Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2 Functional and Variational MethodsSpringer, 20 de mar. de 2015 - 590 páginas 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. |
Conteúdo
Table of Contents | 1 |
Distributions on T and Periodic Distributions | 7 |
2 The Mellin Transform | 24 |
Part B Discrete Fourier Transforms and Fast Fourier Transforms | 59 |
4 The Fast Fourier Transform of GoodWinograd | 66 |
6 Fast Fourier Transform in Two Dimensions | 72 |
7 Some Applications of the Fast Fourier Transform | 78 |
Sobolev Spaces | 92 |
Review of Chapter V | 268 |
Closed Operators | 334 |
3 Linear Operators in Hilbert Spaces | 348 |
Review of Chapter VI | 374 |
Extensions in the Case in which V and H are Spaces | 383 |
2 Examples of Second Order Elliptic Problems | 393 |
Statical Problems of the Flexure of Plates | 420 |
Greens Functions | 441 |
6 Compactness | 123 |
8 Supplementary Remarks | 138 |
Linear Differential Operators | 148 |
2 Linear Differential Operators with Constant Coefficients | 170 |
Parabolic Operators | 202 |
Propagation in Hyperbolic Cauchy Problems | 209 |
WellPosed Cauchy Problem in S | 217 |
Study of the Particular Case P ddt + P | 223 |
4 Local Regularity of Solutions | 230 |
5 The Maximum Principle | 250 |
Review of Chapter VII | 456 |
96 | 482 |
on the Real Line | 485 |
2 Convolution of Distributions | 492 |
3 Fourier Transforms | 500 |
Bibliography | 533 |
551 | |
577 | |
Contents of Volumes 1 36 585 | 584 |
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Mathematical Analysis and Numerical Methods for Science and Technology ... Robert Dautray,Jacques-Louis Lions Visualização parcial - 1999 |
Termos e frases comuns
analytic Banach space boundary bounded open set Cauchy problem Chap characteristic closed compact support condition consider constant coefficients continuous linear continuous linear form converges convolution Corollary deduce defined Definition denote dense differential operator Dirichlet problem elementary solution elliptic operator equation Example exists a constant finite formula Fourier transform function given Green's Green's formula hence Hilbert space hyperbolic operators hyperbolic with respect hypo-elliptic hypothesis inequality injection integral inverse isomorphism kernel l.d.o. with constant Laplacian Lemma linear form linear operator neighbourhood norm notation open set parabolic polynomial Proof properties Proposition regular Remark resp result satisfies scalar product sequence sesquilinear form Sobolev spaces sub-space suppose Theorem topology transpose unique vector space verify ди