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One of the big difficulties students have in a problem that involves many objects is to successfully identify third law interaction pairs. So today, I'd like to look at a problem which shows us how to think about that. So what we're going to look at is third law interaction pairs. Now, the problem I'd like to consider is the following. Suppose we have a block one and another block two sitting on block one on a surface and our surface has friction. And I'd like to push block one with a force F. And now I'd like to use Newton's second law to determine what is the maximum force I can push that block two will not slip. So I'm trying to find F max such that block two does not slip. Now, how do we even begin to think about this? Well, the first thing that we have to decide is when we apply Newton's second law, our first question will be, what is the system that we'll choose? And in this problem, there are three separate ways to think about th...

two big themes in in in lectures that are coming uh well there's several lectures on Signal processing and in particular on wavelet developments so that's a half dozen lectures that that are sort of a unit in the course uh the other major theme is maybe the right word would be optimization how do you how do you identify and compute uh an Optimum uh of course in freshman calculus you have a function f ofx you take its derivative and set it to zero now uh we got to move up from there to functions of several variables so we got partial derivatives and I'll start with that today and then functions of functions so where the unknown that you're looking for is not just uh a point but a function a point in function space we could say so continuous variables and then and then constraints is optimization when there are uh constraints on the allowed on the admissible uh choices that that's a big subject and uh it's partly a world of its own optimization it...