Lec 8 MIT 18.03 Differential Equations, Spring 2006
I usually like to start a lecture with something new, but this time I'm going to make an exception, and start with the finishing up on Friday because it involves a little more practice with complex numbers. I think that's what a large number of you are still fairly weak in. So, to briefly remind you, it will be sort of self-contained, but still, it will use complex numbers. And, I think it's a good way to start today. So, remember, the basic problem was to solve something with, where the input was sinusoidal in particular. The k was on both sides, and the input looked like cosine omega t. And, the plan of the solution consisted of transporting the problem to the complex domain. So, you look for a complex solution, and you complexify the right hand side of the equation, as well. So, cosine omega t becomes the real part of this complex function. The reason for doing that, remember, was because it's easier to handle when you solve linear equations. It's m...