Math

Well. My bad ... after talking with some of you today, I realized that what I presumed Math 126 covered, and what it actually covers are two different things. I apologize for the oversight, and I feel really bad that some of what I've been doing has been a bit beyond your prerequisites. It was not intentional, and it is not too late to adapt.

So, here's what we'll do to rectify the situation. First, we will slow down a bit, and more carefully explain the math that is being used ... part of my speed was based on the incorrect assumption that you had already seen the math before. I'll try not to skip as many steps.

Next, on Wednesday, we'll review everything to date, using nothing more than single integrals, and put things in a somewhat simpler form than we have so far.

On Wednesday, I will also give you a crash-course in multiple integrals and other sorts of math you probably haven't really seen yet. We'll not prove a lot of theorems, or formally justify a lot of it, but rather I'll give you enough information to use some powerful tools we'll find useful. Just enough to get the job done, because believe it or not, having some more powerful tools at our disposal will make things easier in the long run. Really, it won't be a lot, just extending what you already learned in Math 125 a tiny bit.

That being said, from now on I will try to be a bit more aware of what math you are supposed to know already, what I should teach you along the way, and what I should avoid all together. For example: doing integrals over a path, surface, or volume, so far as they are useful to ph106, does not require much more than you've seen in Math 125, you just need to be shown it in a bit different manner. Mainly, it will be Useful to know how to set them up, and what they mean, but most of the time actually solving them is Not.

So anyway: from now on, I will try to be careful. This will be easier if you keep letting me know when I've gone a bit too far, as you did today ... it is not at all a Bad Thing to ask me to explain our methods in more detail when you are not quite sure you follow.