Lecture Notes On Geometrical Aspects Of Partial Differential Equations
Published on 1. March 1992
Book
Hardback
372 pages
978-981-02-0753-3 (ISBN)
Description
This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.
More details
Series
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 25 mm
Weight
689 gr
ISBN-13
978-981-02-0753-3 (9789810207533)
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Schweitzer Classification
Person
Content
Part 1: Infinite dimensional manifolds. Part 2 Differential manifolds and PDE: Cartan distributions and differential manifolds; Lie-Backlund mappings and symmetry groups; Lie-Backlund fields and infinitesimal symmetries; Cartan forms, currents and conservation laws; c-spectral sequence. Part 3 External geometry: Backlund correspondence; differential submanifolds and the normal projection; external fields and forms; Green's formula; characteristic mapping. Part 4 Examples: trivial equations; evolution equations; Cauchy-Kowalevsky equations; Hamiltonian equations; Euler-Lagrange equations; Noether theorem; the classical relativistic string. Part 5 Differential algebras and PDE: differential algebras; fields, forms and differential operators; resolutions of differential algebras; differential ideals; conservation laws of lower dimensions.