Faster access than browser!Similarities between Differential form and Exterior derivative
Differential form and Exterior derivative have 20 things in common (in Unionpedia): Atlas (topology), Élie Cartan, Calculus on Manifolds (book), Chain complex, Closed and exact differential forms, Cotangent bundle, De Rham cohomology, Differentiable manifold, Directional derivative, Divergence theorem, Exterior algebra, Green's theorem, Hodge star operator, Lie derivative, One-form, Pseudo-Riemannian manifold, Pullback (differential geometry), Smoothness, Stokes' theorem, Vector field.
Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
Atlas (topology) and Differential form · Atlas (topology) and Exterior derivative ·
Élie Cartan
Élie Joseph Cartan, ForMemRS (9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups and their geometric applications.
Élie Cartan and Differential form · Élie Cartan and Exterior derivative ·
Calculus on Manifolds (book)
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) by Michael Spivak is a brief (146 pp.) monograph on the theory of vector-valued functions of several real variables (f: Rn→Rm) and differentiable manifolds in Euclidean space.
Calculus on Manifolds (book) and Differential form · Calculus on Manifolds (book) and Exterior derivative ·
Chain complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.
Chain complex and Differential form · Chain complex and Exterior derivative ·
Closed and exact differential forms
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα.
Closed and exact differential forms and Differential form · Closed and exact differential forms and Exterior derivative ·
Cotangent bundle
In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold.
Cotangent bundle and Differential form · Cotangent bundle and Exterior derivative ·
De Rham cohomology
In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes.
De Rham cohomology and Differential form · De Rham cohomology and Exterior derivative ·
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
Differentiable manifold and Differential form · Differentiable manifold and Exterior derivative ·
Directional derivative
In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant.
Differential form and Directional derivative · Directional derivative and Exterior derivative ·
Divergence theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface.
Differential form and Divergence theorem · Divergence theorem and Exterior derivative ·
Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
Differential form and Exterior algebra · Exterior algebra and Exterior derivative ·
Green's theorem
In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green, though its first proof is due to Bernhard Riemann and is the two-dimensional special case of the more general Kelvin–Stokes theorem.
Differential form and Green's theorem · Exterior derivative and Green's theorem ·
Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
Differential form and Hodge star operator · Exterior derivative and Hodge star operator ·
Lie derivative
In differential geometry, the Lie derivative, named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including scalar function, vector field and one-form), along the flow defined by another vector field.
Differential form and Lie derivative · Exterior derivative and Lie derivative ·
One-form
In linear algebra, a one-form on a vector space is the same as a linear functional on the space.
Differential form and One-form · Exterior derivative and One-form ·
Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
Differential form and Pseudo-Riemannian manifold · Exterior derivative and Pseudo-Riemannian manifold ·
Pullback (differential geometry)
Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ*.
Differential form and Pullback (differential geometry) · Exterior derivative and Pullback (differential geometry) ·
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
Differential form and Smoothness · Exterior derivative and Smoothness ·
Stokes' theorem
In vector calculus, and more generally differential geometry, Stokes' theorem (also called the generalized Stokes theorem or the Stokes–Cartan theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
Differential form and Stokes' theorem · Exterior derivative and Stokes' theorem ·
Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
Differential form and Vector field · Exterior derivative and Vector field ·
The list above answers the following questions
- What Differential form and Exterior derivative have in common
- What are the similarities between Differential form and Exterior derivative
Differential form and Exterior derivative Comparison
Differential form has 118 relations, while Exterior derivative has 43. As they have in common 20, the Jaccard index is 12.42% = 20 / (118 + 43).
References
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