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Debnath L. — Linear Partial Differential Equations for Scientists and Engineers
Debnath L. — Linear Partial Differential Equations for Scientists and Engineers

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Название: Linear Partial Differential Equations for Scientists and Engineers

Автор: Debnath L.

Аннотация:

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics. This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.

Key features include: Applications to a wide variety of physical problems in numerous interdisciplinary areas, Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry, Historical comments on partial differential equations, Solutions and hints to selected exercises, A comprehensive bibliography-comprised of many standard texts and reference books, as well as a set of selected classic and recent papers-for readers interested in learning more about the modern treatment of the subject.

Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarilyserve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdiciplinary collaborative research in a variety of fields.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2006

Количество страниц: 630

Добавлена в каталог: 12.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel’s problem      529
Acceleration parameter      620
Adjoint      630
Adjoint operator      143 296
Angular frequencies      239
Associated Legendre function      307 384 385
Backward first difference      602
Banach space      629
Bender — Schmidt explicit formula      613
Benjamin and Feir instability      586 587
Benjamin, Bona and Mahony (BBM) equation      580
bernoulli      3
Bessel equation      289 375
Bessel function      289
Bessel function of the first kind      290
Bessel function of the second kind      291
Bessel’s inequality      175 286
Biharmonic equation      64 404
Biharmonic wave equation      64
Binding energy      389
Birkhoff      10
Blasius problem      527
Bohr radius      388
Born      10
Bound state      392
boundary conditions      15
Boundary element method      668
Boundary integral equation method      668
Boundary-value problem      308 329
Bounded      630
Boussinesq equation      543 675
Brachistochrone problem      678
Burgers equation      81 563 569
Canonical form      49 50 95 96
Cauchy      4—6
Cauchy data      119
Cauchy problem      3 15 36 118
Cauchy sequence      629
Cauchy — Kowalewskaya theorem      6 120
Cauchy — Poisson problem      530
Cauchy — Poisson wave problem      485
Cauchy — Riemann equations      5
Central first difference      602
CFL condition      609
Characteristic      34
Characteristic base curve      34
Characteristic curve      2 33 35 94 537 555
Characteristic direction      33
Characteristic equation      33 94 120
Characteristic initial-value problem      150
Characteristic velocities      549
Clairaut      2
Cnoidal wave      578
Commutator      591
Compatibility condition      349
Complete integral      29
Complete solution      29
Complex Fourier series      194
Conservation law      80
Conservation of vorticity      89
Consistent      604
Continuity equation      85
Continuity theorem      333
Convergence      602
Convolution      448 467
Convolution property      497
Convolution theorem      448 467
Courant      663
Courant parameter      608
Courant — Friedrichs — Lewy convergence criterion      608
Crank — Nicolson formula      626
Crank — Nicolson implicit formula      625
Cummulative truncation      603
Cylindrical wave equation      155 156
Damped wave equation      84
de Broglie wave      542
Debnath      482 485 515 517 519 521 588 590
density      580
Differential operators      16
Differentiation      445 464
Differentiation theorem      209
Diffusion equation      514 566 569
Diffusion equation in a finite medium      482
Diffusion in a finite medium      483
Diffusive      97
Dilatational      73
Dirac delta function      446 470
Dirichlet      5
Dirichlet boundary-value problem      5
Dirichlet condition      235
Dirichlet kernel      203
Dirichlet problem      330 416
Dirichlet problem for a circle      334
Dirichlet problem for a cylinder      363
Dirichlet problem for a rectangle      343 348
Dirichlet problem for a sphere      367
Dirichlet problem for circular annulus      340
Discontinuities      44
Discrete energy spectrum      387
Discrete values of energy      392
Discretization error      603
dispersion relation      541 573
Dispersion relation for water waves      542
Dispersive      97 542
Dispersive wave      540
Domain of dependence      123 125
Double Fourier series      212 213
Du Fort — Frankel explicit algorithm      614
Duhamel formula      481 533
Duhamel principle      165
D’Alembert      3
d’Alembert solution      3 123
d’Alembertian      65
Eigenfunction      237 274
Eigenvalue      237
Eigenvalue problem      236
Einstein      10
Elliptic      92
Elliptic equation      111
Energy      241
Energy density      547
energy equation      163
Energy flux      547
Energy integral      163
Envelope      48
Equation for vibration of a beam      542
Equation, Benjamin, Bona and Mahony (BBM)      580
Equation, Bessel      289 375
Equation, biharmonic      64 404
Equation, biharmonic wave      64
Equation, Boussinesq      543 675
Equation, Burgers      81 563 569
Equation, Cauchy — Riemann      5
Equation, characteristic      33 94 120
Equation, continuity      85
Equation, cylindrical wave      155 156
Equation, damped wave      84
