Singularity functions are a class of discontinuous functions that contain singularities, i.e., they are discontinuous at their singular points.

Apr 16, 2021 · This method of analysis was first introduced by Macaulay in 1919, and it entails the use of one equation that contains a singularity or half-range function to describe the entire beam …

Singularity functions (also called singular functions) are any functions that contain singularities. The singularities can be poles, removable singularities, or essential singularities. Singularity functions can …

The loading of beams can be determined from a superposition of singular-ity functions for the load distribution function q(x). The unit doublet is the distribution function representation for the applied …

When calculating the shear Force and the bending moment diagrams for more complex loading across discontinuities such as concentrated loads and moments. Simple methods are not enough. For the …

It is possible to use singularity functions to generate or synthesize different signals. An example is shown below to show how a rectangular pulse signal can be visualized as the combination of two …

Feb 13, 2026 · Singularities are often also called singular points. Singularities are extremely important in complex analysis, where they characterize the possible behaviors of analytic functions. Complex …

Sep 12, 2023 · The following simplifications are broken up into four categories depending on which singularity function is used and whether it is the sole integrand or part of a more complex expression.

Recall that the point α is called a singular point, or singularity, of the complex function f if f is not analytic at the point , α, but every neighborhood D R (α) of α contains at least one point at which f is analytic.

Oct 31, 2025 · At the end of yesterday’s class, we noted that every singularity of a meromorphic function (i.e. the ratio of two analytic functions) is isolated, so this is a useful notion.