東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Essential partial differential equat...

Griffiths, David F.

Linked to FindBook

Google Book

Amazon

博客來

Essential partial differential equations = analytical and computational aspects /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Essential partial differential equations/ by David F. Griffiths, John W. Dold, David J. Silvester.
Reminder of title:	analytical and computational aspects /
Author:	Griffiths, David F.
other author:	Dold, John W.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xi, 368 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-22569-2
ISBN:	9783319225692

Essential partial differential equations = analytical and computational aspects /
Griffiths, David F.

Essential partial differential equationsanalytical and computational aspects /[electronic resource] :by David F. Griffiths, John W. Dold, David J. Silvester. - Cham :Springer International Publishing :2015. - xi, 368 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

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 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.

ISBN: 9783319225692

Standard No.: 10.1007/978-3-319-22569-2doiSubjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA374

Dewey Class. No.: 515.353

Essential partial differential equations = analytical and computational aspects /
LDR:03127nmm a2200325 a 4500 001 2013535
003 DE-He213
005 20160414135015.0
006 m d
007 cr nn 008maaau
008 160518s2015 gw s 0 eng d
020 $a 9783319225692 $q (electronic bk.)
020 $a 9783319225685 $q (paper)
024 7 $a 10.1007/978-3-319-22569-2 $2 doi
035 $a 978-3-319-22569-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA374
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.353 $2 23
090 $a QA374 $b .G855 2015
100 1 $a Griffiths, David F. $3 1245741
245 1 0 $a Essential partial differential equations $h [electronic resource] : $b analytical and computational aspects / $c by David F. Griffiths, John W. Dold, David J. Silvester.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xi, 368 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Springer undergraduate mathematics series, $x 1615-2085
505 0 $a 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.
520 $a 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.
650 0 $a Differential equations, Partial. $3 518115
650 0 $a Differential equations, Partial $x Numerical solutions. $3 540504
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
700 1 $a Dold, John W. $3 2162998
700 1 $a Silvester, David J. $3 2162999
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springer undergraduate mathematics series. $3 1567980
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22569-2
950 $a Mathematics and Statistics (Springer-11649)