# quiz5a - Math 415.01 TA Younghwan Son Form A Quiz 5 Name...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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" ...
View Full Document

## This note was uploaded on 07/26/2011 for the course MATH 415 taught by Professor Costin during the Spring '07 term at Ohio State.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online