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# quiz5b - Math 415.01 Quiz 5 Name TA Younghwan Son Rec Time...

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Unformatted text preview: Math 415.01 Quiz 5 Name: _________________________ TA: Younghwan Son Rec. Time: _____________________ Form B 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. y"+z\y=0, y’(0)=0, y’(L)=0 (me I. =- ”.. _.. ,_ / ._ ) )x o y .—o —) 7-Ax+B. 1 7 ~A. B“ 7’0)” =5 l3=o. 7,04% 79 (5’0. 7:}; 02».th emu if A%o_ Q] A“? , 7". (Men) A40 ‘ Le+ A='A‘ . ClamciﬂnkhE (an ~. rtlwpo .sr =1M ygg e”+ge”“ y’ ~.— (”dew ~ (”de’w 7/50/ =0 -—--> 9/“ “4—)“ 2° —=; Cl :9 (‘.'/(#0) 0—) £1. VIM” 2) qﬂeﬂL_*/eﬂu¢ :0 ”D W"? in, do =2 (”Me/“-64“; :0 mm Nari: em‘ “2"“ 7‘50 ('.' 3"“ =e’” =7 L =0 (Eydﬁj) 07") =) c, =0 , u) =9 cl =0 . -‘~ >’=o 7W”- {0/ (mm) A)o_ Lei“ A=M‘ , clarodemﬁ; 27/: : r*+,¢‘=o r: tj/A. >’ = c. CvJ/‘HCM ,«x , y’ = — (MUM/xx ﬂaw/M 3f. y/to)=0 —.——) gﬂ=o => 9:0 ('.'/(#0) Y’(L)=o => - (AW/11.20. To gel WWI/ml Iahﬁivx / 5/9111; :0, ﬂL= )‘ﬁ 01=/.»,3 ~- m I“: T“ 2. Let f (x) be deﬁned by f (:1: + 271') = f(:1:) and x :—7er<0 f(x)—{0 :0_<_:1:<7r (1) Sketch the graph of given function for three periods. (2) Find the Fourier series for the given funtion. a.) {369: g: + “2;. a“ 01mg + LnJ/k WK. ° I/VMX 5 =1{[x-‘35'—"—x4~f_ﬁ Ax 7: n n : f O 0 in [-7\ I/V‘AX JX .. (-4)" ,_ I -€an’<] ° = _L (pad-4m) -= /7rn — ~~o~ ﬁn}. J— 7Ul h ”7‘ 71 3%] {twmnxdx - #11 MW o‘x o. x ° ° (=JM‘ 7%! 4 [X‘(—’~;)]_ﬂ ‘ L (‘ Twig “ l (MG-MU _l_ Sm h)‘ 0 ‘..7.‘_[Q..(—7\)(— Y\ )]+7\[ ”1-1.1 _ (01041“) _ _ (,U'i - (_U)H'/ h - —n ’ 71 0’ (" ('Un (4),”, few—g + ”5:, [W “UK + n {MK} .1 Aw co .1 4r/ _ 1 1' li (Hun—(7x + 5—}— IMhX] 2 we I—r—ukj o nteven ...
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quiz5b - Math 415.01 Quiz 5 Name TA Younghwan Son Rec Time...

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