Notes for Tuesday's class

Update: I just heard you went over the same stuff in Cal III about ten minutes later. Excellent! Those of you not in Cal III would probably benefit from talking with you colleagues who are ... sometimes hearing the formal mathematical version is clearer than the physicist's handwaving version.

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I have made some notes for the material we covered in class today. It is not in the book. Only tiny parts of it will be on the test, for that matter. It is very cool though.

The notes are *marginally* more rigorous than what I did in class, and probably follow a more logical path. With the benefit of hindsight, and in the absence of time restrictions, it is much easier to explain these things. Or so it seems to me, YMMV.

I realize I have gone a bit above and beyond what many of you have been exposed to in your previous math classes, but that is in a way the point. Tuesday's lecture was to familiarize you with a few mathematical concepts (in a handwaving way) that will be very useful soon, which you will undoubtedly cover in your math classes in a more rigorous way. We just want to have the machinery in hand, so we can put it to use. The math department will make sure you cover the finer points I missed.

On Thursday, we will go over the main 'take-home' points of what we need to continue on. The details of the derivations are not as important as the main results, and that is what we will focus on from now on. Basically: don't be discouraged if Tuesday's lecture seemed very abstract and difficult, there are only a few key points you need to remember, which I will summarize on Thursday.

Anyway: keep in mind I typed up these notes up in excessive haste this 'evening' over the course of a few hours. There may be many instances of typos/errors/handwaving, and I welcome any corrections, comments, or requests for clarification. Some of you have covered these topics in math classes already; I welcome any suggestions you have for making the material more accessible.

Based on the eye-rolling in class today, I realize I have a few math majors in class (or at least a few people who paid serious attention in calculus classes). I promise not to do such unspeakable things with differentials in the future, and have tried to be marginally more rigorous in the notes. Not enough, mind you, this is where your comments can come in handy :-)