Exterior Differential Systems

Exterior Differential Systems

AngličtinaMäkká väzbaTlač na objednávku
Bryant Robert L.
Springer-Verlag New York Inc.
EAN: 9781461397168
Tlač na objednávku
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Podrobné informácie

This book gives a treatment of exterior differential systems. It will in­ clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde­ pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen­ dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.
EAN 9781461397168
ISBN 1461397162
Typ produktu Mäkká väzba
Vydavateľ Springer-Verlag New York Inc.
Dátum vydania 14. decembra 2011
Stránky 475
Jazyk English
Rozmery 235 x 155
Krajina United States
Čitatelia Professional & Scholarly
Autori Bryant Robert L.; Chern, S.S.; Gardner Robert B.; Goldschmidt Hubert L.; Griffiths P.A.
Ilustrácie VII, 475 p.
Edícia Softcover reprint of the original 1st ed. 1991
Séria Mathematical Sciences Research Institute Publications