Essential Partial Differential Equations: Analytical and Computational Aspects
David F. Griffiths, University of Dundee;
John W. Dold, The University of Manchester;
David Silvester, University of Manchester
Springer International Publishing, 2015
ISBN: 978-3-319-22568-5;
Language: English
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for PDEs and establishes the qualitative behavior of solutions by 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 within the text 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, traveling 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 that are designed to promote and test understanding. The exercises are starred according to level of difficulty. The solutions to odd-numbered exercises are available to all readers, while even-numbered solutions are available to authorized 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. The text is also equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite for using this text is a familiarity with the basic concepts of calculus and linear algebra.
In addition, a set of MATLAB code files is available for download.
