Essential Partial Differential Equations / Springer Undergraduate Mathematics Series (PDF)
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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
David Griffiths trained originally as an applied mathematician and has spent his academic career as a numerical analyst at the University of Dundee specialising in the numerical solution of partial differential equations. He taught the subject at both undergraduate and postgraduate levels for many years andpublished over 50 scientific articles on finite difference and finite element methods. He has previously published two textbooks on finite difference methods for ordinary and partial differential equations. David was joint organising secretary of the Dundee Biennial Conferences on Numerical Analysis from 1983 to 2005. He was awarded a "Certificate of Recognition" from NASA in both 1991 and 1993 for his work on spurious solutions that can arise from approximations of nonlinear differential equations.
David Silvester is a Professor in the School of Mathematics at The University of Manchester. His research concerns numerical solution of partial differential equations, computational fluid dynamics, uncertainty quantification, and high performance computing. He received his doctorate in mathematics from the University of Manchester Institute of Science and Technology in 1984 and has had visiting positions at Stanford University, the University of Maryland at College Park,
- Autoren: David F. Griffiths , John W. Dold , David J. Silvester
- 2015, 1st ed. 2015, 368 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319225693
- ISBN-13: 9783319225692
- Erscheinungsdatum: 24.09.2015
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- Dateiformat: PDF
- Größe: 6.95 MB
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“UK mathematicians Griffiths (Univ. of Dundee) and Dold and Silvester (both, Univ. of Manchester) introduce undergraduates to partial differential equations (PDEs) from both the analytical and numerical points of view. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (D. P. Turner, Choice, Vol. 53 (11), July, 2016)
“This introduction to partial differential equations is designed for upper level undergraduates in mathematics. … The writing is lively, the authors make appealing use of computational examples and visualization, and they are very successful at conveying and integrating physical intuition. … This is probably the best introductory book on PDEs that I have seen in some time. It is well worth a look.” (William J. Satzer, MAA Reviews, maa.org, April, 2016)
“This textbook offers a nice introduction to analytical and numerical methods for partial differential equations. … The book is self-contained and the prerequisites is a standard course in calculus and linear algebra. The textbook appeals to undergraduate students in both scientific and engineering programs in which PDEs are of practical importance.” (Marius Ghergu, zbMATH 1330.35001, 2016)
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