Umfang:
Online-Ressource (XI, 368 p. 106 illus., 1 illus. in color, online resource)
Ausgabe:
1st ed. 2015
ISBN:
9783319225692
Serie:
Springer Undergraduate Mathematics Series
Inhalt:
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
Inhalt:
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 300 exercises, 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
Anmerkung:
Setting the sceneBoundary 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.
Weitere Ausg.:
ISBN 9783319225685
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Griffiths, David F. Essential partial differential equations Cham : Springer, 2015 ISBN 9783319225685
Weitere Ausg.:
ISBN 3319225685
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Partielle Differentialgleichung
;
Numerisches Verfahren
DOI:
10.1007/978-3-319-22569-2
URL:
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