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Midterm Exam turned in (3)

# Midterm Exam turned in (3) - x T 1 EGM 4313 — Midterm...

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Unformatted text preview: x T , 1 EGM 4313 — Midterm Exam NAME: &\ IKE; L4 2 hours — Open book, closed notes, no calculators 1. Consider y’ 4; x - y = in:2 ,e subject to the initial conditions y(0) = 0, y'(0) =1 . %" (a) Write this diﬁerential equation and initial conditions as a system of ﬁrst order diﬂ’erential equations with initiai conditions. . 7:7 ' 7;:‘7l’;‘1’:‘\$l 73(03' 2:920 \/\ , We) ‘ 79;:‘7/27” ‘- XLX", “in 9 Vim} : Y(03:O [VI ]l 7:. Y3 ]\/ VQ(‘9\ : YYDXZ I (13) Write the 4m order Runge~Kutta equations for the numerical solution of this system with a fixed step size of 0.001. _ 1 _ :1__ [VPS'V] xomfk—orom 6' V9 in” xv, (3 pts extra credit): Find the exact solution for y. ”I— ' ‘I EGM 4313 — Midterm Exam NAME: I' ' 5:.» 2 hours — Open book, closed notes, 'no calculators I ljbr05x<ll2 L. =11 2. L = . .. l - “ﬂ” {0for1/2Sx<l Va ’2 (a) Extend ﬁx) as an even periodic ﬁmction and ﬁnd the ﬁrst foar non-zero terms in its FourierSeries. Clo :2. V9. / - ./ a“ =_ a f V9w5(n7rx)dx : L W5m(nrrx3i: rm- i\$ln(ﬂ§5 O a :1 £— :_ 3—— ‘ g as. so- a : ..— 0 H 2; o ’7— ‘?(x) '-' ‘ _ r - ~t- \\ ()b Now let ﬁx) be zero for all x greater than ‘A and ﬁnd the Fourier Cosine transform of RX). @6053 -— F EDI/316\$) C05(u9x)cix «5002] r <— mm»? _L . (1 point extra credit): 11511NJ f: = ? j; 2.... 34. 9’ 11‘ ff EGM 4313 — Midtenn Exam 2 hours — Open book, closed notes, no calculators I 1 o 5 41d (’4 3. LetA-O l 5 . 1.5x 0 0 6 I O O (3) Find the eigenvalues of A. )x :— l I (.9 .. NAMEMM—r— —I,\) no 0 S" ___ l—A '8‘ l "O 0 (9-1 ' (b) Find as many linearly independent eigenvectors of A as is possible. i? I EGM 4313 — Midterm Exam NAME: I I {.055 / 2 hours -— Open book. closed notes, no calcuﬂators ' a 7 _ 4. Find a series solution to VET = 0'" on the unit square subject to the boundary conditions T(x,0)=0,0<x<1 T(0,y)=0,0<y<1 T 2: F(x>6\(y) T(x,1)=l,0<x<1 T(1,y)=2,0<y<1. (Hint: Use superposition.) ' .. EFL: 2.6:: _-;-L :52) :27 -—‘> £303,600 (x :— :c :3: 1:) F 2% :oéﬂvlz‘m) F“ m : sin (n n- y) an -— smurf-x3 Cm (>13 .1 A“ enrrx +_ an e.- mrx unm: Ananm-kghc.” mm an “3:. AhsInkbn‘x) 6x“ (‘0 :- An smMmrﬂ Tim) _._ :4 smkénvberﬂrﬂ 0710:ij :01 Ansmk(07rv33m (NTX) Q\T(";V3" ZAn Smk (mrﬁsm (In???) L‘L’J‘ 'n-ﬂ-A ”QC-DS______(__-_';_MT) 2 wL-Lfé‘. __Lf¢05 (NT ”H w ”T 5’“ (”’73 / H“ or 5: {MT} 50 . , . . : 17X VX Z Z A“ E;nk(nW)5l‘MhTXﬂ-L¥ %nE55-nk(n7rx\5rn (”ﬂ-3)] ) nzf w A _ __ acos(n7r)-;L . M'— nrsr'nmmv) {3) :—-W n n77' 5w (n7) ...
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Midterm Exam turned in (3) - x T 1 EGM 4313 — Midterm...

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