### Math ClubWhen Functions Have No Value(s): Delta Functions And Distributions Steven Johnson (MIT)

Wednesday, February 24, 2021
5:45pm – 6:35pm

Storrs Campus
Online

I will give a brief introduction to the motivations, concepts, and properties of distributions, which generalize the notion of functions $$f(x)$$ to allow derivatives of discontinuities, “delta” functions, and other nice things. In the land of distributions, everything is infinitely differentiable, exchanging limits and derivatives is always okay, and no vague infinities are involved in delta functions. Distributions are central to understanding Fourier transforms, partial differential equations, and many applications of calculus to physics and engineering, but were only formalized in the 1950s. Although this is ultimately a deep subject, the key ideas should be accessible to anyone who has mastered basic calculus.

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