= x0, the load distribution is written As the integration of the delta function results in the Heaviside step function, it follows that the static deflection of a slender beam subject to multiple point loads is described by a set of piecewise polynomials. Also, a point moment acting on a beam can be described by delta functions. Consider two opposing point forces F at a distance d apart. They then produce a moment M = Fd acting on the beam. Now, let the distance d approach the limit zero, while M is kept constant. The load distribution, assuming a clockwise moment acting at x = 0, is written Point moments can thus be represented by the derivative of the delta function. Integration of the beam equation again results in piecewise polynomial deflection. See also Atom (measure theory) Laplacian of the indicator Notes References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . External links KhanAcademy.org video lesson The Dirac Delta function, a tutorial on the Dirac delta function. Video Lectures – Lecture 23, a lecture by Arthur Mattuck. The Dirac delta measure is a hyperfunction We show the existence of a unique solution and analyze a finite element approximation when the source term is a Dirac delta measure Non-Lebesgue measures on R. Lebesgue-Stieltjes measure, Dirac delta measure. Fourier analysis Generalized functions Measure theory Digital signal processing Delta function