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Selvadurai A.P.S. — Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation
Selvadurai A.P.S. — Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation

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Название: Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation

Автор: Selvadurai A.P.S.


This two-volume work mainly addresses undergraduate and graduate students in the engineering sciences and applied mathematics. Hence it focuses on partial differential equations with a strong emphasis on illustrating important applications in mechanics. The presentation considers the general derivation of partial differential equations and the formulation of consistent boundary and initial conditions required to develop well-posed mathematical statements of problems in mechanics. The worked examples within the text and problem sets at the end of each chapter highlight engineering applications. The mathematical developments include a complete discussion of uniqueness theorems and, where relevant, a discussion of maximum and miniumum principles. The primary aim of these volumes is to guide the student to pose and model engineering problems, in a mathematically correct manner, within the context of the theory of partial differential equations in mechanics.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 2000

Количество страниц: 595

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Accumulation Rate, of Chemical      103
Advection diffusion equation      247
Advective Flow Equation, Heat Transfer      114
Advective transport      100
Advective Transport, in Reactor Column      100
Advective Transport, Laplace Transform Solution      109
Advective Transport, of Effluent      119
Advective Transport, Porous Medium      105
Amplification Factor, Wave Motion in Bars      516
Anisotropic Hydraulic Conductivity      164
Antinodes      375
Average Advective Velocity      101
Axisymmetric Free Vibrations, Stretched Membrane      469
Barotropic Inviscid Flow      155
Bessel Function, First Kind      57
Bessel Functions, Orthogonality Properties      62
Bessel Functions, Second Kind, Zero Order      295
Bessel Functions, Series Expansion      62 510
Bessel Functions, Zero Order      295
Bessel functions, zeros of      296
Bessel’s Equation, Zero Order      295
Biot Modulus      283
boundary conditions      77 109
Boundary conditions, Dirichlet      77
Boundary conditions, generalized      326
Boundary Conditions, Groundwater Flow      167
Boundary Conditions, Heat Conduction      168
Boundary Conditions, Ideal Fluid Flow      166
Boundary Conditions, Laplace’s Equation      166
Boundary conditions, mixed      77
Boundary conditions, Neumann      77
Boundary Conditions, Porous Media Flow      167
Boundary conditions, Robin      77
Boundary Conditions, Well — Posed Problems      77
Branch Cuts      37
Branch points      37
Bromwich contour      35
Canonical Forms, Elliptic Equation      131
Canonical Forms, Hyperbolic Equation      132
Canonical Forms, Parabolic Equation      132
Canonical Forms, Partial Differential Equations      125
Canonical Forms, Wave Equation      380
Cauchy Problem, Diffusion Equation      258
Cauchy Problem, Heat Conduction Equation      349
Cauchy’s integral formula      32
Characteristic curves      89 130
Characteristic equations      130
Chemical concentration      100
Chemical diffusion      235
Chemical Diffusion, Annul us, Robin Boundary Conditions      330
Chemical Diffusion, Contaminated Layer      362
Chemical Diffusion, from Finite Region      366
Chemical Diffusion, in Half — Space Region      365
Chemical Diffusion, Radially Symmetric      293
Chemical Mass Transport, Porous Media      244
Chemical Transport      100
Circular Elastic Rod, Longitudinal Waves      520
Circular Elastic Rod, Torsional Waves      522
Circular Membrane, Free Vibrations      505
Circular Membrane, General Formulation      505
Circular Membrane, Separation of Variables      505
Circular Rod, Forced Vibrations of      520
Classification of Second Order Equations      122
Classification, Eigenvalues of Principal Pan      144
Coefficients Matrix, Principal Part      142 144
Complex Conversion Formula, Laplace Transforms      33
Components of a Vector, I Composite Plate, Heat Conduction      354
Compressibility of Fluids      240
Compressibility, Porous Fabric      241
Concentration, of Chemical      101
Confined Aquifer      232
Confined Porous Layer, Groundwater Flow      191
Consistency condition      174 176
Contaminated Layer, Diffusion of Chemicals      362
Continuity Conditions, String Junctions      391
Continuity Equation, Fluid Flow      162
Continuity Equation, Incompressible Fluid      9
Continuous Dependency      81
Convolution theorem      29 32
Convolution Theorem, Inverse Laplace Transform      29
Cross product      2
Curl of a vector field      7
