A Course on Partial Differential Equations (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 197) - Hardcover

Walter Craig

Hardcover

ISBN 10: 1470442922 ISBN 13: 9781470442927

Publisher: American Mathematical Society, 2018

Synopsis

Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view. In addition to the three principal examples of the wave equation, the heat equation, and Laplace's equation, the book has chapters on dispersion and the Schrödinger equation, nonlinear hyperbolic conservation laws, and shock waves. The book covers material for an introductory course that is aimed at beginning graduate or advanced undergraduate level students. Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. Each chapter includes a comprehensive set of exercises, and most chapters have additional projects, which are intended to give students opportunities for more in-depth and open-ended study of solutions of partial differential equations and their properties.

About this title

Review

I really enjoyed reading 'A Course on Partial Differential Equations'. The writing is clear and engaging, the derivations are very well-developed, and the author does a nice job connecting the mathematics with the physical motivation that underlies many of the PDEs discussed in the text... I wish that it would have been available when I was a student...'A Course on Partial Differential Equations' is an excellent book that provides a modern introduction to a fascinating field of mathematics and I highly recommend reading it. --Jason Graham, MAA Reviews

The content is developed in a clear and engaging way, the derivations are very well developed, and the author does a nice job connecting the mathematics with the physical motivation. This volume is a very pleasant book written by a renowned expert in this field. The book offers a nice elementary introduction to a fascinating field of mathematics with multiple relevant applications to various fields. --Vicen iu D. Radulescu, Mathematical Reviews

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• ISBN 10: 1470442922
• ISBN 13: 9781470442927
• Binding: Hardcover
• Language: English
• Number of pages: 205