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Kythe P.K., Schaferkotter M.R. — Partial Differential Equations and Mathematica
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Название: Partial Differential Equations and MathematicaАвторы: Kythe P.K., Schaferkotter M.R. Аннотация: This new book on partial differential equations provides a moreaccessible treatment of this demanding subject. There is a need to introduce technology into math courses; therefore, the authors integrate the use of Mathematica throughout the book, rather than just providing a few sample problems at the ends of chapters.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 1997Количество страниц: 378Добавлена в каталог: 14.05.2008Операции: Положить на полку |
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145 Adaptive grid 321 Auxiliary system 23 28 31 40 325 Ball, open 217 Ball, open, surface area of 218 Ball, open, surface of 217 Base characteristic 24ff 28 Beam 157 Bessel functions 82 106 Binomial theorem 180 Biot number 148 Boundary conditions of first kind 3 Boundary conditions of second kind 3 Boundary conditions of third kind 3 Boundary conditions, Dirichlet 3 105 108 132 150 159 250 280 302 339 344 348 Boundary conditions, essential 276 Boundary conditions, mixed 3 250 Boundary conditions, natural 250 Boundary conditions, Neumann 3 105 250 347 Boundary conditions, nonhomogeneous 146ff Boundary conditions, periodic 104 Boundary conditions, Robin 3 Boundary perturbations 311ff Bounded variation 98ff Calculus of variations 266 Cauchy data 56 237 Cauchy integral formula 183 Cauchy problem 39 55 235 237 Cauchy residue theorem 180 Cauchy — Kowalewsky theorem 55 Cauchy — Riemann operator 259 Cauchy’s Theorem 187 Characteristics 5 24ff 47ff 51 325 Characteristics, base 24ff 28 Characteristics, Cauchy’s method of 39ff Characteristics, curves 49 Circular drum 142 Class 218 Class 218 Class 218 221 Classification 4ff Complement 218 Cone, normal 47 Cone, normal, Monge 47 48 Cone, normal, tangent 47 48 Contour integration 183ff 189 198 Convolution theorem 197 204 215 Cooling ball 144 153 Coordinates, characteristic 118 Coordinates, characteristic, cylindrical 142 Coupling constant 8 Crank — Nicolson 332 334 335 344 Crank — Nicolson, explicit 332 334 Crank — Nicolson, implicit 332 334 Crank — Nicolson, stability of 329 De Moivre’s Theorem 70 Difference equation, consistent 328 Difference operator 328 Difference scheme, central 343 Differences, finite 321ff Differences, finite, backward 323ff 332 Differences, finite, first order 322 Differences, finite, forward 323ff 330 331 332 334 336 344 Differences, finite, second order 323ff 330 335 336 339 Differential form 277 Differential operator, linear 68 Dirac distribution 220ff 232 Dirichlet — Dirichlet case 283 Discontinuity 53 90 distribution 220 Distribution, regular 220 Distribution, singular 220 221 Divergence theorem 14 Duhamel’s principle 203 d’Alembert’s solution 76 96 97 122 213 Eigenfunction expansion 82 103ff Eigenfunctions 104 108 Eigenpair 104 Eigenvalue problem 117 Eigenvalues 104 148ff 155 Electrostatic potential 239 Electrostatics 8 Element, integral 47 Element, integral, plane 47 Element, integral, tangent 47 Envelope 39 Equation(s), 4th order 287 Equation(s), Berger’s 8 Equation(s), Bessel’s 106 241 286 Equation(s), biharmonic 9 Equation(s), characteristic 5 23ff 40 315 Equation(s), cubic Schrodinger 8 Equation(s), difference 328 339 343 348 349 Equation(s), diffusion 204 332 Equation(s), dissipative Klein — Gordon 8 Equation(s), dissipative sine-Gordon 9 Equation(s), eikonal 8 Equation(s), elliptic 4 6 50 132ff 238ff Equation(s), Euler — Lagrange 269 Equation(s), Euler’s 9 274 282 296 Equation(s), first order 22ff Equation(s), Fokker — Planck 255 Equation(s), heat 7 346 Equation(s), heat conduction 15 16 125ff 177 293 Equation(s), heat transfer 14ff Equation(s), Helmholtz 8 241ff Equation(s), hyperbolic 4 6 50 53 118ff 244ff Equation(s), Klein — Gordon 8 Equation(s), Korte de Vries (KdV) 9 Equation(s), Laplace 7 16 203 211 252 261 339 Equation(s), linear with constant coefficients 22ff 63ff Equation(s), linear with variable constants 28ff Equation(s), Maxwell’s 9 Equation(s), Navier — Stokes 9 277 Equation(s), nonlinear first order 38ff Equation(s), parabolic 4 6 50 125ff 23Iff Equation(s), Poisson’s 8 159 275 280 283 302 339 342 Equation(s), Porous media 9 Equation(s), quadratic 4 Equation(s), quasi-linear, first order 2 17 33ff Equation(s), quasi-linear, nonhomogeneous 74ff Equation(s), quasi-linear, second order 49ff Equation(s), Schrodinger 8 255 Equation(s), semilinear heat 8 Equation(s), semilinear Klein — Gordon 8 Equation(s), semilinear Poisson’s 9 Equation(s), semilinear wave 8 Equation(s), sine-Gordon 8 Equation(s), Sturm — Liouville 105 Equation(s), Telegrapher’s 