Intuitive understanding of convolution?

I had a terrible adjunct professor in ODEs and got little or no theory. I'm not in PDEs and my much better professor just (re)introduced convolutions while generalizing the heat equation to Rn - unfortunately it was not a reintroduction for me.

Later chapters in the book deal with transforms, which are, I think "special" convolutions where you mix the subject function with a specific kernel function. Apparently I need to understand this concept.

Any resources for getting an intuitive understanding of what a convolution *is* and why one would want to do such a thing? I played around on Youtube and Wikipedia and I see the mechanics but not the theory.

Thanks
 
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Convolution was first derived somewhere along the progress of when mathematicians were trying to solve the problems associated with Fourier transform.

It would be best if you could find a book on Fourier Transform. You could also find the explanation on Stanford's Youtube channel but I think you would need to start from lecture 1 to understand it.
 

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