Exam1solns - AERSP 313 EXAM 1 . October 16, 2008 6:30 to...

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Unformatted text preview: AERSP 313 EXAM 1 . October 16, 2008 6:30 to 7:45 PM, 010 Sparks Calculators are allowed, but all results must be included on your paper. For multiple part questions: denote where each part of your solutlon begins. 45(91ch hf 1. (30 pts) The trapezoidal rule of integration for a function f(x) between the limits a, and b is given by NJ) Jfijiflflw=hfi%fl+fMQ+fmfl+umjr] (a) (10 pts) Using the trapezoidal rule, find an approximation to the integral 3 d Jifi a: 1 assuming that hsl. (b) (10 pts) Now assume that h:0.5 to find a new approximation to the integral. (c) (10 pts) The two error formulas that we discussed in class for numerical integra- i‘Pi — W = 113 (J% — Jr) Use the formula that applies to this case to calculate the numerical error and find an improved approximation to J. How does this compare to the exact value of J? tion are: m U MI:- 8 Ml:- ‘: Jigl["% 'rCL1\ ycbb "1 [\fiiu]: Why“ \aliD-i‘ ‘12". C23 ((02%; \n=\ q=\ b1} $- 5 l0.» Vvas' 5*” o"; "' egg ~— Ym WEISS * m] = MILD? C3 -. i it 5w 3(Mw7 - mom} wen-0mm )1: 5h". *2.le A: 3h ‘P 2"“; F: d . X “ b ’1 \nuu1uoow1 .3 " l: R91 - O‘R‘lev‘l- ‘ in is - ‘IL ‘3 ‘- lo a a \ M . {a 3 “"3" M” — Legato 2. (25 pts) Find the argument ahd the absolute value or magnitude of f(2) = cosh (2 + where {3.2 4 _L J? ¥=IILQ~€3 \fiLez—e. 317 ‘9 ' 1" J. 4 - ' L1“ Mflmqvfl * Jékeq+€“‘—/T’.\ u. “1% Lit-q * 26‘“ “W ~« : }iEq iv 64%“?- :. fiLe-L-KPEH \HYO C.OL\&J\qh3f~ \CL:‘»\ = Mqu i Grog Ra“ ‘2 tan“ 3. (20 pts) Using the Cauchy-Reimann relationships, ' “9-” m “may 5 “Us: determine if the function, 1 f (2) = 1 + z is analytic. (Hint: Muitiply the numerator and denominator by (1+2), where Z is the complex conjugate of z.) E: ‘R*‘\{ '22 $41 ' _ .‘_.. \x—T‘é -- - ' gm - u: Ta- = “1 ZZa-mem VEVéxzi Y :_ l 1 Hxnhdww w). 5”“4 ‘Yxlwz in ~— \" 24L F11 *‘1 - \H \J - ’_______£___1 __ ‘ “’Z“i ‘X "\[ 111‘ . L" M w Uzi wzw‘ \‘3 _ _ Z Ki :— (HflL—tfifli ‘ (Hum: f“) 7. “V W “ F __.._.._.._._....-—-n z z 1 ’1- ‘ 0 ~24 1H. \1 3 (H753 *X *‘t \ sz*uz\_\{137~ ‘ 2. V4 '5 Ejg’ +‘ \ 1 I) . \§Z ‘L _ C 1“ ¥V 3 L\%1t+11*\[1‘3m u“! 1 *inbH-W a” (Ava-1 ~13th \L‘ 1 2.1 LVN“ U *2.‘ wgluilyq’ Katiqu \f w-vw . I ANAL‘HWQ 4. (25 pts) The Taylor series expansion for a function f($) around a point :15 may be written as, I 2 a m + M) m m + h) m M) + mm + %f"(x) + Fire) + orders“) Derive a central difierence expression for f"(a:) based on f at the three points of mo— 2h, + 2h. Form your final expression in terms of f2,f,_2,fo and h. Your derivation 3:0: z0 bout the order of accuracy of your expression. should support your statement a elm?- Ream = Cug‘fihC'UQ " "11" CHL‘lo\ rbggts (“Hug i906» L ~= s,— zm; * Ms: — 1;»??? is» m was ~~ €3ng “M h . :0 fun. ft¥a+lh\ 3 EMS *YJAQ‘LVQ} + Zhlv‘ho i. q/ngcmbna satin“) 9-; “* Co * Zhfi‘b *ZMIC‘; Misha i“; g“ Ci ‘ 2C9 P LAN“, t OLWW ...
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Exam1solns - AERSP 313 EXAM 1 . October 16, 2008 6:30 to...

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