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|This book is equally essential as a course text, as a work of reference, or simply as a brilliant mathematical exercise.|
|Of course, the study of Euler-Lagrange equations by means of exterior differential |
forms and the method of equivalence is not new. In fact, much of the 19th century
material in this area is so naturally formulated in terms of differential forms (cf.
|The following section studies the relations between the method of differential |
constraints and Lie-Backlund groups of ... of partial differential equations is then
reduced to the problem of the compatibility of a system of exterior differential
|Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.|
|Exterior forms of degree 1 become immediately available as elements of the dual |
space of the tangent space. ... While nineteenth-century mathematics was
primarily concerned with developing specific methods to solve specific equations,
it is ...
|methods are very natural and effective. However, in many other situations the use |
of the exterior calculus, often combined with the method of moving frames of E.
Cartan, leads to decisive results in a way which is very diflicult with tensors alone
|Rather, exterior product or ADP of an r-form and a p-form yield an (r + p)-form. An |
r-form u> is written in terms of differential dx' as: u = Lji'...irdxi' f\--- f\dxir. (4.66) So,
r-forms u are called differential forms. Though tensor methods are very natural ...
Michiel Hazewinkel - 1994 - Preview
|In the study of submanifolds of the manifold M, Cartan's method of exterior forms |
is usually applied in conjunction with the moving-frame method (see, for example
, ). The method is named after E. Cartan, who, from 1899 onward, made ...
|This calculus of differential forms is the promised generalization of ordinary |
vector calculus. ... tools of the calculus of differential forms are so efficient that we
now go to some lengths to cast problems into a form amenable to these methods.
|35 Differential Form Methods in the Theory of Variational Systems and |
Lagrangian Field Theories ROBERT HERMANN* 53 Jordan Road, Brookline, MA
02146, U.S.A. (Received: 30 June 1987; revised: 7 March 1988) Abstract. This
paper will ...
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