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Debnath L. — Linear Partial Differential Equations for Scientists and Engineers
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Название: Linear Partial Differential Equations for Scientists and EngineersАвтор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 2006Количество страниц: 630Добавлена в каталог: 12.05.2008Операции: Положить на полку |
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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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