Авторизация
Поиск по указателям
Lions J-L., Dautray R. — Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2: Functional and Variational Methods
Обсудите книгу на научном форуме Нашли опечатку?
Название: Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2: Functional and Variational MethodsАвторы: Lions J-L., Dautray R. Аннотация: These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 608Добавлена в каталог: 12.02.2014Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
3-point scheme 84 Abstract variational problem 375 Accretive boundary value problem 453 Accretive extension 372 Accretive operator 372 Adjoint operator 353 361 Adjoint sesquilinear form 353 Algebra 497 Algebra of convolutions 497 Algebra of distributions 498 Algebra, Banach 318n Algebra, normed 318n Analytic semi-groups 225 Analyticity of solutions 234 Antidual of a topological space 281 Antilinear form 281 Automorphisms of 518 Babuska's paradox 424 Backward Cauchy problem 204 223 Baire's lemma 276 Baire's property 276 Ball 271 Banach algebra 318n Banach space 272 Banach — Steinhaus theorem 275 Banach's approximation problem 330 Bessel functions 42 Bessel functions, integral representation 43 Bessel functions, recurrence relations 43 Bessel — Parseval Inequality 302 Bessel's equation 42 Bicharacteristic 159 Bicharacteristic curve 161 Bicharacteristic solution 160 Bidual 285 Biharmonic equation 55 Biharmonic operator 450 Bijection 539n Bilinear form 292 Bochner — Schwartz theorem 526 Bounded operator 274 Cauchy problems 164 204 209 214 217 Cauchy sequence 272 Cauchy — Kowalewsky theorem 164 Cauchy — Riemann operator 176 188 Cauchy — Schwartz inequality 121 293 Cayley transform 362 Cesaro mean 17 Cesaro summability 15 Characteristic cone 158 Characteristic hyperplane 157 Characteristic polynomial 171 Characteristic vector 157 Characteristics 157 Characteristics, multiple 159 Characteristics, simple 159 Chinese remainder theorem 71 Closable operator 335 Closed graph theorem 280 Closed image theorem 348 Closed operator 335 361 Closure of an operator 335 Codimension 307 Coercive sesquilinear form 368 Collocation method 80 Compact operator 123 Compactness (weak) 289 comparison of operators 241 Comparison principle 261 Complete family 300 Complete metric space 272 Composition of operators 307 316 Cone, future 492 Cone, past 492 Constant force operator 245 Continuity 332 Continuous operator 274 Contraction 297n Convergence of operators 313 Convergence, strong 287 317 Convergence, weak 287 318 Convergence, Weak-star 290 Convex set 285 Convexity inequalities 133 Convolution algebra 497 Convolution of distributions 492 Convolution of functions 458 Convolutive support 496 Convolutor 521 Cooley — Tukey transform 64 Cracks 406 Cyclic convolution 69 Cyclic convolution of order 2 72 Cyclic convolution of order 3 73 Cyclic convolution of order 6 75 d'Alembertian 180 230 Decomposable operator 190 Degenerate operator 322 density 273 461 Denumerable total family 300 Diagonalisation of operators 15 25 29 51 Differentiability 332 Differential quotients, method of 430 Differentiation in 338 Diffusion of neutrons 440 Dirac distribution 466 Dirac distribution on a surface 487 Dirac measure 466 Dirac measure, primitives of 482 Dirac's periodic distribution 9 Direct Cauchy problem 205 223 Dirichlet problems 17 20 32 53 112 379 Dirichlet's lemma 6n Discrete Fourier Transform 59 Discretisation of Poisson problem 84 Displacement operators 319 Dissipativity 251 Distance 272 Distributions of positive type 525 Distributions of rapid decay 521 Distributions of slow growth 507 Distributions with compact support 475 Distributions with convolutive support 496 Distributions, bounded 526n Distributions, convolution of 492 494 Distributions, differentiation of 467 488 Distributions, homogeneous 519 Distributions, invariant under rotation 489 Distributions, invariant under translation 489 Distributions, normal space of 97 Distributions, periodic 7 Distributions, positive 467 Distributions, restriction of 474 Distributions, tempered 507 Distributions, tensor product of 480 Division problem 483 Domain of a linear operator 305 Domain of dependence 210 Dual of a topological space 281 Elasticity operator 419 Elastostatics 411 Elementary solution of an operator 149 183 Elliptic problems of 2nd order 393 Energy space 