Exam3_solutions - SSM 317-01 Engineering Mathematics...

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Unformatted text preview: SSM 317-01 Engineering Mathematics Wednesday, November 19, 2003 Open Book Exam 50 Minutes Examination Number 3 If you are taking the course for 2 units, answer only questions 1 and 3 in 35 minutes. Otherwise, answer all questions. Questions have equal weight. 1. (a. 10 pts.) Is the family of functions [Qo (x), Q1 (x), Q2 (x)} orthogonal on the interval [0,1]? Q0 (x) =1 Q1(x) = 2x — 1 Q2(x)=6x2 ——6x+1 (b. 10 pts.) If the answer to (a) is yes, find the coefficients co, c1 in the approximate expansion f (x) = ch0 (x) + CIQ’ (x) where f (x) = x3. Mote here we want to use a weight function of p(x)=1.) 4 2. Evaluate: (Vxfififi here f5=4yi+yj+zk S:z=l—y2 -15x51,—1$y51,220 (Note: S is only the “top” surface.) 3. Find the first three non-vanishing coefficients in the Fourier expansion of f (t) : f0“) f(I+3)=f(f) J, 35/14 3/7 @qu. 3" 2003 [Wag 00000.19) JaA-‘v LIICZx-x) dx: 5:, QaC‘DaIl/‘J ‘4“ " iffééd‘z‘éXfi/J 41-: I _ __ { CI 2' HQ. Lei/j £00 6?. wan HR \ a / / a. Col oi—lf'] .9 grqm¢+rz‘%c. 5 ' K’LX. V I.— y"{) —/2,r¢/ J .. ‘49,“; —> Cr": 231010.] F F" b J M -7 XX )1 = i O O ry=[o..(, —-Zy_7 o ( —2), Glace/C I‘ve EX}: Paflvfl 097‘6-uqre/f 24+ yzq five, ghhr/Vormq/ (Aron/J Fog-177‘ ffrq/‘967l... 14/0. [4174 f FRI/‘7 z [final/.7 97" V'Sa: ‘5 "7L Kilo/0791‘ :37 2‘17: Z, 41*‘VV‘I4/‘o Sa’hf’fofl #- 57‘0135‘! \\ C ’ Pfiranf Lara! 1.. n ._J—: ““—'----——-—--—--c' rt’1ijL'eJ 4* ( I , Svmr’éé - 9 *£*2 3‘ .. L CI 1.5" .6 At" 01’ V 4 add ._ J £3: éfr‘; “ I If 3 ‘r go; A, _traC(x)dx- gjaang .1 ‘r J. _ / "-‘- gfig- (CI/1’: 9.12:) —z 1 tr I ‘r q ‘.-'- "j K (’95- m c/ i -- a #17le n w) w x u; a: m J h =lf' : L "75': SH? ‘3 5 Ti," ray-r; :3 "7V ’7 ‘r - I"? 3»— - :3: 0 {film h ’5 6'" ’”"‘=Ser '— "7"[5W07/W7—9‘», _Z 2- a,: 775/53,: —'-—-- _'Z, 7}, r" “'“5 “'3’ 1:2: _ 1471’ 117(‘5 q152wjrq7r;0 .. :1. _ 3 a 0:3 -- 37” 5;)?de 3%: L.) “L T5 - 77' alt-=0 q_— '2‘ n " '1“_L’ 505”? rye/1 1" 5-77, 1‘: 0 JJ ...
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Exam3_solutions - SSM 317-01 Engineering Mathematics...

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