Applied Mathematics 2270A/B Lecture Notes - Lecture 17: Algebraic Equation
19 Nov 2018
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Recall: this is one of the steps that we do in order to solve the des the easier way. This means the laplace transform of a y"(t) only depends on y(t). Laplace transforming a y""(t) would yield (after some work): And there is only 1 unknown function in this equation. If we find that, it"s just an algebraic equation! Extra bit (tau is a dummy variable for the integration): Just some algebra and laplace transforming (and inverse laplace transforming). L [ f"(t) ] = s l [ f(t) ] - f(0) L [ f"(t) ] still exists (assuming it is of exponential order) I will use integration by parts on each of these integrals in the sum. So its the same as a regular laplace transform except it has this little bit with the jump function at the end to account for the discontinuity.
