Selvadurai A.P.S. — Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation :: Электронная библиотека попечительского совета мехмата МГУ

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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.

Аннотация:

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:

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

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Предметный указатель

Heat Exchanger Problem      114
Heat exchangers      87
Heat generation      237
Heated Plate, Prescribed Initial Temperature      354
Heaviside step function      24
Helmholtz Equation, from Diffusion Equation      301
Helmholtz Equation, Inhomogeneous Form      489
Homogeneity of Partial Differential Equations      76
Horizontal Divergence, Shallow Water Waves      529
Hydraulic Anisotropy      164
Hydraulic Conductivity      164 165
Hydraulic Conductivity, Porous Media Flow      165
Hydraulic Potential      163
Hydrodynamic Loads, on Stretched Strings      437
Hyperbolic partial differential equations      122
Hyperbolic Partial Differential Equations, Canonical Form      132
ideal fluid flow      154
Ideal Fluid Flow, Boundary Conditions      166
Identity, Definition      13
Imperfectly Insulated Disc, Diffusion in      334
Impulse Function, Stretched Infinite String      408
Incompressibility, of Fluid      154
Independent Variables, Transformation      125
Infinite Domain Solutions      337
Initial conditions      109
Initial Conditions, Diffusion Equation      257
Initial Conditions, Partial Differential Equations      80
Insulated Rod, Heat Conduction      355
Integral Transforms, Fourier, Laplace, Hankel      20
Intrinsic Permeability, Porous Media Flow      165
Inverse Fourier transform      45
Inverse Hankel transform      57
Inverse Laplace transforms      23
Inverse Laplace Transforms, Convolution Theorem      29
Inverse Laplace Transforms, Special Theorems      38
Inversion Integral, Laplace Transforms      32
Irrotational Fluid Flow      154
Irrotational Fluid Flow, Kelvin’s Theorem      154
Irrotational Fluid Flow, Laplace’s Equation      152
Isothermal Moisture Diffusivity      249
Isothermal Plug Flow      87
Isotropic Porosity      101
Isotropic Tension, Stretched Membranes      454
Jacobian      127
Kelvin’s Theorem, Irrotational Fluid Flow      154
Kinematic viscosity      253
Kinetic Energy Density, Stretched String      396
Kinetic Energy Potential, Stretched Membrane      540
Lam $\acute{e}$ Coefficients      17
Laplace Transform Approach, Finite String      437
Laplace Transform Inversion      23 32
Laplace Transform Inversion, Bromwich Contour      35
Laplace Transform Inversion, Convolution Theorem      29
Laplace Transform Inversion, Poles      37
Laplace Transform Inversion, Residues      35
Laplace Transform Solution, Advective Transport Problem      109
Laplace Transform, Complex Inversion      33
Laplace transform, definition      21
Laplace Transform, Derivatives      22
Laplace transform, inverse      23 32
Laplace Transform, Shift Theorem      30
Laplace Transform, Special Theorems      38
Laplace’s Equation, Annular Sector      202
Laplace’s Equation, Boundary Conditions      166
Laplace’s Equation, Derivation      152
Laplace’s Equation, Direct Solution Procedure      178
Laplace’s Equation, Dirichlet Problem      171
Laplace’s Equation, Dirichlet Problem, Cavity      223
Laplace’s Equation, Dirichlet Problem, Circle      199
Laplace’s Equation, Dirichlet Problem, Half-Plane      184
Laplace’s Equation, Dirichlet Problem, Half-Plane Region      204
Laplace’s Equation, Dirichlet Problem, Semi-Infinite Strip      187