Equation, diffusion      514 566 569
Equation, elliptic      111
Equation, energy      163
Equation, Euler      38 65 88 89 100
Equation, Euler — Lagrange      9 629 633 634 646
Equation, Euler — Poisson — Darboux      598
Equation, Fokker — Planck      62 90 264 436
Equation, fractional axisymmetric wave-diffusion      518
Equation, fractional diffusion      510 514
Equation, fractional diffusion-wave      511
Equation, fractional partial differential equation      510
Equation, fractional Schrodinger      520
Equation, fractional wave      512
Equation, Hamilton — Jacobi      9
Equation, heat      64 76 84
Equation, Helmholtz      64 75 85 330 372 494
Equation, Hermite      323
Equation, hyperbolic      111
Equation, Klein — Gordon (KG)      64 542
Equation, Korteweg — de Vries (KdV)      88 542 574 593
Equation, Lagrange      8
Equation, Laguerre      323
Equation, Laplace      3 64 330 361
Equation, Lax      592
Equation, Legendre      302 384
Equation, Legendre associated      306
Equation, linear Schrodinger      82 582
Equation, linearized Korteweg — de Vries (KdV)      83
Equation, Maxwell      3 84
Equation, Navier      72 73
Equation, nonhomogeneous wave      139
Equation, nonlinear      29
Equation, nonlinear diffusion      80
Equation, nonlinear hyperbolic      550
Equation, nonlinear Schrodinger (NLS)      83 583 585
Equation, parabolic      111
Equation, partial differential      12
Equation, Poisson      64 85 330 429
Equation, potential      3 5
Equation, quasi-linear partial differential      28 89
Equation, Schrodinger      64 317 330 382 404 542 581
Equation, spherical wave      153
Equation, Sturm — Liouville      274
Equation, Tchebycheff      323
Equation, telegraph      64 84 87 147 436
Equation, time dependent Schrodinger      382
Equation, vorticity      89
Equation, wave      64 67 69 73 511 535 536 542
Equation, wave and heat      372
Equation, Whitham      545 548
Error function      452
Euler      3
Euler equation      38 65 88 89 100
Euler — Lagrange equation      9 629 633 634 646
Euler — Lagrange variational principle      634
Euler — Lagrange variational problem      632
Euler — Poisson — Darboux equation      598
Euler’s equation of motion      85
Even extension      192
Explicit finite difference methods      608
Fermat      7
Fermat principle in optics      635
Fermi — Pasta — Ulam model      88
Fine structure corrections      389
Finite difference approximations      602
Finite element method      663
Finite Fourier cosine transform      500
Finite Fourier sine transform      499
Finite Hankel transform      505
First canonical form      95
Fitzgerald      10
Five-point formula      621
Flood wave      552
Flux      580
Fokker — Planck equation      62 90 264 436
Forsyth      6
Forward first difference      602
FOURIER      4
Fourier coefficients      173
Fourier cosine transform      443 456 500
Fourier integral representation      218 219
Fourier integral theorem      4 217
Fourier integrals      214
Fourier method      232
Fourier series      171 173
Fourier sine integral formula      443
Fourier sine transform      443 457
Fourier transform      440
Fourier — Legendre series      284
Fractional axisymmetric wave-diffusion equation      518
Fractional derivative      480 482 499
Fractional diffusion equation      510 514
Fractional diffusion-wave equation      511
Fractional partial differential equation      510
Fractional Rayleigh problem      517
Fractional Schrodinger equation      520
Fractional Stokes and Rayleigh problem      515
Fractional unsteady Couette flow      517
Fractional wave equation      512
Fundamental harmonic      239
Fundamental period      169
Fundamental solution      451
Galerkin approximation method      655
Gauss      5
Gaussian probability density      404
General Parseval relation      227
General solution      30 107
Generalized coordinates      638
Generalized solution      130
Gibbs      186
Gibbs phenomenon      181 185 208 225
Global convergence      174
Goursat      6
Goursat problem      149
Gravitational potential      76
Green      5
Green’s function      312 407—409 451
Group velocities      541
Group velocity      546
hadamard      3
Hadamard example      121
Hamilton      8
Hamilton equations of motion      8 643
Hamilton — Jacobi equation      9
Hamiltonian      382
Hamiltonian function H      642
Hamilton’s principle      8 636
Hankel transform      489
Harmonic      330
Harmonic function      5 330
harmonic oscillator      320
Heat conduction in a rectangular volume      381
Heat equation      64 76 84
Heat flow in a rectangular plate      375
Heaviside unit step function      453 470
Helmholtz equation      64 75 85 330 372 494
Helmholtz operator      415 418
Hermite equation      323
Hermite function      265
Hermite polynomials      320
hilbert      10
Hilbert space      629
Homogeneous      13 29
Hydrogen atom      382
Hyperbolic      92
Hyperbolic equation      111
Ill-posed problem      549
Implicit finite difference method      624
Implicit Richardson formula      626
Impulse function      454
Infinite square well potential      389
Initial boundary-value problem      15
Initial condition      15 37
Initial data      37
Initial-value problem      3 15 36 118
Inner product      629
Integral surface      33
Integration      465
Integration theorem      209
Inverse Fourier cosine transform      500
Inverse Fourier sine transform      500
Inverse Fourier transform      440
Inverse Hankel transform      489 505
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