exams - A P P M 2360 F all 2008 F inal E xam D ecem ber 15...

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Unformatted text preview: A P P M 2360 F all 2008 F inal E xam D ecem ber 15 2008 ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture section (4) your instructors' name, and (5) a gTadillg table. You must work all of the problems OIl the exam. Show ALL of your work in your bluebook and box in your final answer. A correct answer with no relevant work may receive no credit, while an incorrect answer accompanied by some correct work may receive partial credit. 'Lext boob, class notes, calculators and ANY electronic devices are NOT permitted. A x" x 11". two-sided, sheet of note,,", is allowed. I. (L() points) ,1/ = "(JS (t)(S ifl(l) !I 1. /)y>J (l:2 points ) Find t lu- gl:neral solution ( ) f r .II 1 / .If 1 /2 + 1 1 (2(j I)(lints) Consider t.lu- differential equation u ./1 ( j ) ( , : - ; point s) Find the gl:rH 'ral solution of t hr- h()rnogl:Jl(~)\js quation. (k) i III p()ints I Fu! it part i.ular s()lllt ion (If the II()[th()[IIog('JI('O llS "quation. ('2 points) Find the gl'IlI'ral solut ion of the nO ldIO lnog('IW ()U Soquation. "A (2:) 1)()inl,s.1('ollsidn t.lu: S ,Y c;t"lll of ,litfcJ('ntial ('(l'lat.ions ... . / f .1'1 .r I .1/ l .1/ ,-:r t- il- - a) ('2(1 points) Find t lio gC lll'!'al sol ut ion. Make sure your solution is rr-al. yr I C, IIi,inls) S kl'lclt tilt' pha. port rait for t h ~VSt('1l1 c~1() points i (\!llsid cr the autonomous system of DEs J.iY( 1]11 p o iIltS ) D dl'l'lllilH ' all t hr ('qllilihriuIlI P O iIlt.S .md t ln- .Incobi.ui ruat.rix corresponding to I'ilch "'Illilil'rillIlI point ~.J,' I", 1'(liIII>;, hIlIl lilt' "I,t;"Il\'alllt':-; " I lilt' .I;II'IlI'I<l11 llIld liS ,' t lu-ru tu dl'tl'rlllillt' t l: stal,illt\ .u u l 111<' 1 \ 'jJ ( ' (it "(l'liliilrIll[lJ 11',,1' .-x.uupl. s;"ldl .. spiral. C "lltn, star. 1'1{') fill' ('itch fixe-d pou It of t h III JilliIlI'ar :-;\'sl "Ill. ;Y' I C , P ,)iIlh) S kptch t.lie- plta,sf' por t.r.ut of lilt' uonliuoar S ,"S t"lll ineIudiru; all till' nullcliuo and tIll' . dir"(lloI!.S ()N .u r.l IlET\\'EEI\' nulkluu-. i\lakt' sun' vour figllre is hig and chiaro .1 ; .1/ I .II 1 " I-il 2, " II II ~J.J.-Y((j p "illb j \V rit" tIt" svst.cru III til" Ior m Ax ~ b alld filld tJH' df't,'rlllillartl of t.ho m atrix A hi III !,,,irrr>i I)"t"rrrlilll' it J-:'Ilr:tlilliis (I \ h"\,, I I ,S ,dllliIJTI "Tid. if 111.,\ .l. find lrll tilt'-olut iou-'. P LE A S E T \lB N O \ E I L qU E S T IO N ;, C O N T IN U E S O N N E X T P A C E . Exam #1 APPM 2360 Fall 2007-- - - - -- - - - - - - - - - - - - - - - --- - - - - - - - - - - - - - - - - - - - ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture section (4) your instructor's name, and (5) a grading table. You must work all of the problems on the exam....
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exams - A P P M 2360 F all 2008 F inal E xam D ecem ber 15...

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