Laplace’s Equation, Engineering Applications      151
Laplace’s Equation, Existence of Solutions      173
Laplace’s Equation, Fluid Flow      152
Laplace’s Equation, Fourier Transform Solution      204
Laplace’s Equation, Generalized Results      169
Laplace’s Equation, Green’s Function, Half-Plane      210
Laplace’s Equation, Half-Plane with Line Source      210
Laplace’s Equation, Maximum Principle      218
Laplace’s Equation, Methods of Solution      177
Laplace’s Equation, Neumann Problem      171
Laplace’s Equation, Neumann Problem, Consistency Condition      174 176
Laplace’s Equation, Physical Principles      151
Laplace’s Equation, Plane Polar Coordinates      195
Laplace’s Equation, Porous Media Flow      165
Laplace’s Equation, Robin Problem      172
Laplace’s Equation, Separation of Variables      181 195
Laplace’s Equation, Solution for a Quarter Plane      224
Laplace’s Equation, Steady State Heat Conduction      165
Laplace’s Equation, Uniqueness Theorem      214
Laplace’s operator      6
Laplace’s Operator, Curvilinear Coordinates      20
Laplace’s Operator, Cylindrical Coordinates      158
Laplace’s Operator, Elliptical Coordinates      459
Laplace’s Operator, Plane Bipolar Coordinates      460
Laplace’s Operator, Plane Polar Coordinates      459
Laplace’s Operator, Rectangular Cartesian Coordinates      157
Laplace’s Operator, Spherical Coordinates      158
Laplacian of Scalar Fields      6
Laplacian of Vector Fields      6
Laplacian, Orthogonal Curvilinear, Coordinates      17
Lemma, Definition      13
Lemma, Dubois — Reymond      108 154 162 239 247 457
Linearity of Partial Differential Equations      74
Local Average Velocity      101
Local Equations, Existence of      108 247 457
Longitudal Wave Motion, in Bars      512
Longitudinal Vibrations, in Bars      513
Longitudinal Vibrations, in Circular Rod      520
Longitudinal wave velocity      515
Loss Rate, of Chemical      103
Mass conservation equation      153
Mass Conservation, Fluid Flow      162
Mass Conservation, Porous Media Flow      162
Mass Transport, Porous Media      244
Material time derivative      526
Maximum principle, diffusion equation      349
Maximum Principle, Laplace’s Equation      218
Maximum Wave Amplitude      375
Membranes, Dynamics o      453
mixed boundary condition      77
Mixed Boundary Condition, Diffusion Equation      257
Mnemonic Operation, for Vector Product      2
Moisture Diffusion Equation      235
Moisture Diffusivity, Isothermal      249
Molecular diffusion      244
Multiple Fourier Transfonns      52
Neumann boundary condition      77
Neumann Boundary Condition, Diffusion Equation      255
Neumann Problem, Laplace’s Equation      171
Neumann Problem, Laplace’s Equation, Compatibility Condition      174
Newtonian Viscosity, Effects on Wave, Motion      512
Newtonian viscous fluid      253
nodes      375
Non — Distorted Waves      380
Non — Propagating Waves, in String      451
Order of Partial Differential Equations      73
Orthogonal curvilinear coordinates      14
Orthogonal eigenfunctions      310
Orthogonality Properties, Bessel Func¬tions      62
Oxygen Diffusion, in Silicon      250
Parabolic partial differential equations      122
Parabolic Partial Differential Equations, Canonical Fbrm      132
Partial Derivatives of Vectors      4
Partial Differential Equations, Canonical Forms      129
Partial Differential Equations, Classification of Second Order Equations      122
Partial differential equations, elliptic      122 127
Partial differential equations, first order      87
Partial Differential Equations, Fundamental Concepts      71

