A 'Derivation' of the Laplace Transform kernel

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Here is use the differentiation property of the Laplace transform to "derive" the kernel of the Laplace transform integral.
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Amazing explanation!!! Is there a way I can get in contact with you, Professor Dave?
I’m an electrical engineer with a few questions which most teachers I had could never really answer, and I do believe you might be able to help me. Do you have any email I could address a more detailed message? Thanks in advance 😊

larzcaetano
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You were in beautiful soft focus at the beginning of this video ; but after about 7 minutes everything became clear. 😀

johncallan