(DE23) Convolutions and Integral Equations

In this video, we revisit the Laplace transform and more of its ability to help us solve both differential and integral equations. We introduce the convolutions of two (or more) functions in the spatial domain, and discuss how the product of their Laplace transforms in the frequency domain is connected to the convolution of the functions in the spatial domain, and how this can allow us to gain access to the inverse Laplace transform of a wider variety of functions, and in turn solve more differential equations. We also introduce the Volterra integral equations, and solve a particular subset that is referred to as convolution equations.

*--The Let's Learn, Nemo Community--*

#differentialequation #convolutiontheorem #integralequation

[LetsLearnNemo]

Slight typo: At 24:18, make sure to have sin^2(t) on the second integral. Once carried out, the final result of sine convoluted with itself will be (1/2)*(sin x - x cos x).