Foundations of the Classical Theory (v. 1) (Encyclopaedia of Mathematical Sciences) - Hardcover

Hardcover

ISBN 10: 3540520023 ISBN 13: 9783540520023

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1991

Synopsis

Partial differential equations are as old as calculus itself, occurring as examples in the papers of Newton and Leibniz. Since the beginning, they have been strongly linked to physics and other sciences. This volume presents an introduction to the classical theory, emphasizing along the way physical methods and physical interpretations. The book beings with a derivation of some of the classical partial differential equations, and a discussion of the limitations of the physical models upon which the derivations are based. The second chapter discusses the classical methods for studying PDEs, including the theory of distributions and the Petrovskij classification into elliptic, parabolic and hyperbolic equations. Among the more advanced methods discussed are spectral theory, the method of planar waves and the theory of semigroups. Every topic considered is placed in its present context in mathematical research, yet the book never loses sight of the non-specialist reader with an interest in physical applications.

About this title

Review

From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for the nonspecialists and physicists but in my opinion almost every specialist will find something new for herself/himself in the text. ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993

From the Back Cover

From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..."
The Mathematical Intelligencer, 1993
"... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..."
Acta Scientiarum Mathematicarum, 1993

"... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume."
Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Courant-Hilbert "Methods of Mathematical Physics", but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. The book gives a good and readable overview of the subject. ... carefully written, well translated, and well produced."
The Mathematical Gazette, 1993

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1991
• Language: English
• ISBN 10: 3540520023
• ISBN 13: 9783540520023
• Binding: Hardcover
• Number of pages: 264
• Editor: IU.V.Egorov, Shubin M. A., Egorov IU.V.