Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Differential_form> ?p ?o. }
Showing items 1 to 41 of
41
with 100 items per page.
- Differential_form abstract "In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics.For instance, the expression f(x) dx from one-variable calculus is called a 1-form, and can be integrated over an interval [a,b] in the domain of f:and similarly the expression: f(x,y,z) dx∧dy + g(x,y,z) dx∧dz + h(x,y,z) dy∧dz is a 2-form that has a surface integral over an oriented surface S:Likewise, a 3-form f(x, y, z) dx∧dy∧dz represents a volume element that can be integrated over a region of space.The algebra of differential forms is organized in a way that naturally reflects the orientation of the domain of integration. There is an operation d on differential forms known as the exterior derivative that, when acting on a k-form produces a (k+1)-form. This operation extends the differential of a function, and the divergence and the curl of a vector field in an appropriate sense that makes the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem special cases of the same general result, known in this context also as the general Stokes' theorem. In a deeper way, this theorem relates the topology of the domain of integration to the structure of the differential forms themselves; the precise connection is known as De Rham's theorem.The general setting for the study of differential forms is on a differentiable manifold. Differential 1-forms are naturally dual to vector fields on a manifold, and the pairing between vector fields and 1-forms is extended to arbitrary differential forms by the interior product. The algebra of differential forms along with the exterior derivative defined on it is preserved by the pullback under smooth functions between two manifolds. This feature allows geometrically invariant information to be moved from one space to another via the pullback, provided the information is expressed in terms of differential forms. As an example, the change of variables formula for integration becomes a simple statement that an integral is preserved under pullback.".
- Differential_form wikiPageID "221519".
- Differential_form wikiPageRevisionID "604325712".
- Differential_form hasPhotoCollection Differential_form.
- Differential_form subject Category:Differential_forms.
- Differential_form type Abstraction100002137.
- Differential_form type DifferentialForms.
- Differential_form type Form106290637.
- Differential_form type LanguageUnit106284225.
- Differential_form type Part113809207.
- Differential_form type Relation100031921.
- Differential_form type Word106286395.
- Differential_form comment "In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan.".
- Differential_form label "Differentiaalvorm".
- Differential_form label "Differential form".
- Differential_form label "Differentialform".
- Differential_form label "Forma diferencial".
- Differential_form label "Forma diferencial".
- Differential_form label "Forma differenziale".
- Differential_form label "Forma różniczkowa".
- Differential_form label "Forme différentielle".
- Differential_form label "Дифференциальная форма".
- Differential_form label "微分形式".
- Differential_form label "微分形式".
- Differential_form sameAs Diferenciální_forma.
- Differential_form sameAs Differentialform.
- Differential_form sameAs Forma_diferencial.
- Differential_form sameAs Forma_diferentzial.
- Differential_form sameAs Forme_différentielle.
- Differential_form sameAs Forma_differenziale.
- Differential_form sameAs 微分形式.
- Differential_form sameAs 미분형식.
- Differential_form sameAs Differentiaalvorm.
- Differential_form sameAs Forma_różniczkowa.
- Differential_form sameAs Forma_diferencial.
- Differential_form sameAs m.01gbgc.
- Differential_form sameAs Q1047080.
- Differential_form sameAs Q1047080.
- Differential_form sameAs Differential_form.
- Differential_form wasDerivedFrom Differential_form?oldid=604325712.
- Differential_form isPrimaryTopicOf Differential_form.