Partial Differential Equations, General Concepts      71
Partial Differential Equations, Homogeneity      76
Partial differential equations, hyperbolic      122 127
Partial Differential Equations, in Fluid Mechanics      121
Partial Differential Equations, in Heat Conduction      121
Partial Differential Equations, in Porous Media Flow      121
Partial Differential Equations, in Wave Mechanics      121
Partial Differential Equations, Initial Conditions      80
Partial Differential Equations, N Independent Variables      140
Partial differential equations, nonlinear      75 76
Partial Differential Equations, Order of      73
Partial differential equations, parabolic      122 127
Partial Differential Equations, Plate Flexure      79
Partial Differential Equations, Porous Media Flow      78
Partial Differential Equations, Principal Part      141
Partial Differential Equations, Quasilinear      76 89
Partial Differential Equations, Reduction to Canonical Forms      125
Partial differential equations, second order      121
Partial Differential Equations, Well — Posed      77 81
Pbase      376
phase velocity      376 449
Piecewise continuity      21
Plane Wave Motion, Stretcbed Membrane      460
Plate on Viscous Fluid, Stress Diffusion      252
Poles, Laplace Transform Inversion      37
Pore Fluid Pressure Diffusion, in Bar      360
Pore Fluid Pressure Diffusion, in Geological Dyke      359
Pore Fluid Pressure Diffusion, in Half — Space      358
Pore Fluid Pressure Diffusion, in Layers      357
Pore Fluid Pressure Diffusion, in Seam      361
Porosity      101 159
Porous Media Flow, Boundary Conditions      167
Porous Media Flow, Hydraulic Conductivity      165
Porous Media Flow, in Aquifers      231
Porous Media Flow, Laplace’s Equation      165
Porous Media Flow, Mass Conservation      162
Porous Media, Advective Transport      105
Porous Media, Diffusion from Line Source      341
Porous Media, Fluid Flow      159
Porous Media, Pressure Diffusion      240
Porous Media, Pressure Diffusion, in a Bar      279
Porous Media, Pressure Transients      235 240
Porous Seam, Groundwater Flow      232
Potential Energy, of Stretched Membrane      540
Power Transmission, Stretched String      396
Pressure Diffusion, Porous Media      240
Pressure potential      163
Pressure Transients, in Embedded Layer      363
Pressure Transients, Porous Media      235 240
Principal Part, Coefficients Matrix      142
Principal Part, Eigenvalues      143
Principal Part, Partial Differential Equations      141
Principal Part, Symmetry      144
Probability integral      272
Product Solutions, Diffusion Equation      302 304 337
Propagating Wave Solution      377
Propagating Waves, in String      450
Quarter Plane, Heat Conduction      338
Quarter Plane, Laplace’s Equation      224
Quasilinear First Order, Partial Differential Equations      89
Radiation condition      399
Reactor Column, Advective Transport      100
Rectangular Membrane, Double Fourier Transform Approach      489
Rectangular Membrane, Forced Vibrations      489
Rectangular Membrane, Free Vibrations      482 487
Rectangular Membrane, Harmonic Loading      492
Reference Density, of Fluid      241
Reflecting Waves, at Boundary      386
Residues, Laplace Transform Inversion      35
Resonant Frequency, Vibrating Rod      522
Right — Handed System      2
Robin boundary condition      77
Robin Boundary Condition, Boundary of Disc      334
Robin Problem, Laplace’s Equation      172
Scalar field, gradient of      4
Scalar Field, Laplacian of      6
Scalar product      1
Scalar Product, Derivative of      3
Second Order Equations, N Independent Variables      140
Second Order Partial Differential Equations      121
Self Reciprocity, Hankel Transforms      57
Semi — Infinite String, D’Alembert’s Solution      389
Semi — Infinite String, Forced Motion      397
Semi — Infinite String, Reflected Waves      386
Semi — Infinite String, Reflection      389
Separation of Variables, Diffusion Equation      266 313 324
Separation of Variables, Heat Conduction Equation      313
Separation of variables, Laplace’s equation      181 195
Separation of Variables, Vibration of Finite String      422
Separation of Variables, Vibrations of Circular Membranes      505
Series Expansion of Bessel Functions      62
Series Expansion of Bessel Functions,      510
Shallow water waves      87 525
Shallow Water Waves, Horizontal Divergence      529
Shear Modulus, Elastic Material      524
Shear Wave Velocity      524 551
Shift Theorem, Laplace Transforms      30
Specific Kinetic Energy, Stretched String      394
Standing Wave Solution      377
standing waves      375
Stationary waves      375
Steady State Heat Conduction, Laplace’s Equation      165
Stiffness of Spring Support      447
Stokes’ First Problem      252
Stretched Finite String, Trial Function Solution      418
Stretched Finite String, Vibrations      418
Stretched Finite String, Wave Motion      415
Stretched Infinite String, Forced Motion      402
Stretched Membrane, Annular, Boundary Displacements      227
Stretched Membrane, Axisymmetric Free Vibrations      469
Stretched Membrane, Boundary Deflections      228
Stretched Membrane, Circular, Eigenfunction Expansion      495
Stretched Membrane, Circular, Forced Vibrations      501
Stretched Membrane, Circular, Free Vibrations      492
Stretched Membrane, Circular, Hankel Transform Analysis      501
Stretched Membrane, Circular, Harmonic Motion      497
Stretched Membrane, Circular, Polar Symmetry      501
Stretched Membrane, Equation of Motion      454
Stretched Membrane, Fourier Transform Solution      463
Stretched Membrane, Free Vibrations      463
Stretched Membrane, Green’s Function      473
Stretched Membrane, Hankel Transform Solution      473
Stretched Membrane, Isotropic Tension      454
Stretched Membrane, Kinetic Energy Potential      540
Stretched Membrane, Plane Wave Motion      460
Stretched Membrane, Potential Energy      540
Stretched Membrane, Rectangular, Forced Vibrations      489
Stretched Membrane, Rectangular, Free Vibrations      475 482 487
Stretched Membrane, Square, Eigenfunction Solution      478
Stretched Membrane, Square, Free Vibrations      475 480
Stretched Membrane, Uniqueness Theorem      535
Stretched Membrane, Waves in      453
Stretched String, Damping      451
Stretched String, Energy Dissipation      451
Stretched String, Forced Vibrations      437
Stretched String, Fourier Analysis      385
Stretched String, Green’s Function      404
Stretched String, Harmonic Waves      385
Stretched String, Impulse Function      408
Stretched String, Kinetic Energy Density      396
Stretched String, Laplace Transform Solution      404
Stretched String, Newtonian Viscosity Effects      451
Stretched String, Non — Classical Effects      446
Stretched String, Non — Propagating Waves      451
Stretched String, Outgoing Waves      404
Stretched String, Power Transmission      396
Stretched String, Propagating Waves      450
Stretched String, Time Harmonic Loading      410
Stretched String, Transition Condition      451
Stretched String, Vibrations of      440

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