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＜電子ブック＞
Mathematical Analysis and Numerical Methods for Science and Technology : Volume 2 Functional and Variational Methods / by Robert Dautray, Jacques-Louis Lions

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
大きさ	XVI, 590 p : online resource
著者標目	*Dautray, Robert author Lions, Jacques-Louis author SpringerLink (Online service)
件　名	LCSH:Partial differential equations LCSH:Numerical analysis LCSH:Mathematical physics LCSH:System theory LCSH:Calculus of variations FREE:Partial Differential Equations FREE:Numerical Analysis FREE:Theoretical, Mathematical and Computational Physics FREE:Systems Theory, Control FREE:Calculus of Variations and Optimal Control; Optimization
一般注記	III. Functional Transformations -- A. Some Transformations Useful in Applications -- §1. Fourier Series and Dirichlet’s Problem -- §2. The Mellin Transform -- §3. The Hankel Transform -- Review of Chapter III A -- B. Discrete Fourier Transforms and Fast Fourier Transforms -- §1. Introduction -- §2. Acceleration of the Product of a Matrix by a Vector -- §3. The Fast Fourier Transform of Cooley and Tukey -- §4. The Fast Fourier Transform of Good-Winograd -- §5. Reduction of the Number of Multiplications -- §6. Fast Fourier Transform in Two Dimensions -- §7. Some Applications of the Fast Fourier Transform -- Review of Chapter III B -- IV. Sobolev Spaces -- §1. Spaces H1(?), Hm(?) -- §2. The Space Hs(?n) -- §3. Sobolev’s Embedding Theorem -- §4. Density and Trace Theorems for the Spaces Hm(?), (m ? ? * = ?\z0{) -- §5. The Spaces H-m(?) for all m ? ? -- §6. Compactness -- §7. Some Inequalities in Sobolev Spaces -- §8. Supplementary Remarks -- Review of Chapter IV -- Appendix: The Spaces Hs(?) with ? the “Regular” Boundary of an Open Set ? in ?n -- V. Linear Differential Operators -- §1. Generalities on Linear Differential Operators -- §2. Linear Differential Operators with Constant Coefficients -- §3. Cauchy Problem for Differential Operators with Constant Coefficients -- §4. Local Regularity of Solutions* -- §5. The Maximum Principle * -- Review of Chapter V -- VI. Operators in Banach Spaces and in Hilbert Spaces -- §1. Review of Functional Analysis: Banach and Hilbert Spaces -- §2. Linear Operators in Banach Spaces -- §3. Linear Operators in Hilbert Spaces -- Review of Chapter VI -- VII. Linear Variational Problems. Regularity -- §1. Elliptic Variational Theory -- §2. Examples of Second Order Elliptic Problems -- §3. Regularity of the Solutions of Variational Problems -- Review of Chapter VII -- Appendix. “Distributions” -- §1. Definition and Basic Properties of Distributions -- §2. Convolution of Distributions -- §3. Fourier Transforms -- Table of Notations -- of Volumes 1, 3–6 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 HTTP:URL=https://doi.org/10.1007/978-3-642-61566-5

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