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＜電子ブック＞
Essential Partial Differential Equations : Analytical and Computational Aspects / by David F. Griffiths, John W. Dold, David J. Silvester
(Springer Undergraduate Mathematics Series. ISSN:21974144)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	XI, 368 p. 106 illus., 1 illus. in color : online resource
著者標目	*Griffiths, David F author Dold, John W author Silvester, David J author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics LCSH:Mathematics -- Data processing  全ての件名で検索 FREE:Differential Equations FREE:Mathematical Physics FREE:Computational Mathematics and Numerical Analysis
一般注記	Setting the scene -- Boundary and initial data -- The origin of PDEs -- Classification of PDEs -- Boundary value problems in R1 -- Finite difference methods in R1 -- Maximum principles and energy methods -- Separation of variables -- The method of characteristics -- Finite difference methods for elliptic PDEs -- Finite difference methods for parabolic PDEs -- Finite difference methods for hyperbolic PDEs -- Projects This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific an d engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra HTTP:URL=https://doi.org/10.1007/978-3-319-22569-2

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