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- Integrability_conditions_for_differential_systems abstract "In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example. A Pfaffian system is one specified by 1-forms alone, but the theory includes other types of example of differential system.Given a collection of differential 1-forms αi, i=1,2, ..., k on an n-dimensional manifold M, an integral manifold is a submanifold whose tangent space at every point p ∈ M is annihilated by each αi.A maximal integral manifold is a submanifold such that the kernel of the restriction map on formsis spanned by the αi at every point p of N. If in addition the αi are linearly independent, then N is (n − k)-dimensional. Note that i: N ⊂ M need not be an embedded submanifold.A Pfaffian system is said to be completely integrable if N admits a foliation by maximal integral manifolds. (Note that the foliation need not be regular; i.e. the leaves of the foliation might not be embedded submanifolds.)An integrability condition is a condition on the αi to guarantee that there will be integral submanifolds of sufficiently high dimension.".
- Integrability_conditions_for_differential_systems wikiPageID "968734".
- Integrability_conditions_for_differential_systems wikiPageRevisionID "542595547".
- Integrability_conditions_for_differential_systems hasPhotoCollection Integrability_conditions_for_differential_systems.
- Integrability_conditions_for_differential_systems subject Category:Differential_systems.
- Integrability_conditions_for_differential_systems subject Category:Differential_topology.
- Integrability_conditions_for_differential_systems subject Category:Partial_differential_equations.
- Integrability_conditions_for_differential_systems type Artifact100021939.
- Integrability_conditions_for_differential_systems type DifferentialSystems.
- Integrability_conditions_for_differential_systems type Instrumentality103575240.
- Integrability_conditions_for_differential_systems type Object100002684.
- Integrability_conditions_for_differential_systems type PhysicalEntity100001930.
- Integrability_conditions_for_differential_systems type System104377057.
- Integrability_conditions_for_differential_systems type Whole100003553.
- Integrability_conditions_for_differential_systems comment "In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example.".
- Integrability_conditions_for_differential_systems label "Forma Pfaffa".
- Integrability_conditions_for_differential_systems label "Integrability conditions for differential systems".
- Integrability_conditions_for_differential_systems label "Pfaffsche Form".
- Integrability_conditions_for_differential_systems label "Пфаффово уравнение".
- Integrability_conditions_for_differential_systems label "微分方程式系の可積分条件".
- Integrability_conditions_for_differential_systems sameAs Pfaffsche_Form.
- Integrability_conditions_for_differential_systems sameAs 微分方程式系の可積分条件.
- Integrability_conditions_for_differential_systems sameAs Forma_Pfaffa.
- Integrability_conditions_for_differential_systems sameAs Q382583.
- Integrability_conditions_for_differential_systems sameAs Q382583.
- Integrability_conditions_for_differential_systems sameAs Integrability_conditions_for_differential_systems.
- Integrability_conditions_for_differential_systems wasDerivedFrom Integrability_conditions_for_differential_systems?oldid=542595547.
- Integrability_conditions_for_differential_systems isPrimaryTopicOf Integrability_conditions_for_differential_systems.