Question

Derivation for unit step(heaveside) function even if its a recurrence formula from a power series!
\[also \_u'(t)\_and\_then f(t) * u'(t) = ?? <---- from\_convolution\]
\[a_k=integral 0 to k f(t)*u_c'(k-t) dt <-------- the\_convolution\_integral\]
im thinking about my bounds 0 to k, this would tell me the coefficient that belongs on \[e^{-lnK}\] lets say or \[X^{K}\], i would need the laplace transform of the convolution to see all the coefficients \[a_0~to~ a\_inf\]
and suppose I convolute f(t) * U_c ' (t) this is the dirac delta impulse func at c then oh wud this convolution give me a function where i only have a point at c which is f(c)
or would the laplace of that convolution give me something that looks like the impulse function except the height just stops at f(c) instead going to infinity there like a normal impulse function