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Quiz1_Fall_2007_solutions

# Quiz1_Fall_2007_solutions - Name 50 LOFT—(0M:’/” MAE...

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Unformatted text preview: Name: 50 LOFT—(0M ' . ' .//./,:’/” MAE 105: Introduction to Mathematical Physms QUIZ 1: October 4, 2007 All work should be shmmﬁir complete wede Useful formulae: sinZB =% (1 — cos 26'), sin A sin B =-:- [cos (A -- B) — cos (A + 3)] / 1. Evaluate sin(———) sin(—)dr, for 2&1 3 L '73 . . 4%x (1)m=n=} L85: m)olx 3 ,LC- COSP-L‘E'Eﬂdx' :31;[ .. _L__ SIM. Jig-XL o I] o L— 2‘ 2m?— ---0 = 1—. (Answer) iii} :1 [0 O] L (ii)m¢n L 9 5° sm(wﬂlj§-(vm)da = _L (Ema—um: atoms: it Lg #[%Ch—“)D —\$M(ns+n)l.l_.:]:n - SMASMB" Ii Lwtﬂubi (iii)m=n=0 a 530mm _.,- J. 2. In the diffusion of heat, say down a red, the flux (4:) is given in terms of the temperature gradient an: t) am: t) and thermal conductivity (k) as if) — - it .‘Why 15 there a negative sign in ﬁont of k9 If; 0‘3?me Famed/3&2“ al-th-IWiDa aMWMM [fan 3% o, posuhre (or Moog, sofa» No we“ 9% WﬁﬁWg 3” = L‘T' (<0 '3! T. >Tz) a _. “X 1"- 7- ’- X; XI 3. Write down the boundary conditions for heat conduction down a rod of length “L” and the Type (I Qw‘” or II) for the following situations. k ‘2, (a) Two ends oftheroddippedinice water. T(x= O t)‘ -.- T617- L’ f) :0 -—-3 e 72‘ (b) Both ends of the rod insulated g—EC‘LW—OB O _L(x=Lt)=-O —' ...
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