Band 18
Exterior Differential Systems
Aus der Reihe
Mathematical Sciences Research Institute Publications
-
- Englisch ausgewählt
Fr. 182.00
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
14.12.2011
Abbildungen
VII, 475 p.
Verlag
Springer UsSeitenzahl
475
Maße (L/B/H)
23.5/15.5/2.7 cm
Gewicht
733 g
Auflage
Softcover reprint of the original 1st ed. 1991
Sprache
Englisch
ISBN
978-1-4613-9716-8
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.
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