8 Equation(s), traffic 7 Equation(s), transient Fourier 235 Equation(s), transport 7 8 Equation(s), Tricomi 6 20 Equation(s), ultrahyperbolic 6 Equation(s), wave 7 97 180 212 334 346 Error, discretization 329 Error, discretization, truncation 328 344 345 Euler’s formula 90 Existence 25 27 30 Field point 247 Finite differences 321ff Flow, porous media 9 Flow, porous media, of viscoelastic fluid 189 Flow, porous media, of viscous fluid 189 Flow, porous media, traffic 16ff Fourier coefficients 88 Fourier cosine series 101 Fourier cosine theorem 195 Fourier integral theorem 195 Fourier sine series 100 102 127 Fourier sine theorem 195 Fourier theorem I 90 Fourier theorem II 100 Fourier transform 195ff Fourier transform of derivatives 196 Fourier transform, convolution theorem 196 Fourier transform, formula 198ff Fourier transform, properties of 196 Fourier — Bessel expansion 108ff Function(s), Bessel 82 106 245 Function(s), characteristic 218 Function(s), Dirac delta 178ff 217 221ff 248 263 Function(s), Hankel 241 Function(s), harmonic 224ff 251ff Function(s), Heaviside 54 178 Function(s), indicator 218 220 Function(s), modified Bessel 242 Function(s), monotone 99 Function(s), nondecreasing 99 Function(s), nonincreasing 99 Function(s), orthogonal 52ff Function(s), periodic 90 97 Function(s), periodic Dirichlet 307 Function(s), test 219 287ff Functional 219 Functionally independent 29ff Functionally independent, continuous 220 Functionally independent, linear 219 Fundamental solution 177 General solution 2 Geometric optics 8 Gibbs phenomenon 102 Gravitational potential 221 Green’s identity 13 225 232 350ff Green’s identity, first identity 227 351 Green’s identity, functions 217ff 230ff 250ff Green’s identity, second identity 257 351 grid 323 349 Harmonic motion 123 Harmonics 103 Heaviside function 54 178ff 220 224 Hilbert space 109 218 Hooke’s law 10 Huygens’ principle 247ff Impulsive force 221 Infinite series 82 Initial condition 3 130 Initial curve 26ff 31 Inner product 82 Inner space 218 Integral surfaces 24 30 45 47 Isocline 46 Jacobian 50 52 Kernel 160 Laplace inversion theorem 183 187 Laplace transform 161 162ff 179 180 183 189ff 233 236 244 245 Laplacian 108 142 231 238 257 Line integrals 267ff Lipschitz condition 99 Maclaurin series 254 Mainardi — Codazzi relations 22 Mathematica functions 361ff Mathematica functions, notebooks and packages list 368 Maximum principle 228ff Mesh point 323 340 Method of characteristics 22ff Method of moments 267 296 Method of separation of variables 51 82 103 117ff 235 307 312 Method of undetermined coefficients 78 Method of variation of parameters 78 Method, Cauchy’s 39ff Method, collocation 266 395 Method, Fourier series 150 Method, Galerkin 266 279ff Method, Gauss elimination 330 Method, inverse operator 63ff Method, Lagrange’s 28 Method, least-square 267 295 Method, perturbation 305ff Method, Rayleigh — Ritz 266 283ff Method, weighted residual 266ff Monge axis 47 Monge cone 47 Monge pencil 47 Multi-index 220 Neighborhood 218 Node 323 347 Norm 218 Notation 1 Operator pair 64 Operator, difference 328 Operator, Laplace 108 Operator, linear 68 Orthogonal eigenfunctions 222 Orthogonal expansions 82ff Orthogonal functions 82 Orthogonal polynomials 86 Orthogonal set 83 88 108 Orthogonality 82ff 88 Orthonormal 83 Orthonormal, set 83 Parabolic cylinder 35 Partial derivatives 1 Partial differential equations, elliptic 4 6 19 50 Partial differential equations, homogeneous 2 Partial differential equations, hyperbolic 4 6 19 50 Partial differential equations, linear 2 Partial differential equations, nonhomogeneous 2 4 Partial differential equations, order 1 Partial differential equations, parabolic 4 19 50 Partial differential equations, quasi-linear 2 17 331ff Particular integral 65 Particular integral, solution 2 4 75 Particular integral, ultrahyperbolic 6 Perturbation methods 305ff Point charge 221 Point charge, mass 221 Poisson integral representation 203 Polynomials, Chebyshev, 1st kind 86 Polynomials, Chebyshev, 2nd kind 86 Polynomials, Hermite 86 Polynomials, Jacobi 86 Polynomials, Laguerre 86 Polynomials, Legendre 86 87 Principal part 49 Quadratic form 6ff Quantum field theory 8 Quantum field theory, mechanics 8 Quasi-linear equations 2 17 Reciprocity relations 231 Residual 279 Residue 181 Riemann — Lebesgue lemma 107 Rotation of axes 24 60ff Series of orthogonal functions 88ff Series, Fourier 90 109 156 Series, generalized Fourier 88 Series, infinite 82 Series, Maclaurin 254 Series, orthogonal 82 Series, Taylor’s, truncated 321 Series, trigonometric Fourier 82 89 90ff 111 Shock waves 33 Solution, general 2 29 73 Solution, particular 2 4 75 Source point 230ff 233 Spherical coordinates 144ff Strip 48 Strip, characteristic 48
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