Theory and Applications of Partial Differential Equations: 46 (Mathematical Concepts and Methods in Science and Engineering, 46) - Hardcover

Bassanini, Piero; Elcrat, Alan R.

Hardcover

ISBN 10: 0306456400 ISBN 13: 9780306456404

Publisher: Springer, 1997

Synopsis

This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

About this title

Review

`Informative and clearly and concisely written...Bassanini and Elcrat offer an excellent pedagogical resource.'
Choice, October 1998

Synopsis

This masterful text introduces first-year graduate students to the basic ideas of the theory of partial differential equations in the context of the three fundamental equations of classical mathematical physics - the wave and heat equations and the Laplace equation. The authors avoid abstractions and succeed in demonstrating ideas by way of relatively simple, straightforward applications. Their book also deals with more advanced topics, including: the De Giorgi-Nash-Moser theorem; nonlinear Dirichlet problems for elliptic equations; distributions and Sobolev spaces; and, hyperbolic conservation laws in one space variable.

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 0306456400
• ISBN 13: 9780306456404
• Binding: Hardcover
• Number of pages: 453