# 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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