Exterior Differential Systems and Equivalence Problems: 73 (Mathematics and Its Applications, 73) - Hardcover

Kichoon Yang

Hardcover

ISBN 10: 0792315936 ISBN 13: 9780792315933

Publisher: Springer, 1992

Synopsis

tEl moi, "0, si j'avait su comment en revenir, je One service mathematics has rendered the n 'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlinea- ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other s- ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One s- vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

About this title

Synopsis

This monograph presents a concise account of exterior differential system theory so that it can be quickly applied to problems. The first part deals with the general theory: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are carefully laid out, quasi-linear differential systems are examined in detail, and explicit examples of the Spencer cohomology groups and the characteristic variety are given. The second part deals with applications to problems in differential geometry: the isometric embedding theorem of Cartan-Janet and its various geometric ramifications are discussed, a proof of the Andreotti-Hill theorem on the C-R embedding problem is given, and embeddings of abstract projective structures are discussed. Aimed at researchers and graduate students who would like an introduction to exterior differential systems, this volume should also be useful to those whose work involves differential geometry and partial differential equations.

Edition details

• Publisher: Springer
• Publication date: 1992
• Language: English
• ISBN 10: 0792315936
• ISBN 13: 9780792315933
• Binding: Hardcover
• Number of pages: 207