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Quiz1_Solutions(2)

# Quiz1_Solutions(2) - Name/Lﬂ 0N3 73W 5 ’6‘(DINTj SID...

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Unformatted text preview: Name: {/Lﬂ 0N3 73W 5 ’6‘ (DINTj. SID: MW 105: Introduction to Mathematical Physics QUIZ 1: April 9, 2010 /~ - All work should be shown for complete credit M Useful formulae: sinze =% (1 —- cos 26), sinA sin B =% [cos (A — B) — cos(A + 8)] V i u L l . Evaluate simm) sin(ﬂ)dx , for 0 L L L L. - - L Syn 25“fo G>m=n X'— st—T‘fldﬁ 2' S 0-952191“- “I" am T O O l 0 m : J.[L~ .’—_ Sunumn J4 (W1 5. I“! AM W’ “‘0" M{%”)=0’ :— 19:47 3 W : L/Z. (ii)m¢n L ~ , §L€M(vﬂg)3"~(“iL—*)dm = i. J [ksbmoﬁﬁt — wmm; M: 7L? [3»«(m-K)EE&~5W[M+nME 0 ° 0 (iii)m=n=0 in = you {new}; 0 ,/" MW & 9N5 2. In the diffusion of heat, say down a rod, the ﬂux (4)) is given in terms of the temperature gradient 61:1”) and thermal conductivity (k) as 4) = - k 87;?) . Why is there a negative sign in front of k? Meow. ‘MW’4 331"“ W” Wtrﬂww [A4354 ayosMﬁquMS‘fAWWOg’W Wméﬂll ”ll-(Mt N7. 41 : TL—Tt < 0 § T|>TL « ~ I I 3, ‘1’" BET-f“; X a( M 3. Write down the boundary conditions for h'eat con'duction down a rod of length “L”, and the Type (I or II) for the following situations: (a) Two ends oftheroddippedinicewater. T(l;0 {:3 _—; O TOL: L/{J _._ 0 NEW; (b) Both ends of the rod insulated QL(1:o,t); o ﬂGPL’JCﬁo [Tégrd 3w ’6“, ...
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