Laplace transform with a Heaviside function

Laplace transform with a Heaviside functionby Nathan GriggThe formulaTo compute the Laplace transform of a Heaviside function times any other function , useL{uc(t)f(t)}=e csL{f(t+c)}.Think of it as a formula to get rid of the Heaviside function so that you can just computethe Laplace transform off(t+c), which is words: To compute the Laplace transform ofuctimesf, shiftfleft byc, take theLaplace transform , and multiply the result bye cs. Remember that to shift left, youreplacetwitht+ other way to write the formulaYou will sometimes see the formula written asL{uc(t)f(t c)}=e csF(s),whereF(s) isthe Laplace transform off(t). This is a correct formula that says the same thing as thefirst formula, but it is aterribleway to compute the Laplace transform .

Laplace transform, you need to do some trigonometric magic. If cis a multiple of ˇ=2 or ˇ, you can probably gure it out by drawing some triangles. Otherwise, pull out your trig identities!1 This is not a product rule One common misconception about this Laplace transform formula is that it is a kind of product rule, that the Laplace transform of u

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