User talk:SamHB
MVCalc Course Structure
You're a killjoy. EDuser 01:51, 29 April 2015 (EDT) I was thinking of working on lecture 3 tonight and I noticed some oddities in the order of topics. For example, I had planned to cover tangent planes in a lecture or two after the gradient and extrema? I don't know what I was thinking, but I just wanted to say, if you find you would like to refer in a lecture piece to info not yet presented, or if you think one topic naturally flows into another which is for some reason in a different lecture or something, please, feel free to switch up the course order. It may well be necessary, actually! Just remember to change the order both on the pages and on the outline given in lecture 1. JacobB 01:07, 7 January 2010 (EST)
- PS: have you considered archiving your talk page? just a suggestion JacobB 01:08, 7 January 2010 (EST)
Earlier you asked about arching your page. I do it just by cutting and pasting everything to User talk:SamHB/Archive 1, and then putting at the top of my talk page For older discussions, see the archives:<1>. JacobB 18:20, 7 January 2010 (EST)
- Done. Great minds think alike. I had believed there was some complicated procedure involving renaming files, that one had to do in order to get the history correct. But I looked around at how existing sysops do it, and they don't bother with any of that. Good enough for me. SamHB 19:55, 7 January 2010 (EST)
A rambling philosophical comment: While reading your wave equation stuff, I was appalled at the way you were approaching it, fiddling around (get it?) with the physics, in advance of doing the mathematics. Then I had an epiphany: You and I have very different ways of approaching these problems. We are each very good at what we do. You approach it in terms of "What is the pedagogically right way to present the material in a sequence of lectures, in a fixed order, with quizzes and exercises and such?" I approach it in terms of "What is the pedagogically right way to present the material in terms of separate pages, that the student can follow in whatever order they want, by clicking whatever hyperlinks interest them?" I recently sort of messed up one of your lectures by moving around the concepts of "vector functions" vs. "vector fields". Feel free to move it back. I will put explanation of these concepts in the separate pages, and defer to you on the order in the lectures. Meanwhile, I need to improve the wave equation page, explaining what sorts of mathematical functions satisfy the equation, and then showing how it arises in a large number of physical problems.
About your specific questions about lecture 3, I need to look more closely at your overall order. You seem to have a more "geometric" approach rather than a "pure math" approach. For example, I would be inclined to cover local maxima/minima in arbitrary dimensions early on, just after talking about partial derivatives, so that all that remains in "extrema" problems is the issue of checking the boundaries. What is the correct order of gradients, directional derivatives, and parametric surfaces? Hard to say. I'd have to write up a draft of these topics first. Maybe I'll do that, but not now. I'm too psyched about the wave equation at the moment.
I hope at least some of this makes sense. SamHB 22:59, 7 January 2010 (EST)
- I think you're absolutely right about our styles, and I don't want you to defer to me, at all! I think we can create a blend of styles which will yield the best of both worlds. I like what you did with the vector functions/fields, no need to change it back! I'm going to peruse our articles for a bit now, and I'll get back to you in a bit.
- BTW, wave equation wasn't done by a long shot. I hadn't talked about boundary conditions, damping effects, etc., let alone solutions. Feel free to add; just know that my version wasn't what I considered a finished product. JacobB 00:19, 8 January 2010 (EST)
Jacob:
As usual, I've put my foot in my mouth. There is nothing wrong with your wave equation section. It just had a style different from mine, that led to the insight of why our styles are different. I didn't even read it all the way through. I just looked at the first few sentences and extrapolated the trajectory from the initial velocity vector. Of course we will check each other's work very carefully when the time is right.
I've gone through the recent email from you and Andy, and noticed that Andy unblocked me largely for the purpose of assisting with the "calc 3" class. Therefore it would be kind of unsociable for me to run off and only write whatever individual pages strike my fancy at any given instant. So here's my first serious comment, based on your outline. But it's on another page. It seems to me that discussing this stuff here, rather than on the actual course talk page seems a little cabal-like and antisocial. So, having gotten personal stuff out of the way, I'm going to continue on the other page.
SamHB 22:11, 8 January 2010 (EST)
image uploaded
the image you emailed me is available here. JacobB 17:59, 9 January 2010 (EST)
course structure and existence proofs
As promised, I'm doing a whole bunch of math material tonight, but I wanted your thoughts on something, and there's also a favor I'd like to ask.
First up, as part of the restructuring we discussed to cover more PDE material, I'm thinking of combining all the integral definitions and calculations into a single lecture, and then the integral changes under coordinate transforms + applications into another lecture. That'll free up one lecture for some more PDE stuff. What do you think of this? I may or may not have done it by the end of tonight, so you can check it out on the lecture 1 page and see what you think.
Second, I'm just going to state the conditions under which the integrals exist, and that they can be evaluated as iterations of single integrals yadda yadda yadda. Would you like to make some existence proofs and link to them from the lectures? JacobB 23:26, 12 January 2010 (EST)
- I reorganized the course a little bit, freeing up lectures 7&8. I'm also thinking of deleting lecture 4 and moving a discussion of velocity and acceleration earlier in the course, and skipping completely or downsizing the intended coverage of Frenet frame and curvature.
- So, as of right now, that's two lectures freed up, and possibly another, which is tons of space for the extra PDE stuff you wanted to add (which I think is a great idea!). The course structure STILL needs work - any further idea you have would be welcome. JacobB 04:27, 13 January 2010 (EST)
Well, I seem to be falling farther and farther behind your ambitious pace of writing. I really don't have a lot of time to devote to this, so I need to make the most of my time. I haven't even had time to do more than a cursory reading of the CLEP website that you gave.
My particular areas of interest are integration in its various forms, and curvilinear coordinate systems. That means, for example, the various forms of Stokes' theorem, and line integrals / surface integrals, etc. All this stuff is hard to cover properly; my bookshelves are filled (exaggeration) with books that do it badly, and don't really explain what a "differential form" is, or what it means to integrate it. Doing this really right (e.g. Spivack Calculus on Manifolds) requires some mathematical machinery (exterior forms, or, if you like, alternating covariant tensor fields) that goes well beyond what is appropriate here. But I'd like to give it an intuitive but not mathematically rigorous treatment.
The starting point should be the change of variable theorem. Students already know the basics of that from Calc 1 and Calc 2, of course. But we can take it to the next step, showing how it ties together the material on parametric curves/surfaces, and integrals over same. How? You change to the coor