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Lie's Structural Approach to PDE-Systeme Hardcover Olle Stormark-
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eBay-Artikelnr.:295211985572
Artikelmerkmale
- Artikelzustand
- Features
- Ex-Library
- ISBN
- 9780521780889
Über dieses Produkt
Product Identifiers
Publisher
Cambridge University Press
ISBN-10
0521780888
ISBN-13
9780521780889
eBay Product ID (ePID)
1706798
Product Key Features
Number of Pages
590 Pages
Language
English
Publication Name
Lie's Structural Approach to Pde Systems
Subject
General, Differential Equations / Partial
Publication Year
2000
Type
Textbook
Subject Area
Mathematics
Series
Encyclopedia of Mathematics and Its Applications Ser.
Format
Hardcover
Dimensions
Item Height
1.3 in
Item Weight
38.2 Oz
Item Length
9.4 in
Item Width
6.2 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-054436
Reviews
'... a worthwhile and successful attempt to introduce the ideas of Sophus Lie.’H. Boseck, Zentralblatt für Mathematik, Review of the hardback: '... a worthwhile and successful attempt to introduce the ideas of Sophus Lie.' H. Boseck, Zentralblatt für Mathematik, Review of the hardback: '... a worthwhile and successful attempt to introduce the ideas of Sophus Lie.' H. Boseck, Zentralblatt f r Mathematik, Review of the hardback: '… a worthwhile and successful attempt to introduce the ideas of Sophus Lie.' H. Boseck, Zentralblatt fr Mathematik, '... a worthwhile and successful attempt to introduce the ideas of Sophus Lie.' H. Boseck, Zentralblatt für Mathematik, "The book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations; it will be a valuable resource for graduate students and researchers in related fields." Mathematical Reviews
Dewey Edition
21
Series Volume Number
Series Number 80
Illustrated
Yes
Dewey Decimal
515/.353
Table Of Content
Preface; 1. Introduction and summary; 2. PDE systems, pfaffian systems and vector field systems; 3. Cartan's local existence theorem; 4. Involutivity and the prolongation theorem; 5. Drach's classification, second order PDEs in one dependent variable and Monge characteristics; 6. Integration of vector field systems n satisfying dim n' = dim n + 1; 7. Higher order contact transformations; 8. Local Lie groups; 9. Structural classification of 3-dimensional Lie algebras over the complex numbers; 10. Lie equations and Lie vector field systems; 11. Second order PDEs in one dependent and two independent variables; 12. Hyperbolic PDEs with Monge systems admitting 2 or 3 first integrals; 13. Classification of hyperbolic Goursat equations; 14. Cartan's theory of Lie pseudogroups; 15. The equivalence problem; 16. Parabolic PDEs for which the Monge system admits at least two first integrals; 17. The equivalence problem for general 3-dimensional pfaffian systems in five variables; 18. Involutive second order PDE systems in one dependent and three independent variables, solved by the method of Monge; Bibliography; Index.
Synopsis
This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques., Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear PDE systems without using power series techniques, it describes a general approach to PDE systems based on ideas developed by Lie, Cartan and Vessiot. The central theme is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields., This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.
LC Classification Number
QA377 .S846 2000
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