#test function

[isomorphismes]

Test functions and [tempered] distributions require the notion of topological vector space … distributions can be traced back to Green's functions in the 1830’s to solve ordinary differential equations … the 1936 work of Sergei Sobolev on hyperbolic PDE’s.

Laurent Schwartz introduced the term "distribution" by analogy with a distribution of electrical charge, possibly including not only point charges but also dipoles and so on.

tempered distribution

topological vector space

(^ if there is a dipole, there must be a notion of subtraction, hence the need for a vector, and to speak of this very conceptually, use a TVS)

[peeterjoot]

Derivative of a delta function

Derivative of a delta function

[Click here for a PDF of this post with nicer formatting]

In the geometric algebra formulation of Maxwell’s equation (singular in GA), the Green’s function for the spacetime derivative ends up with terms like

\begin{equation}\label{eqn:derivativeOfDeltaFunction:20} \frac{d}{dr} \delta( -r/c + t – t’ ), \end{equation}

or \begin{equation}\label{eqn:derivativeOfDeltaFunction:40} \frac{d}{dt} \delta(…

View On WordPress

[rockofcalifa]

when ur faulty python code makes the test function throw an error: just asserts