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Unformatted text preview: ‘ Name:
 _ t  Quiz 12 Math 54  Summer 2008
August 13, 2008 Derive a formal solution to the initialboundary value problem 3% 32a E5(x,t)=5;§ (0<x<L,t>0)
u(0,t) = a, u(L,t) = b (t > 0)
u(a:,0) = f(x) (0 < a: < L)
g—ZL—(acﬁ) = g(m) (0 < m < L) You may use your knowledge of the formal solution of the wave equation with
homogeneous boundary conditions. Make sure you explain how to compute any coefﬁcients
in your solution. , ‘ ' 3; — .
“(k2 general $o\\;\\m O‘Q 53 "I 5;: 0090‘ lvxomosmeoog
Bauhalwxj ' cmiliws 100$}: MlL‘t\=O ‘ is 201 E0“ (20$(ﬁE‘l') 4 bﬁs‘m Sin . 'Mx‘B = n ‘ y
{A 9A0: gawk” 05% = 8% ‘W‘A'k inwatvneoos ‘ . N __ \y—a
cmol‘rl‘ms m(0\t\=q\ Mufﬂ =5 6 MONA  TX *0. les “We. auroral saluliwx our (PDE 03%er ‘Huz funnel»? )ﬁ  m ‘v\ :n "I (lowlaims is 0 Moot) =04” bf" + Ebﬂwﬂtl 5‘5 (1.)) i “a 3‘ Sin ) @\\)55an “As ouc conéi‘l‘lvws‘ “Q ﬂaw; re ;
. 00 I‘ my  u @“Sin “3‘. =— Q+ §E“X +;Qn$\ﬂl L )) 860— w: L ...
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This note was uploaded on 01/12/2010 for the course CALC ii taught by Professor Scottarmstrong during the Winter '08 term at University of California, Berkeley.
 Winter '08
 scottarmstrong

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