Introductory applications of partial differential equations: with emphasis on wave propagation and diffusion
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1995
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| Series: | A Wiley interscience publication
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 471 S. graph. Darst. |
| ISBN: | 0471311235 |
Staff View
MARC
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| 100 | 1 | |a Lamb, George L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory applications of partial differential equations |b with emphasis on wave propagation and diffusion |c G. L. Lamb |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1995 | |
| 300 | |a XII, 471 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a A Wiley interscience publication | |
| 650 | 4 | |a Diferansiyel denklemler, Kısmi | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Differential equations, Partial | |
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Record in the Search Index
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| adam_text | CONTENTS
Preface xi
1 One Dimensional Problems—Separation of Variables 1
1.1 Introduction 1
1.2 One Dimensional Heat Conduction 4
1.2.1 Boundary and Initial Conditions 6
1.3 Steady State Solutions 6
1.4 Time Dependent Heat Flow—Separation of Variables 10
1.4.1 Elementary Solutions 11
1.4.2 Synthesis of Elementary Solutions—Fourier Series 13
1.4.3 Changing the Boundary Conditions—Insulated Ends 17
1.5 Steady State Heating by a Localized Source—Delta
Function 21
1.6 Inhomogeneous Boundary Conditions 28
1.7 Inhomogeneous Heat Equation—Source Terms 33
1.8 Wave Equation—Vibrating String 38
1.8.1 General Wave Equation 39
1.8.2 Solution by Separation of Variables 41
1.8.3 Energy Flow on the String 45
1.8.4 Source Terms—Inhomogeneous Wave Equation 46
1.9 d Alembert s Solution of the Wave Equation 49
2 Laplace Transform Method 60
2.1 Vibrating String 60
2.2 Diffusion Equation 65
2.3 Miscellaneous Examples 74
2.3.1 Impulse Acting on a String 74
2.3.2 Long Time Behavior 75
2.3.3 Total Heat Flow through an End 77
2.4 Point Source Problem—Preview of Green s Function 79
3 Two and Three Dimensions 85
3.1 Introduction 85
3.2 Steady State Temperature Distribution in Rectangular
Coordinates—Laplace s Equation 86
vii
viii CONTENTS
3.3 Time Dependent Diffusion in Rectangular Coordinates 93
3.4 Waves on a Membrane—Rectangular Coordinates 98
3.4.1 Normal Modes 99
3.4.2 Guided Waves 101
3.5 Orthogonal Curvilinear Coordinates 105
3.5.1 Cylindrical Coordinates 108
3.5.2 Spherical Coordinates 108
3.5.3 Oblate Spheroidal Coordinates 111
3.6 Spherical Symmetry 114
3.6.1 Spherical Standing Waves 115
3.6.2 Spherical Traveling Waves 116
3.7 Circular and Cylindrical Symmetry 118
3.7.1 Steady State Temperature in a Pie Shaped Region 118
3.7.2 Laplace s Equation in an Annular Circle 121
3.7.3 Vibrating Membrane 126
3.7.4 Steady State Temperature in a Cylinder 131
4 Green s Functions 142
4.1 Introductory Example 142
4.1.1 Reciprocity 145
4.2 General Procedure for Constructing Green s Functions in
One Dimension 155
4.3 One Dimensional Steady Waves 158
4.3.1 Scattering of Waves on a String 160
4.3.2 Significance of Boundary Terms 162
4.4 Method of Images 165
4.5 A Non Self adjoint Green s Function 167
4.6 Green s Function for a Damped Oscillator 174
4.6.1 A Generalization 177
4.7 One Dimensional Diffusion and Wave Motion 179
4.7.1 Diffusion Equation 179
4.7.2 Wave Equation 183
4.8 Two and Three Space Dimensions—Green s Theorem 188
4.9 Green s Function in Free Space 191
4.9.1 Boundary Condition at Infinity 192
4.10 Two Dimensional Problems 199
4.11 Inversion and the Method of Images for a Circle 205
4.12 Eigenfunction Expansion Methods 210
4.13 Modified Green s Functions—One Dimension 221
CONTENTS ix
5 Spherical Geometry 226
5.1 Solution of Laplace s Equation 226
5.2 Source Terms and the Multiple Expansion 235
5.2.1 Axial Multipoles 236
5.3 Inversion—Green s Function for a Sphere 240
5.4 Spherical Waves 245
5.4.1 Spherical Bessel Functions 247
5.4.2 Radiation from a Point Source 248
5.4.3 Reduction to a Plane Wave 250
5.4.4 Scattering of a Plane Wave by a Sphere 251
6 Fourier Transform Methods 255
6.1 Fourier Sine and Cosine Transforms 255
6.2 Examples 258
6.2.1 Green s Function for Steady Waves on a Semi
infinite String 258
6.2.2 Temperature Distribution in a Quarter Plane 260
6.2.3 d Alembert Solution for a Semi infinite String 262
