Partial differential equations in mechanics: 1 Fundamentals, Laplace's equation, diffusion equation, wave equation
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Engineering online library
|
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XIX, 595 S. graph. Darst. |
| ISBN: | 3540672834 |
Staff View
MARC
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| 100 | 1 | |a Selvadurai, Antony P. S. |d 1942- |e Verfasser |0 (DE-588)122052633 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations in mechanics |n 1 |p Fundamentals, Laplace's equation, diffusion equation, wave equation |c A. P. S. Selvadurai |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a XIX, 595 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
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| _version_ | 1821933041625333760 |
| adam_text | Contents
1. Mathematical preliminaries 1
1.1 Components of a vector 1
1.2 Dot or scalar product 1
1.3 Cross or vector product 2
1.4 Derivative of a vector 3
1.5 Results involving derivatives 3
1.6 Partial derivatives of vectors 4
1.6.1 The gradient of a scalar field 4
1.6.2 The divergence of a vector field 6
1.6.3 The Laplacian of a scalar or vector field 6
1.6.4 The curl of a vector field 7
1.6.5 Other formulae involving V 7
1.7 Divergence of a vector field: an application 7
1.8 Divergence or Green s theorem 9
1.9 Green s theorem in two dimensions 13
1.10 Orthogonal curvilinear coordinates 14
1.11 Gradient and Laplacian in orthogonal curvilinear coordinates 17
1.12 Integral transforms 20
1.12.1 Laplace transform 21
1.12.2 Fourier transforms 41
1.12.3 Hankel transforms 57
1.13 PROBLEM SET 1 63
2. General concepts in partial differential equations 71
2.1 Fundamental concepts 72
2.1.1 The order of a partial differential equation 73
2.1.2 The linearity of a partial differential equation 74
2.1.3 Homogeneity of a partial differential equation 76
2.2 Well posed problems 77
2.2.1 Boundary conditions 77
2.2.2 Initial conditions 80
2.2.3 Well posed problems 81
2.3 PROBLEM SET 2 82
3. Partial differential equations of the first order 87
3.1 General concepts 87
3.2 Examples involving first order equations 90
3.3 Advective transport in reactor column 100
3.3.1 Governing equation one dimensional case 101
3.3.2 Governing equation generalized formulation 105
3.4 A heat exchanger problem 114
3.5 PROBLEM SET 3 116
4. Partial differential equations of the second order 121
4.1 Classification of second order partial differential equations . . 122
4.2 Reduction to canonical forms 125
4.3 Applications of the procedures 132
4.4 Classification of second order pdes
for n independent variables 140
4.5 PROBLEM SET 4 148
5. Laplace s equation 151
5.1 Derivation of Laplace s equation 152
5.1.1 Irrotational flow in fluid mechanics 152
5.1.2 Flow of fluids in porous media 159
5.2 Boundary conditions 166
5.2.1 Boundary conditions for fluid flow 166
5.2.2 Boundary conditions for porous media flow 167
5.2.3 Boundary conditions for heat conduction 168
5.3 Generalized results 169
5.4 Methods of solution of Laplace s equation 177
5.4.1 Direct solution procedure 178
5.4.2 Separation of variables method Cartesian coordinates 181
5.4.3 Separation of variables method
plane polar coordinates 195
5.5 Integral transform solution of Laplace s equation 204
5.6 Line source within a half plane region 210
5.7 Uniqueness theorem 214
5.8 A maximum principle 218
5.9 PROBLEM SET 5 220
6. The diffusion equation 235
6.1 Derivation of the diffusion equation 235
6.1.1 Heat conduction in solids 236
6.1.2 Pressure transients in porous media 240
6.1.3 Chemical mass transport in porous media 244
6.1.4 Drying of porous solids 248
6.1.5 Thermal oxidation of silicon 250
6.1.6 Motion of a plate on a viscous fluid 252
6.2 Initial conditions and boundary conditions 254
6.2.1 Dirichlet type boundary condition 254
6.2.2 Neumann type boundary conditions 255
6.2.3 Combined boundary conditions 256
6.2.4 Mixed boundary conditions 257
6.2.5 Initial conditions 257
6.2.6 Change in dependent variable
for homogeneous initial conditions 259
6.3 Methods of solution of the diffusion equation 262
6.3.1 Direct solution procedure 262
6.3.2 Trial function approach 264
6.3.3 Separation of variables method Cartesian coordinates 266
6.3.4 Separation of variables method
plane polar coordinates 292
6.4 Some generalized results