269 Equivalent norms 280 Equivalent semi-norms 271 Estimates of analyticity 237 Euler's relation (identity) 160 519 Extension by reflexion 117 Extension of a linear operator 282 307 Extension, canonical 116 Extension, m-extension 114 Family, complete 300 Family, orthonormal 299 Family, total 300 Fast Fourier transform in two dimensions 77 Fast Fourier transform of Cooley and Tukey 64 Fast Fourier transform of Good and Winograd 66 Fast Fourier transform, applications 78 Fast solvers for Laplacian 84 Finite part 469 Five-point scheme 85 Flexure of plates 420 Force of an operator 242 Form, antilinear (or semi-linear) 281 Form, bilinear 292 Form, linear 281 Form, sesquilinear 292 351 367 Forward Cauchy problem 204 Fourier coefficient 5 10 301 Fourier cotransform 501 Fourier inversion formula 503 Fourier transforms 356 500 Fourier transforms in 500 Fourier transforms in 506 Fourier transforms in 56 Fourier transforms of distributions with compact support 509 Fourier transforms of measures 523 Fourier transforms of tempered distributions 506 Fourier transforms, calculation of 510 Fourier transforms, fast 61 64 66 Fourier transforms, partial 513 Frechet space 272 Fredholm alternative 378 Fredholm operator 348 Function of positive type 525 Function of rapid decay 502 Function of slow growth 523 Fundamental solution 183n Future cone 492 Galerkin method 374 Garding's inequality 389 Gevrey class 240 Global regularity 426 437 Good — Winograd transform 66 Graph of an operator 306 Green — Ostrogradski formula 379 Green's function 441 445 Green's kernel 441 Hahn — Banach theorem 282 374 Hamiltonian system 160 192 Hankel transform 2 40 47 Hankel transform, table of 57 Hankel — Bochner transformation 56n Harnack estimate 267 Harnack's inequality 250 Heat operator 192 Hermitian form 357 Hermitian operator 353 Hermitian scalar product 291 Hermitian symmetry 353 Hilbert space 291 Hilbert space, separable 300 Hilbert — Schmidt operator 357 Holmgren's theorem 166 Holomorphic semi-groups 225 Holomorphy 305 Homeomorphism 321n Hyperbolic operator 190 Hyperbolic operator of order 2 198 Hypoellipticity 177 230 Image of a distribution 481 Image of a linear operator 305 Inclusion properties 461 Indices of deficiency 307 Indices of nullity 307 Inductive limit in Frechet spaces 273 Inequalities in Sobolev spaces 125 Inequality of Cauchy — Schwarz 293 Inequality of Garding 389 Inequality of Korn 414 Inequality of Poincare 126 Inequality of Young 459 Infinite matrices 311 323 338 352 Injection 539n Injection of Sobolev 139 Injective mapping 539n Integral operators 312 319 324 352 360 Integro-differential forms 398 Interpolate 60 Invariance under translation 272 Inverse image 481 485 Invertibility of operators 319 Involutive mapping 323 Isometric operator 355 Isometry 41 355 Kernel of a linear operator 305 Korn's inequality 414 Landau's notation 523n Laplace operator 173 Laplace — Beltrami operator 147 156 Laplacian 173 Lax — Milgram Theorem 368 376 Leibniz's formula 152 476 Lifting operator 110 Linear differential equations 479 Linear differential operators 148 Linear form 281 Local operator 149 Local regularity of solutions 230 Locally finite operator 149 Lorentz group 491 Love — Kirchhoff theory 420 M-extension 114 Matrices, infinite 311 323 338 352 Maximum principles 251 259 265 Measure of mass +1 466 Measure of slow growth 523 Measure, absolutely continuous 466 Measure, density of 466 Measure, positive 467 Measure, summable 465 Measure, tempered 523 Meixner's condition 37 Mellin transform 2 24 Mellin transform, table of 40 Mixed problem 394 Monomial pseudo-functions 471 Multiplicator 520 Mutually transposed operators 309 Neumann problems 380 448 Neumann series 320 Neutrons, global balance of 410 Newtonian potentials 185n Nikodym open sets 129 Non-local boundary conditions 397 Norm 270 Normal space of distributions 97 Normed algebra 318n Normed vector space 272 Nuclear operator 331 Nullity 307 One-parameter semi-groups 226 Open mapping theorem 278 Operator in Banach or Hilbert spaces, adjoint 353 361 Operator in Banach or Hilbert spaces, bounded 274 325 Operator in Banach or Hilbert spaces, compact 327 Operator in Banach or Hilbert spaces, continuous 274 Operator in Banach or Hilbert spaces, degenerate 322 Operator in Banach or Hilbert spaces, Fredholm 348
Реклама
|
|
О проекте