In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...

and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α...

complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms have...

vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values...

In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold M...

shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry...

has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory...

calculus, a differential or differential form is said to be exact or perfect (exact differential), as contrasted with an inexact differential, if it is...

field. Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional...

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...

. More generally, any covariant tensor field – in particular any differential form – on N {\displaystyle N} may be pulled back to M {\displaystyle M}...

In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal...

In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. The notion was introduced...

In differential geometry, a Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the...

to introduce the notion of the pullback of a differential form. Roughly speaking, when a differential form is integrated, applying the pullback transforms...

In mathematics, differential forms on a Riemann surface are an important special case of the general theory of differential forms on smooth manifolds...

In differential geometry, an equivariant differential form on a manifold M acted upon by a Lie group G is a polynomial map α : g → Ω ∗ ( M ) {\displaystyle...

In algebra, the ring of polynomial differential forms on the standard n-simplex is the differential graded algebra: Ωpoly∗([n])=Q[t0,...,tn,dt0,...,dtn]/(∑ti−1...

Gauss's law for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem...

putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) way. Given...

language of differential geometry and differential forms is used. The electric and magnetic fields are now jointly described by a 2-form F in a 4-dimensional...

geometrical significance if the differential is regarded as a particular differential form, or analytical significance if the differential is regarded as a linear...

other mathematical theories including vector calculus, differential geometry, and differential forms. With a geometric algebra given, let a {\displaystyle...

of differential form. In contrast, an integral of an exact differential is always path independent since the integral acts to invert the differential operator...

In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...

equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which...

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other...

geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept was introduced...

that is linear in both arguments Differential form, a concept from differential topology that combines multilinear forms and smooth functions First-order...