UNIVERSITI MALAYSIA PERLIS. EQT 102 Engineering Mathematics II [Matematik Kejuruteraan II]
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1 SUIT UNIVERSITI MAAYSIA PERIS Peperikn Akhir Semeter Pertm Sidng Akdemik 15/16 Jnuri 16 EQT 1 Engineering Mthemtic II [Mtemtik Kejurutern II] M : 3 jm Plee mke ure tht thi quetion pper h SEVEN (7) printed pge including thi front pge before you trt the exmintion. [Sil ptikn kert oln ini mengndungi TUJUH (7) muk urt yng bercetk termuk muk hdpn ebelum nd memulkn peperikn ini.] Thi quetion pper h FOUR (4) quetion. Anwer A quetion. [Kert oln ini mengndungi EMPAT (4) oln. Jwb emu oln.] SUIT
2 SUIT Quetion 1 [Soln 1] - - (EQT1) () Solve the prtil differentil eqution [Seleikn permn pembezn epr] u 3x yin x co3 y, uing the initil condition u, y y. [menggunkn yrt wl u, y y. ] x (5 Mrk/ Mrkh) (b) Uing the method of eprtion of vrible, olve the following prtil differentil eqution [Dengn menggunkn kedh pemihn pembolehubh, eleikn permn pembezn berikut] u u 5, t x uing the initil conditi on u, t 3e t. t [menggunkn yrt wl u, t 3 e.] (1 Mrk/ Mrkh) (c) By uing the method of vrition of prmeter, find the generl olution of the following differentil eqution [Dengn menggunkn kedh ubhn prmeter, dptkn penyelein m bgi permn pembezn berikut] d y x 4 y xe. dx (15 Mrk/ Mrkh)...3/- SUIT
3 SUIT Quetion [Soln ] (EQT1) () By uing the definition of plce trnform, find f() t function f( t ). [Dengn menggunkn definii jelmn plce, cri f() t for the given bgi fungi f() t yng diberi.] 3, t f ( t), t 3 1, t 3 (7 Mrk/ Mrkh) (b) Find the invere plce trnform of [Cri jelmn plce ongng bgi] 4 4 F ( ). ( 4) (8 Mrk/ Mrkh) (c) Solve the following initil vlue problem by uing plce trnform. [Seleikn mlh nili wl berikut dengn menggunkn jelmn plce.] 4t 4 4 6, 1 nd y y y y e y 1 (15 Mrk/ Mrkh)...4/- SUIT
4 SUIT Quetion 3 [Soln 3] (EQT1) () Determine whether the following function i odd, even or neither. [Tentukn m d fungi berikut merupkn fungi gnjil, genp tu bukn kedu-duny.] (i) f x x in3x ( Mrk/ Mrkh) f x 5x 8 co x ( Mrk/ Mrkh) (ii) (iii) f x in 3xin x ( Mrk/ Mrkh) (b) A periodic function f x i defined [Stu fungi berkl f x ditkrifkn ebgi] f x 1, 1 x 1 1, x 1, x 1 f x x Aume tht f( x) i n even function, find the correponding Fourier erie expnion. [Anggpkn bhw f( x) dlh tu fungi genp, dptkn kembngn iri Fourier yng epdn.] (1 Mrk/ Mrkh)...5/- SUIT
5 SUIT (EQT1) (c) A periodic function f x i defined [Stu fungi berkl f f x ditkrifkn ebgi] x 1 x, x 1 1 x, x 1 x, x f x x. (i) Sketch the grph of f (x) for the rnge π x π. [krkn grf bgi f (x) pd jult π x π.] (3 Mrk/ Mrkh) (ii) Bed on c(i), determine the type of function f (x) nd tte your reon. [Berdrkn pd c(i), tentukn jeni fungi f (x) dn nytkn ln nd.] ( Mrk/ Mrkh) (iii) Find the Fourier erie expnion for f (x). [Cri kembngn iri Fourier untuk f( x ). ] (9 Mrk/ Mrkh)...6/- SUIT
6 SUIT Quetion 4 [Soln 4] (EQT1) Police found ded body in hotel room t 1..m midnight. The initil body temperture w 3 C. After hour, the body temperture went down to3 C. The urrounding temperture remin t 3 C. By uing Newton lw of cooling given by [Poli menjumpi myt di dlm hotel pd jm 1. tengh mlm. Suhu wl bdn terebut dlh 3 C. Selep jm, uhu bdn terebut menurun kepd 3 C. Suhu bilik dlh kekl pd Dengn menggunkn hukum penyejukn Newton diberikn oleh] T T Ae kt, 3 C. find the time of deth of the victim where T i the temperture of the body t time t, T i the urrounding temperture nd k i contnt. Aume tht the norml body temperture i37 C. [cri wktu kemtin mng di mn T dlh uhu bdn pd m t, T dlh uhu perekitrn dn k dlh utu pemlr. Anggpkn uhu norml bdn mnui dlh 37 C. ] (1 Mrk/ Mrkh) -oooooo- SUIT
7 SUIT APPENDIX [AMPIRAN] Defintion of plce Trnform [Tkrifn Jelmn plce] t { f t } F e f t dt (EQT1) Tble of plce Trnform [Jdul Jelmn plce] f t { f t } F f t { f t } F n! t n, n 1,,3,.. n1 t e in t co t inh t coh t e t in bt e t co bt 1 t n e t b b b n! n1 n d n d t n n f t 1 F e t f t F y t Y y y t Y y y Formul Fourier Serie [Rumu Siri Fourier] nπx nπx f x nco bnin n1 1 f x dx 1 nx π n f xco dx 1 nx π bn f xin dx SUIT
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