| |Anubis | let the sunshine in! |
| michael1 | Anubis: You learn better ways of doing that with something called integration by substitution that's much more concrete. |
| TRWBW | michael1: well if everything is nice, and i forget the exact definition, but usually, given f:R^n->R^m, if you take a projections p_i(v):R^m->R and an the other side use functions e_j(x):R->R^n, then d/dx p_i(f(e_j(x))) is the entry M_i_j in the matrix for the derivative of f, so it reduces to 1 dimensional calculus |
| buggler | for the case of R -> R, look at the derivative of e^(2x) at say the point x=0. you'll get a 1x1 matrix [2e^(2*0)] = [2]. This is a linear transformation x --> 2x. so the line 2x is the linear part of the best affine approximation. and indeed, if we shift it up so that it touches the point (0,1), we get 2x + 1 being the best affine approximation to e^(2x) at x=0 |
| Hierofant | TRWBW - thanks. I have a structural engineer that says the moment isn't properly resisted in the connections. But he's old and rednecky and I think I need a 2nd opinion |
| TRWBW | Hierofant: i was just saying mathematically, doesn't mean the thing won't break ;) |
| Hierofant | yeah, heh. I just needed confirmation of the one-pin principle |
| michael1 | eh, I think I'm gonna watch some more MIT OCW linear algebra lectures before I try to understand calculus in multiple dimensions |
| buggler | yeah, strang it up |
| michael1 | :) strang is a very good lecturer a bit old and, uh, well, dry, but a good teacher |
| buggler | try imitate everything he does except his eye twitch |
| michael1 | hehe :p I love how MIT puts out all the lectures of popular classes |
| buggler | although you can try that too if you're after the eccentric pro look |
| michael1 | it's gonna save my ass next year in physics c (since the teacher at my school is more interested in astronomy than mechanics/emag) |
| sniper89 | so guys, no ideas on tan 25 + cot 115 = 0? |
| kilimanjaro | i prefer books to lectures I'm a visual person I guess |
| Olathe | The slopes at 90 degrees from each other are negative reciprocals. |
| michael1 | kilimanja: Have you seen the MIT lectures yet? they're quite good. |
| Olathe | So, tan(25) = -1/tan(115) |
| michael1 | I'd give em a shot if I were you; they're free. |
| kilimanjaro | michael1, I just can't pay attention to lectures I always go off on my own little tangent or I force myself to pay attention and I feel like a prisoner I just don't see what a lecture has over a book, but I understand that it is just a matter of personal preference |
| michael1 | are you in higher education now? (college/university) |
| kilimanjaro | yes, i am finishing my sophomore year |
| michael1 | where at? |
| kilimanjaro | UT Dallas, but I am moving to UT austin next semester |
| michael1 | ah, I was thinking of applying there (I'm interested in CS) |
| kilimanjaro | come to #not-math |
| F | hey guys. :) |