Lec 20 MIT 18.03 Differential Equations, Spring 2006
Okay, those are the formulas. You will get all of those on the test, plus a couple more that I will give you today. Those will be the basic formulas of the Laplace transform. If I think you need anything else, I'll give you other stuff, too. So, I'm going to leave those on the board all period. The basic test for today is to see how Laplace transforms are used to solve linear differential equations with constant coefficients. Now, to do that, we're going to have to take the Laplace transform of a derivative. And, in order to make sense of that procedure, we're going to have to ask, I apologize in advance, but a slightly theoretical question, namely, we have to have some guarantee in advance that the Laplace transform is going to exist. Now, how could the Laplace transform fail to exist? Can't I always calculate this? And the answer is, no, you can't always calculate it because this is an improper integral. I'm integrating all the way up to infi...