Current Density, in Fluid Flow      8
Curvilinear coordinates      14 17
Curvilinear coordinates, gradient      17
Curvilinear coordinates, Laplacian      17
Darcy’s Law, Groundwater Flow      164
Darcy’s Law, Porous Media Flow      164
Darrieus — Egg Beater      546
Datum Potential      163
Del operator      5
Derivative of Scalar Products      3
Derivative of Vectors      3
Diffusion equation      235
Diffusion Equation, Advection Effects      247
Diffusion equation, boundary conditions      254
Diffusion Equation, Cauchy Problem      258
Diffusion Equation, Change of Dependent Variable      259
Diffusion Equation, Combined Boundary Condition      256
Diffusion equation, derivation      235
Diffusion Equation, Direct Solution Procedure      262
Diffusion Equation, Dirichlet Boundary Conditions      254
Diffusion Equation, Drying of Porous Solids      248
Diffusion Equation, Eigenfunction Solution      323
Diffusion Equation, Elastic Drive Equation      243
Diffusion Equation, Error Function Solution      340
Diffusion Equation, Exponential Decay Term      301
Diffusion Equation, Generalized Results      301
Diffusion Equation, Homogeneous Initial Conditions      259
Diffusion equation, initial conditions      254 257
Diffusion Equation, Maximum Principle      349
Diffusion Equation, Mixed Boundary Condition      257
Diffusion Equation, Neumann Boundary Condition      255
Diffusion Equation, Plane Polar Coordinates      323
Diffusion Equation, Plane Problem      323
Diffusion Equation, Pressure Transients      243
Diffusion Equation, Product Solutions      302 304 337
Diffusion Equation, Radially Symmetric      293 298
Diffusion Equation, Reduction to Helmholtz Equation      301
Diffusion Equation, Separation of Variables      266 293 312 324
Diffusion Equation, Sturm — Liouville Problem      321
Diffusion Equation, Thermal Oxidation      250
Diffusion Equation, Transient Viscous Flow      252
Diffusion Equation, Trial Function Approach      264
Diffusion Equation, Two — Dimensional      323
Diffusion Equation, Uniqueness Theorem      345
Diffusion, coefficient of      246
Diffusion, Contaminant in Porous Medium      341
Diffusion, in a Half — Space      266
Diffusion, Insulated Disc with Robin Boundary Conditions      334
Diffusion, Line Source in Infinite Space      341
Diffusion, Low Permeabilty Material      240
Diffusion, Pore Fluid Pressure      357 358
Diffusion, Radially Symmetric      341
Diffusion, Semi — Infinite Plane      339
Diffusive Transport, of Chemicals      246
Diffusive Transport, of Solute      246
Dirac delta function      24
Direct Solution Procedure      178
Dirichlet boundary condition      77
Dirichlet Boundary Condition, Diffusion Equation      254
Dirichlet conditions      58
Dirichlet Problem, Laplace’s Equation      171
Dissipation Effects, Wave Equation      452
Divergence of a vector field      6 7
Divergence theorem      9 10
Dot product      1
Double Fourier Transform      53
Drying, Porous Solids      248
Dubois — Reymond lemma      108 154 162
Dubois — Reymond Lemma,      239 247 457
Dynamic viscosity      253 452
Dynamics, of Stretched Membranes      453
D’Alembert’s Solution, Semi — Infinite String      389
D’Alembert’s Solution, Wave Equation      378 388
Effluent Transport in Shallow Stream      119
Eigenfunction Solution, Diffusion Equation      323
Eigenfunction Solution, Stretched Square Membrane      478
Eigenfunction Solutions      306 307
Eigenvalues of Principal Part, Classification Based on      144
Eigenvalues, Principal Part      143
Einstein’s summation convention      11
Elastic Drive Equation      243
Elastic Waves in Bar      515
Elastically Supported String, free Vibrations      448
Elastically Supported String, Wave Motion      446
Elliptic partial differential equations      122
Elliptic Partial Differential Equations, Canonical Form      131
Energy Transmission, Stretched String      393
Equation of Motion, Stretched Membrane      454
Error function      272
Eulerian Continuity Equation      9
Euler’s differential equation      197
Existence of Solutions, Laplace’s Equation      173
Existence, of Local Equation      108 247 457
Exponential order      21
Exponential Order, Fourier Transforms      42
Faltung theorem      32
Finite Double Fourier Transform      54
Finite Fourier transform      48
Finite Fourier Transform, Derivative of      49
Finite Fourier Transform, Inverse of      51
Finite Hankel Transforms      58
Finite String, Elastic Restraint      434
Finite String, Natural Modes      426
Finite String, Normal Modes      426
Finite String, Vibration of      440
First Order Partial Differential Equations      87
First Order Partial Differential Equations, General Concepts      87
Fluid Density, Pressure Dependency      241
Fluid Flow in Deteriorated Concrete      232
Fluid Flow, Porous Media      159
Forced Motion, Finite String      440
