Download math 54 - list of cheat sheet and more Lecture notes Algebra in PDF only on Docsity! MATH 54 - LIST OF CHEAT SHEET - TYPOS/SUGGESTIONS PEYAM RYAN TABRIZIAN Here are a couple of typos on the old cheat sheet I found so far! 1) and 2) are absolutely crucial, so make sure you correct your cheat sheets. Update: There’s another typo (see (10)), and I added two suggestions (11) and (12). I won’t update the cheat sheets again, because those are just very small typos and easy to spot, but make sure to note them! Update: See (14) for a suggestion on how to solve x′′ = Ax in case Grunbaum asks for it! (1) IMPORTANT In Grunbaum’s mass-spring system for N = 3 and on the H.O. handout, v3 = √ 2 2 −1√ 2 2 I put − √ 2 2 instead of √ 2 2 . (2) Also, for the coupled mass-spring system, the general case, the ma- trix A is wrong, it’s supposed to be: A = −2 1 0 · · · 0 1 −2 1 0 · · · 0 0 1 −2 1 0 · · · ... ... ... ... ... ... 0 0 · · · 1 −2 1 0 0 0 0 1 −2 Date: Friday, December 9th, 2011. 1 2 PEYAM RYAN TABRIZIAN (3) For the Fourier sine series, it’s supposed to be: bm = 2 T ∫ T 0 f(x) sin (mπx T ) Btw, the formulas for a0 are CORRECT. It looks different from the formula from the book, but that’s because the book divides by 2 at the end, i.e. the book considers a0 2 . Here I’m dividing by 2 at the beginning so that you won’t have to think about this anymore when you’re calculating am. (4) For the heat equation, step 4, it’s supposed to be T (t) = Ãme λt . (5) For the quadratic forms-section, it’s supposed to be y = P Tx (6) The definition of the Wronskian of 2 function is wrong: W̃ (t) = [ f(t) g(t) f ′(t) g′(t) ] (7) For ’orthogonality’, it should be y = c1u1 + · · ·+ cnun (8) IMPORTANT For the generalized eigenvectors, it should be (A− λI), not (A+ λI) (9) On some cheat sheets, it says if Case 2 doesn’t work, start with m = 0. That should be m = 1. (10) For undetermined coefficients, I put yp(t) = ts (Amt m + · · ·+ A1t+ 1) ert That 1 is supposed to be an A0 (just a constant). Similarly for the other equation with sin and cos.
