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Partial Differential Equations: Classical Theory with a Modern Touch

Nandakumaran, AK and Datti, PS (2020) Partial Differential Equations: Classical Theory with a Modern Touch. Cambridge University Press, Cambridge, pp. 1-356. ISBN 9781108839808

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Abstract

The subject of partial differential equations (PDE) has undergone great change during the last 70 years or so, after the development of modern functional analysis; in particular, distribution theory and Sobolev spaces. In the modern concept, the PDE is visualized in a more general setup of functional analysis, where we look for solutions in a sense weaker than the usual classical sense to address the more physically relevant solutions. Though the aim of the present book is to introduce the fundamental topics in a classical way as in any first book on PDE, the authors have demonstrated the basic topics in a way that opens the doors to the modern theory. Readers can immediately and naturally sense the importance of studying these topics in a modern approach. As a lead, after introducing method of characteristics for first order equations, the authors have immediately discussed the importance of introducing the notion of weak solutions to two important classes of first order equations, namely conservation laws and Hamilton�Jacobi equations. The implication is that physically relevant solutions cannot be obtained within the realm of classical solutions. Almost all the chapters cover something about modern topics. Also included are many exercises in most chapters, which help students get better insight. Hints or answers are provided to some selected exercises. © A. K. Nandakumaran and P. S. Datti 2020.

Item Type: Book
Publication: Partial Differential Equations: Classical Theory with a Modern Touch
Publisher: Cambridge University Press
Additional Information: The copyright for this article belongs to Cambridge University Press
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 30 Oct 2024 06:51
Last Modified: 30 Oct 2024 06:51
URI: http://eprints.iisc.ac.in/id/eprint/86533

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