get better at calculus

I’m working on sections 8.9 and 9.1 from my calculus book today, and my study guide for the differential equations class I’m taking next quarter just got here in the mail a few hours ago. I’m taking differential equations and vector calculus because it sounds like a lot of fun. I’m going to take Flash animation (web based) as well. I’ve been using a flashcard program called mnemnosyne to help me reeducate myself as far as the trig identities through calculus 2 – just any identities I can get my brain to memorize I’m going to try for. oin to try to waat any videos as possible as well. I may have to put Go on hold for a bit, though I did just get a nice new book (get strong at joseki) which looks fun.

just took my final for calc 3. I am still in a good mood even though I probably only got a B. I am going to study a little over the break and try to shore up my math skills so I can understand what I’ve learned…

Well, Calc 3 is going well. We’re covering infinite series, MacLauren and Taylor series, just now, and just got into “special MacLaurin Series” like the series representations of sin, cos, arctan, ln, e to the x), etc. These are good to learn and recognize in case you see them in a problem where you’re trying to get a function back out of a series representation. One of the examples struck me because it turned out to be sin(6/x), from the sum from zero to infinity of ((-1) to the n * (x/6)^(2n+1))/(2n+1)!, so that means I’m going to have to know the special MacLauren series pretty well to handle permutations of them that might come up in problems (the exclamation mark at the end means ‘factorial’, a number that’s the product of all the numbers leading up to another number. So 6! = 6 times 5 times 4 times 3 times 2, 5!=5 times 4 times 3 times 2, etc. These turn out to be useful for defining sin, cos etc as polynomials with an infinite number of terms.

Once upon a time I wanted to know how to do calculus; now I know what feels like a lot, but is really only a tiny portion, since I’ve just taken calculus 1 and 2 and am starting into calculus 3 at the community college near here. I’d like to really get a lot better at this subject and maybe some more geometric or visual areas too.
I’d like to figure out what I’m doing with my life and build a practical skill tree/map to approach / encapsulate / achieve that end, then work my way through the knowledge tree.