6.3 Convolution Theorems 266
6.4 Complex Fourier Transforms 272
6.4.1 Approach to the Boundary 276
6.5 Fourier Transforms in Two and Three Dimensions 281
6.6 Circular Symmetry, Fourier Bessel Transform 286
6.7 Green s Functions for Time Dependent Wave Equation in
» One, Two, and Three Dimensions 291
6.7.1 One Dimension 291
6.7.2 Two Dimensions 293
6.7.3 Three Dimensions 294
7 Perturbation Methods 297
7.1 First Order Corrections 297
7.2 Equal Frequencies (Degeneracy) 303
7.3 Variational Methods 307
7.3.1 Differential Equation Approach (Rayleigh s Method) 307
7.3.2 Integral Equation Approach 312
8 Generalizations and First Order Equations 317
8.1 Classification of Second Order Equations 317
8.2 Uniqueness and General Properties of Solutions 325
8.2.1 Laplace s Equations 326
X CONTENTS
8.2.2 Uniqueness 327
8.2.3 Diffusion Equation 327
8.2.4 Wave Equation 328
8.3 First Order Equations 331
8.4 Burger s Equation 343
9 Selected Topics 352
9.1 Oscillating Heat Source on a Beam 352
9.2 Temperature Distribution in a Pie Shaped Region 356
9.3 Babinet s Principle 361
9.4 Comparison of Wave Motion in One, Two, and Three
Dimensions—Fractional Derivatives 364
9.5 Modified Green s Function for a Sphere 370
9.6 Oscillation of an Inhomogeneous Chain 373
9.7 Point Source Near the Interface between Two Half Spaces 376
9.8 Waves in an Inhomogeneous Medium 379
9.9 A Hybrid Fourier Transform 382
9.10 Invariants of the Linear Parabolic Equation 387
Appendix A Fourier Series 391
Appendix B Laplace Transform 410
Appendix C Sturm Liouville Equations 426
Appendix D Bessel Functions 436
Appendix E Legendre Polynomials 450
Appendix F Tables of Sums and Integral Transforms 462
References 466
Index 467
|
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| id | DE-604.BV010573723 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:55:16Z |
| institution | BVB |
| isbn | 0471311235 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007048587 |
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| physical | XII, 471 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley interscience publication |
| spelling | Lamb, George L. Verfasser aut Introductory applications of partial differential equations with emphasis on wave propagation and diffusion G. L. Lamb New York [u.a.] Wiley 1995 XII, 471 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley interscience publication Diferansiyel denklemler, Kısmi Partiële differentiaalvergelijkingen gtt Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Physik (DE-588)4045956-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007048587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lamb, George L. Introductory applications of partial differential equations with emphasis on wave propagation and diffusion Diferansiyel denklemler, Kısmi Partiële differentiaalvergelijkingen gtt Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4045956-1 |
| title | Introductory applications of partial differential equations with emphasis on wave propagation and diffusion |
| title_auth | Introductory applications of partial differential equations with emphasis on wave propagation and diffusion |
| title_exact_search | Introductory applications of partial differential equations with emphasis on wave propagation and diffusion |
| title_full | Introductory applications of partial differential equations with emphasis on wave propagation and diffusion G. L. Lamb |
| title_fullStr | Introductory applications of partial differential equations with emphasis on wave propagation and diffusion G. L. Lamb |
| title_full_unstemmed | Introductory applications of partial differential equations with emphasis on wave propagation and diffusion G. L. Lamb |
| title_short | Introductory applications of partial differential equations |
| title_sort | introductory applications of partial differential equations with emphasis on wave propagation and diffusion |
| title_sub | with emphasis on wave propagation and diffusion |
| topic | Diferansiyel denklemler, Kısmi Partiële differentiaalvergelijkingen gtt Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Diferansiyel denklemler, Kısmi Partiële differentiaalvergelijkingen Differential equations, Partial Partielle Differentialgleichung Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007048587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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