Exterior Differential Systems

Häftad, Engelska, 2011

Del i serien Mathematical Sciences Research Institute Publications

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Beskrivning

An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. 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.

Produktinformation

Utgivningsdatum:2011-12-14
Mått:155 x 235 x 25 mm
Vikt:742 g
Format:Häftad
Språk:Engelska
Serie:Mathematical Sciences Research Institute Publications
Antal sidor:475
Förlag:Springer-Verlag New York Inc.
ISBN:9781461397168

Utforska kategorier

Topologi inom Naturvetenskap och teknik

Innehållsförteckning

I. Preliminaries.- §1. Review of Exterior Algebra.- §2. The Notion of an Exterior Differential System.- §3. Jet Bundles.- II. Basic Theorems.- §1. Probenius Theorem.- §2. Cauchy Characteristics.- §3. Theorems of Pfaff and Darboux.- §4. Pfaffian Systems.- §5. Pfaffian Systems of Codimension Two.- III. Cartan-Kähler Theory.- §1. Integral Elements.- §2. The Cartan-Kähler Theorem.- §3. Examples.- IV. Linear Differential Systems.- §1. Independence Condition and Involution.- §2. Linear Differential Systems.- §3. Tableaux.- §4. Tableaux Associated to an Integral Element.- §5. Linear Pfaffian Systems.- §6. Prolongation.- §7. Examples.- §8. Families of Isometric Surfaces in Euclidean Space.- V. The Characteristic Variety.- §1. Definition of the Characteristic Variety of a Differential System.- §2. The Characteristic Variety for Linearc Pfaffian Systems; Examples.- §3. Properties of the Characteristic Variety.- VI. Prolongation Theory.- §1. The Notion of Prolongation.- §2. Ordinary Prolongation.- §3. The Prolongation Theorem.- §4. The Process of Prolongation.- VII. Examples.- §1. First Order Equations for Two Functions of Two Variables.- §2. Finiteness of the Web Rank.- §3. Orthogonal Coordinates.- §4. Isometric Embedding.- VIII. Applications of Commutative Algebra and Algebraic Geometry to the Study of Exterior Differential Systems.- §1. Involutive Tableaux.- §2. The Cartan-Poincaré Lemma, Spencer Cohomology.- §3. The Graded Module Associated to a Tableau; Koszul Homology.- §4. The Canonical Resolution of an Involutive Module.- §5. Localization; the Proofs of Theorem 3.2 and Proposition 3.8.- §6. Proof of Theorem 3.8 in Chapter V; Guillemin’s Normal Form.- §7. The Graded Module Associated to a Higher Order Tableau.- IX. PartialDifferential Equations.- §1. An Integrability Criterion.- §2. Quasi-Linear Equations.- §3. Existence Theorems.- X. Linear Differential Operators.- §1. Formal Theory and Complexes.- §2. Examples.- §3. Existence Theorems for Elliptic Equations.