internformat
MARC
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| 100 | 1 | |a Hanna, J. R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fourier series and integrals of boundary value problems |c J. Ray Hanna |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1982 | |
| 300 | |a XI, 271 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 500 | |a 2. Aufl. u.d.T.: Hanna, J. R.: Fourier series, transforms, and boundary value problems. 1990 | ||
| 650 | 7 | |a Fourier-reeksen |2 gtt | |
| 650 | 7 | |a Randwaardeproblemen |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Fourier Analysis | |
| 650 | 4 | |a Fourier series | |
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804114719293833216 |
|---|---|
| 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 sODE, 7
1.5 Linear PDEs, 9
1.6 Classification of a Linear PDE of Second Order, 9
1.7 Boundary Value Problems with PDEs, 10
1.8 Second Order Linear PDEs with Constant Coefficients, 12
1.9 Separation of Variables, 21
2. Orthogonal Sets of Functions 26
2.1 Orthogonality and Vectors, 26
2.2 Orthogonal Functions, 28
2.3 Complex Functions, 32
2.4 Additional Concepts of Orthogonality, 33
2.5 The Sturm Liouville Boundary Value Problem, 35
2.6 Uniform Convergence of Series, 44
2.7 Series of Orthogonal Functions, 47
2.8 Approximation by Least Squares, 49
2.9 Completeness of Sets, 51
3. Fourier Series 54
3.1 Piecewise Continuous Functions, 54
3.2 A Basic Fourier Series, 59
3.3 Even and Odd Functions, 63
3.4 Fourier Sine and Cosine Series, 63
3.5 Complex Fourier Series, 66
3.6 Uniform Convergence of Fourier Series, 72
3.7 Differentiation of Fourier Series, 76
3.8 Integration of Fourier Series, 78
3.9 Double Fourier Series, 80
3.10 Finite Fourier Transforms, 83
ix
x CONTENTS
4. Fourier Integrals 88
4.1 Uniform Convergence of Integrals, 88
4.2 A Generalization of the Fourier Series, 93
4.3 Fourier Sine and Cosine Integrals, 96
4.4 The Exponential Fourier Integral, 98
4.5 Fourier Transforms, 103
5. Mathematical Models and Boundary Value Problems 109
5.1 The Vibrating String, 109
5.2 Verification and Uniqueness of the Solution of the Vibrating
String Problem, 116
5.3 The Vibrating String with Two Nonhomogeneous
Conditions, 119
5.4 Longitudinal Vibrations Along an Elastic Rod, 121
5.5 Heat Conduction, 127
5.6 Verification and Uniqueness of the Solution for the Heat
Problem, 132
5.7 Gravitational Potential, 135
5.8 Laplace s Equation, 136
6. Continuation of Models and Boundary Value Problems 143
6.1 The Vibrating Membrane, 143
6.2 The Vibrating String with an External Force, 150
6.3 Nonhomogeneous End Temperatures in a Rod, 153
6.4 A Rod with Insulated Ends, 156
6.5 A Semi Infinite Bar, 162
6.6 An Infinite Bar, 164
6.7 A Semi Infinite String, 169
6.8 A Semi Infinite String with Initial Velocity, 172
7. Bessel Functions and Boundary Value Problems 179
7.1 Bessel s Equation, 179
7.2 The Gamma Function and the Bessel Function, 181
7.3 Additional Bessel Functions, 184
7.4 Differential Equations Solvable with Bessel Functions, 187
7.5 Special Bessel Functions and Identities, 188
7.6 An Integral Form for Jn(x), 193
7.7 Singular SLPs, 196
7.8 Orthogonality of Bessel Functions, 197
7.9 Orthogonal Series of Bessel Functions, 200
7.10 Bessel Functions and Cylindrical Geometry, 203
CONTENTS Xi
7.11 Temperature in a Circular Disk with Insulated Faces, 204
7.12 Vibrations of a Circular Membrane Dependent on Distance
from Center, 207
7.13 Steady State Temperature in a Right Semicircular
Cylinder, 209
7.14 Harmonic Interior of a Right Circular Cylinder, 213
8. Legendre Polynomials and Boundary Value Problems 218
8.1 Legendre s Differential Equation, 218
8.2 Rodrigues Formula for Legendre Polynomials, 223
8.3 A Generating Function for Pn(x), 226
8.4 The Legendre Polynomial Pn(cos0), 228
8.5 Orthogonality and Norms of Pn(x), 229
8.6 Legendre Series, 231
8.7 Legendre Polynomials and Spherical Geometry, 235
8.8 Steady State Temperature Distribution in a Sphere, 238
8.9 Potential for a Sphere, 240
8.10 The Generalized Legendre Equation, 243
References and Additional Reading 249
Answers to Exercises 251
Index 267
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T15:11:11Z |
| institution | BVB |
| isbn | 0471081299 |
| language | English |
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| physical | XI, 271 S. |
| psigel | TUB-www |
| publishDate | 1982 |
| publishDateSearch | 1982 |
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| publisher | Wiley |
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| series2 | Pure and applied mathematics |
| spelling | Hanna, J. R. Verfasser aut Fourier series and integrals of boundary value problems J. Ray Hanna New York [u.a.] Wiley 1982 XI, 271 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 2. Aufl. u.d.T.: Hanna, J. R.: Fourier series, transforms, and boundary value problems. 1990 Fourier-reeksen gtt Randwaardeproblemen gtt Mathematik Boundary value problems Fourier Analysis Fourier series Mathematics Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s 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=000153078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hanna, J. R. Fourier series and integrals of boundary value problems Fourier-reeksen gtt Randwaardeproblemen gtt Mathematik Boundary value problems Fourier Analysis Fourier series Mathematics Fourier-Reihe (DE-588)4155109-6 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4155109-6 (DE-588)4048395-2 |
| title | Fourier series and integrals of boundary value problems |
| title_auth | Fourier series and integrals of boundary value problems |
| title_exact_search | Fourier series and integrals of boundary value problems |
| title_full | Fourier series and integrals of boundary value problems J. Ray Hanna |
| title_fullStr | Fourier series and integrals of boundary value problems J. Ray Hanna |
| title_full_unstemmed | Fourier series and integrals of boundary value problems J. Ray Hanna |
| title_short | Fourier series and integrals of boundary value problems |
| title_sort | fourier series and integrals of boundary value problems |
| topic | Fourier-reeksen gtt Randwaardeproblemen gtt Mathematik Boundary value problems Fourier Analysis Fourier series Mathematics Fourier-Reihe (DE-588)4155109-6 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Fourier-reeksen Randwaardeproblemen Mathematik Boundary value problems Fourier Analysis Fourier series Mathematics Fourier-Reihe Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000153078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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