quiz5a - Math 415.01 TA: Younghwan Son Form A Quiz 5 Name:_

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Unformatted text preview: Math 415.01 TA: Younghwan Son Form A Quiz 5 Name:_ ______________________ -- Rec. Time: ___________________ __ Show all work; answers with insufficient support will not receive credit. GOOD LUCK! 1. Find the eigenvalue and eigenfuntions of the given boundary value problem. Assume that all eigenvalues are real. 3/" + M = 0, y'(0) = 0, y(L) = 0 yllr-D => => 7= AX+B. 7’=A~ A=o l3=o 7:0 (—mn'a/ raid-far.) damferzkfi'c a7“: r*-,u*=o :9 than, (1:9. (3' ##o). (i) _... (ill -L e’“) =0 => C‘ =0 (.5 . Hence .1)’=o (Ml/l“! LLh‘m) 2. M) = 252/2, —2 s x s 2 ; f(:r + 4) = f(a:) . (1) Sketch the graph of given function for three periods. .f (2) Find the Fourier series for the given funtion. ' Mfe : Lu and 70m as even. ~4 1 A 4 fl . -f’(x,= _f.1g+mf:l ammo? +énxmli-I’z" (I) A=7i11 flygnigolx =0. ’r 1‘ em x QAJ aOJJ 3 J. a. “ J. X __ .25- : .3 (1 an : ’1 f {(x)dx : I = /; T Jx “ 6 p 3 .‘L a T ( {Ivan—l V 2:wa 2; ._. / * W - " 6; —— X i an I [a {(x) 601.1... J;( -fo 7£(X) J J— l :13 31x1 Manx )— A _’ i L .1 MIX _ J .3; ___ 01X -[:X a“: 0 am ”"+ A L ,1 NIX 2 1 MIX _»— co; —— dx = 0 *fif[’x’fi‘°5':)]o' L K L f .. Q ( L .1 "IX - ———- 051m —- ~ —~ -—- (NHL 0) L rm (J 0(X s «L g n z 4)“ ~— I" k "—W — 73 6") n1?“ ":1; ’ )- n 7‘ go I — .1 9 ’ n 60 Mix . {00- '7; 4%! WV“) 5 J" ...
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quiz5a - Math 415.01 TA: Younghwan Son Form A Quiz 5 Name:_

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