mid2384v1 - NIAT2384 Ordinary differential Equations and...

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Unformatted text preview: NIAT2384 Ordinary differential Equations and Numerical lVIethods NIIDTERM EXAlV’I (Fall, 2009) Professor: Joseph Khoury Duration: 80 minutes Last Name: Swag/ix a First Name: Student Number: This is a Closed book exam. Only basic c:al<::ulators are allowed. Graphing or prograi‘ui’nable calculators are not allowed. The test has 6 questions worth a total of 30 points. The Test has 9 pages. Please write your answers in a complete and clear way. You may use the back of the pages or the two additional 1,)ages at the end if you miss space. You must answer all tl’ie questions. Good Luck! NIAT 2384 Midterm Exam, October 23 1. [7’ points] Solve the Initial Value Pmblem: {2373/2 4- Sigma :1:)d:1: + "9 sin :1: -%~ 4:1:2y)dy : O, 3/(0) : 1. W a g” A l g: » , 3 _ ‘f 27*: .c, b :4 if; M, g _'k a w; V, _ Am Wkgg ?$§fi,m m: f4 ESEE W g m Q, l; {1; :1 y 2.: mamfég 4%, 5,3432% mm ‘4; g ‘4? 3 , Z {\‘QE‘X? $73??? Qfiaxgéfl %€%?2$:’fikfi{}§{§)é ? :3 :3 fiéé“ R??? 5%}. '4 ,3 3* £5? 5’“ V’éfiwg ’ gag 4:: :X Y a»? é? wéf’mx if“ {f} r4 A?” E 1% g " s‘x Efl / %%§?:§ij gvggwg} £5?” 4;: éfXAY a?» 5%? :Mffi vk{?:§ (”W‘fxlmawg W E”; $31? as: MAT 2384 lVIidterm Exam, October 23 2. {4 points] Solve the lnitial Value Problem: 3 a 31;“ (*3 2125173 21(1): 1- ggmlfiifivw 73w 3:3 5:» fiwésmm, Qmémwucizm {3:733 lelr; $5332; ”3% f» {33%; {~31 X} “:2 {X , 3:32?» @5ng fgéég 3113*»: 95»; Ejlérjfiaxm BEAT 2384 NIidterm Exam, October 23 3. [4 points] Solve the Initial Value Problen’lz 51:33/”+;2:t3/ + 163;:(1), 3,: > (3, M1) 2 l, y’fil) : -—1 afiww m a? a Emgfi, w WWW; WWW“ WW W 2 is W W W i “a ' c ; «up ya , ~ 1 . éi 4 ,_, 359:; QMMka‘ghh WW}? 0‘ m {W W {WWEVWW 3;; "W WWW> W W WW w} W4} Wm a: i“: ii a: : ¥wj£§ @mgk wfiwa~W~ KWWW ”WWW Wywwg WWWZQW‘W WW if {>1} :2: {:3} {WWW {W32 Wgaggfiigéfig> 3 $:{E}§ “2 mg; WCZ: wé :4; flag“? 3% {aw Wajgimkgm M \f {:32} 2:, €62; {iii {my} Mé §}W<\L{ {WK} R‘IAT 2384 Midterm Exam, October 23 4. [4 points] Give the general solution for each of the following ODESZ 1) 3/” + 43/ + 411/ = U 9 5 ) 31“" + 43/ + 8y r: 0 SWW {xii ”Eva QWQ’LQJ‘ §5f® QE‘EC, g?v{3v§3w m :X rt? :X '4? i? w ”‘3 £3?ng ,2 @‘ng": Liv: \5 NEW-J6; :: {iifi :: “.53 153;: $3; 3;” 2:» fag, sigfwmi: %thm 5% \‘f i x) :2. CE {2&- @fiiix} Mg, {:2 <2; 3;?“ {EX} 3 KIAT 2384 NIidterm Exam, October 23 5. [5 points] Give the general solution for the following ODE: , H1 f i y “ 33/ ~ 23/ m 0- 6 m?) W? h {w s i g ‘s ' i ”r E ":8 " N“ {I ‘1 ‘ P I % ggmiwuw fa: gm:wm:flg:g if: :f‘wfi W: :3 :X "‘ (:3? a4:é£?¢i§§a:~aw 5‘“ :1: WE m a. {“:w?: NIAT 23841 Nlidterm Exam, October 23 6. [6 points] Use the fixed point iteration 111ethod to find the mat of .3 [ ~ :1: 4 4:1: + 1 : U in the interval [0,1] to 4 decimal plmgxes. Use 1:0 2: 0.2 and make sure that the conditions for convergence of the iteration sequence are satisfied. 3? ,3 . a a § § Li g L: a; M WEWWW W 3:3 51 We 3% ex Siege fives“? m ea? fimiffi‘ggé— mm % We {3% 336% Ha*&c%%e& 1 w « ‘ é ’ «Q; $39 ‘3; {EM 23%:ng fie 5;»? Wufiwm we Leia we; Mg my} W e ’3 Lg M a“ A m“ A G: ”:3 £3 {(2% i1 EM {beggi’im ’35“ ’” be. Wig; amkdiéffigféw ”59% :3 7 3:} L £3 } 3‘ 3 \g a“ Sgé§l©e3 ”:1 {3 ggigg w e 3: m X%33%*¥€)W QM: geaw‘aigé / J L? ...
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