Forced Motion, Semi — Infinite String      397
Forced Motion, Stretched String      402 410
Forced Vibration, Circular Membrane      501
Forced Vibration, Finite String      437
Forced Vibration, Hankel Transform Analysis      501
Forced Vibration, of Circular Rod      520 522
Forced Vibration, Stretched Rectangular Membrane      489
Fourier Analysis, Stretched String      385
Fourier integral      55
Fourier Integral, Representation      56
Fourier Transform Analysis, Rectangular Membrane      489
Fourier Transform Approach, Finite String      437
Fourier Transform Solution, Laplace’s Equation      204 224
Fourier Transform, Definitions      41
Fourier Transform, Derivatives      42
Fourier Transform, Double      53
Fourier Transform, Exponential Order      42
Fourier transform, finite      48
Fourier Transform, Finite Double      54
Fourier Transform, General Theorems      45
Fourier transform, inverse      45
Fourier Transform, Inverse of Finite      51
Fourier Transform, Multiple      52
Fourier Transform, Self Reciprocity      46
Fourier’s law of heat conduction      165
Free Vibration, Stretched Finite Membranes      475
Free Vibrations, Applications of Hankel Transforms      499
Free Vibrations, Circular Membrane      492
Free Vibrations, Elastically Supported Spring      448
Free Vibrations, Stretched Circular Membrane      499
Free Vibrations, Stretched Rectangular Membrane      482 487
Free Vibrations, Stretched Square Membrane      475 480
Gauss’ Theorem      11
General Concepts, First Order Partial Differential Equations      87
Geoenvironmental Problems, Diffusive Mass Transport      244
Geothermal Heat Pump      114
Gradient of a Scalar Field      4
Gradient operator      5
Gradient, Orthogonal Curvilinear Coordinates      17
Green’s first identity      12
Green’s function      210
Green’s Function, Laplace’s Equation for Half — Plane      210 211
Green’s Function, Laplace’s Equation, Fourier Transform Application      211
Green’s Function, Stretched Membrane      473
Green’s Function, Stretched String      404
Green’s Identities, in Two Dimensions      14
Green’s second identity      13
Green’s Theorem      9
Green’s Theorem, for the Plane      14
Green’s Theorem, in Two Dimensions      13
Groundwater Flow, Boundary Conditions      167
Groundwater Flow, Confined Layer      191
Groundwater Flow, Confined Porous Layer      191
Groundwater Flow, Darcy’s Law      164
Groundwater Flow, in Aquifers      231
Groundwater Flow, in Confined Aquifers      232
Groundwater Flow, in Rock Outcrop      233
Groundwater Flow, Inhomogeneous Domain      229
Groundwater Flow, Maas Conservation      162
Groundwater Flow, Porous Media      159
Groundwater Mechanics, Diffusion Equation      243
Hankel integral      57
Hankel transforms      57
Hankel Transforms of Derivatives      58
Hankel Transforms, Analysis of Circular Membranes      499
Hankel Transforms, Analysis of Free Vibrations      499
Hankel Transforms, Finite      58
Hankel Transforms, General Theorems      59
Hankel Transforms, Inverse      57
Hankel Transforms, Self Reciprocity      57
Harmonic Motion, Stretched Circular Membrane      497
Harmonic Waves, Stretched String      385
Heat conduction equation      235 237
Heat Conduction Equation Cauchy Problem      349
Heat Conduction, Admissible Solutions      275
Heat Conduction, Annular Sector      221
Heat Conduction, Boundary Conditions      168
Heat Conduction, Boundary Heating of Half — Space      285
Heat Conduction, Boundary Heating of Slab      289
Heat Conduction, Composite Plate      354
Heat Conduction, Error Function Solution      266
Heat Conduction, Fourier’s Law      165
Heat Conduction, General Formulation      236
Heat Conduction, Imperfectly Insulated Disc      334
Heat Conduction, Insulated Plate      222
Heat Conduction, Insulated Rod      355
Heat Conduction, Intially Heated Disc      298
Heat Conduction, Magmatic Dyke      368
Heat Conduction, Newton Boundary Condition      256
Heat Conduction, Newton Boundary Condition, in a Plate      282
Heat Conduction, of Insulated Bars      273
Heat Conduction, One — Dimensional Problem      309
Heat Conduction, Partly Insulated Plate      364
Heat Conduction, Periodic Boundary Conditions      285
Heat Conduction, Prescribed Initial Temperature in Plate      313
Heat Conduction, Quarter Plane      338
Heat Conduction, Radially Symmetric      293
Heat Conduction, Rectangular Plate      221
Heat Conduction, Robin Boundary Condition      256
Heat Conduction, Semi — Infinite Medium      285
Heat Conduction, Semi — Infinite Plane      339
Heat Conduction, Semi — Infinite Region      266
Heat Conduction, Semi — Infinite Strip      363
Heat Conduction, Separation of Variables      313
Heat Conduction, Sturm — Liouville Problem      309
Heat Conduction, Theory      236
Heat Conduction, Uniqueness of Solution      345
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