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Encyclopedia of Mathematics and Its Applications Ser.: Lie's Structural Approach to PDE Systems by Olle Stormark (2012, Trade Paperback)
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Lie's Structural Approach to PDE Systems by Olle Stormark. Author Olle Stormark. 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.
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-101107403324
ISBN-139781107403321
eBay Product ID (ePID)109110207
Product Key Features
Number of Pages590 Pages
Publication NameLie's Structural Approach to Pde Systems
LanguageEnglish
Publication Year2012
SubjectGeneral, Differential Equations / Partial
TypeTextbook
AuthorOlle Stormark
Subject AreaMathematics
SeriesEncyclopedia of Mathematics and Its Applications Ser.
FormatTrade Paperback
Dimensions
Item Height1.2 in
Item Weight29 Oz
Item Length9.2 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
Dewey Edition21
ReviewsReview 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 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, "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
Series Volume NumberSeries Number 80
IllustratedYes
Dewey Decimal515/.353
Table Of ContentPreface; 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.
SynopsisThis 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 NumberQA374
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