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Publication

Calculus of variations with differential forms

Bernard Dacorogna, Saugata Bandyopadhyay, Swarnendu Sil
2015
Journal Articles

Abstract

We study integrals of the form integral(Omega) f (d omega), where 1

Official source

https://infoscience.epfl.ch/entities/publication/e05da5ef-41d2-47f9-b3e3-f64c26b40b7b

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Bernard Dacorogna, Saugata Bandyopadhyay, Swarnendu Sil
2015
Journal Articles

Abstract

We study integrals of the form integral(Omega) f (d omega), where 1

Official source

https://infoscience.epfl.ch/entities/publication/e05da5ef-41d2-47f9-b3e3-f64c26b40b7b

About this result

Related concepts (29)

Integral

In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Today integration is used in a wide variety of scientific fields.

Elliptic integral

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (1750). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse. Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the form where R is a rational function of its two arguments, P is a polynomial of degree 3 or 4 with no repeated roots, and c is a constant.

Gaussian integral

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function over the entire real line. Named after the German mathematician Carl Friedrich Gauss, the integral is Abraham de Moivre originally discovered this type of integral in 1733, while Gauss published the precise integral in 1809. The integral has a wide range of applications. For example, with a slight change of variables it is used to compute the normalizing constant of the normal distribution.

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