associated with the diffusion equation 301
6.4.1 Reduction to Helmholtz equation 301
6.4.2 Product solutions for the diffusion equation 302
6.4.3 Sturm Liouville problems 306
6.5 Separation of variables method
for spatially two dimensional problems 312
6.5.1 Spatially two dimensional problems
Cartesian coordinates 313
6.5.2 Spatially two dimensional problems
plane polar coordinates 323
6.5.3 Product solutions and solutions for infinite domains . . 337
6.6 Uniqueness theorem 345
6.7 A maximum principle 349
6.8 PROBLEM SET 6 353
7. The wave equation 369
7.1 Wave motion in strings 371
7.1.1 Harmonic waves 374
7.1.2 d Alembert s solution 378
7.1.3 Fourier analysis of the stretched string 385
7.1.4 Reflection and transmission at boundaries 386
7.1.5 Energy in a string 393
7.1.6 Forced motion of a semi infinite string 397
7.1.7 Forced motion of an infinite string 402
7.2 Wave motion in stretched finite strings 415
7.2.1 Waves in a stretched finite string 415
7.2.2 Vibrations of a stretched finite string:
trial function approach 418
7.2.3 Vibrations of a stretched finite string
variables separable solution 422
7.2.4 Vibrations of a stretched string:
variable boundary conditions 431
7.2.5 Forced vibration of a stretched finite string 437
7.3 Wave motion in stretched strings: non classical effects 446
7.3.1 Elastically supported string 446
7.3.2 Energy dissipation and damping in a stretched string . 451
7.4 Waves and vibrations in stretched membranes 453
7.4.1 Equation of motion for a stretched membrane 454
7.4.2 Plane wave motion in a stretched infinite membrane . . 460
7.4.3 Free vibrations of a stretched membrane
of infinite extent 463
7.4.4 Symmetric free vibrations of the stretched membrane . 469
7.4.5 Green s function for the vibration
of a stretched membrane 473
7.5 Vibrations of stretched finite membranes 475
7.5.1 Vibrations of a stretched square membrane 475
7.5.2 Free vibrations of a stretched rectangular membrane . . 482
7.5.3 Forced vibrations of a stretched rectangular membrane 489
7.5.4 Free vibrations of a stretched circular membrane 492
7.5.5 Hankel transform analysis of free vibrations
of a stretched circular membrane 499
7.5.6 Hankel transform analysis of forced vibrations
of a stretched circular membrane 501
7.5.7 Vibrations of a circular membrane general formulation 505
7.6 Wave motion and vibrations in membranes:
non classical effects 511
7.7 Wave equation for problems in solid mechanics 512
7.7.1 Longitudinal wave motion in a slender elastic rod .... 513
7.7.2 Torsional waves in a slender circular elastic rod 522
7.8 Shallow water waves 525
7.9 Uniqueness theorem 531
7.10 PROBLEM SET 7 541
Bibliography 557
Index 587
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| any_adam_object | 1 |
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| id | DE-604.BV013218494 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:43:23Z |
| institution | BVB |
| isbn | 3540672834 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009007127 |
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| physical | XIX, 595 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Engineering online library |
| spellingShingle | Selvadurai, Antony P. S. 1942- Partial differential equations in mechanics |
| title | Partial differential equations in mechanics |
| title_auth | Partial differential equations in mechanics |
| title_exact_search | Partial differential equations in mechanics |
| title_full | Partial differential equations in mechanics 1 Fundamentals, Laplace's equation, diffusion equation, wave equation A. P. S. Selvadurai |
| title_fullStr | Partial differential equations in mechanics 1 Fundamentals, Laplace's equation, diffusion equation, wave equation A. P. S. Selvadurai |
| title_full_unstemmed | Partial differential equations in mechanics 1 Fundamentals, Laplace's equation, diffusion equation, wave equation A. P. S. Selvadurai |
| title_short | Partial differential equations in mechanics |
| title_sort | partial differential equations in mechanics fundamentals laplace s equation diffusion equation wave equation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013218493 |
| work_keys_str_mv | AT selvaduraiantonyps partialdifferentialequationsinmechanics1 |
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0202 PHY 013f 2004 A 106-1
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