Robert L Bryant

(Author)

Exterior Differential Systems (Softcover Reprint of the Original 1st 1991)Paperback - Softcover Reprint of the Original 1st 1991, 14 December 2011

Exterior Differential Systems (Softcover Reprint of the Original 1st 1991)
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Part of Series
Mathematical Sciences Research Institute Publications
Print Length
475 pages
Language
English
Publisher
Springer
Date Published
14 Dec 2011
ISBN-10
1461397162
ISBN-13
9781461397168

Description

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.

Product Details

Authors:
Robert L BryantS S ChernRobert B GardnerHubert L GoldschmidtP a Griffiths
Book Edition:
Softcover Reprint of the Original 1st 1991
Book Format:
Paperback
Country of Origin:
NL
Date Published:
14 December 2011
Dimensions:
23.39 x 15.6 x 2.49 cm
ISBN-10:
1461397162
ISBN-13:
9781461397168
Language:
English
Location:
New York, NY
Pages:
475
Publisher:
Weight:
675.85 gm

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