Current (mathematics)
In mathematics, more particularly in functional analysis, differential topology, and geometric measure theory, a k-current in the sense of Georges de Rham is a functional on the space of compactly supported differential k-forms, on a smooth manifold M. Formally currents behave like Schwartz distributions on a space of differential forms. In a geometric setting, they can represent integration over a submanifold, generalizing the Dirac delta function, or more generally even directional derivatives of delta functions (multipoles) spread out along subsets of M.
Read more about Current (mathematics): Definition, Homological Theory, Topology and Norms, Examples
Famous quotes containing the word current:
“But there, where I have garnered up my heart,
Where either I must live or bear no life;
The fountain from the which my current runs
Or else dries up: to be discarded thence,
Or keep it as a cistern for foul toads
To knot and gender in!”
—William Shakespeare (1564–1616)