FinalExam_Review

# FinalExam_Review - \$5M BIT—Final Review Problems 1 Using...

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Unformatted text preview: \$5M BIT—Final Review Problems 1] Using Laplace 'I‘ransl'orrns,I solve the integral equation for ﬁt): - 3 on) = fuygomo .— ajdu + {1 -— tJe‘. Hm: use oonvolution theorem. I 2] Find the inverse Laplace Transform of F{s] = 32:12 a: :2: and graph ﬁt) on U 5 t 5 4. . + . . o" ﬂint. multiply ﬁe} b} F. 3) Solve the heat (diffusion) equation on a bar insulated at one end only and check your answer. PDE: cuuﬂ=nhﬂﬁagmﬂgt BC’s: arm, t] = {i 11(4, 3) I: '3 IC: n{s,D} = 3 cos 4} Evaluate the surface integral g E - n rial where S is glosecl hemisphere shown and ,ﬂa, y, z} = mi + yj + zit. Cheek by using the divergence theorem. 2 I: e'oos I5 5) Let f = f(zly}l where y = e" sin 3 use the chain rule to show frr+j§9 = egrtfmm'i' fig-y)- i5 Hint; note that -—I = a. {91" 6] Using Laplace Transforms, solve this wave equation on a ﬁnite string 2n”:unl}5s5£,05t<m EC’s : u[ﬂ,t} = U n{£,i] = o IC’s ‘. afa, D] = sin. ago: what!) = I] [,f“ E'f’lq/ /(€Vr'ag4 Mt): iii/(L4) yCﬁ-h) db; +6!-—t)::t TeX-5c- Lqpfﬂrca 0?] >1 £t)= J-(t) -eé .-.-.. 5%h( E} vii—SM) @155 éqg/d: Caygr‘ - mic ?‘CA'JF = “er—swag) + 5.? sI-n(q(m)m~a *‘ ém ﬂea) qée-z) +--' 6459573- 535? ("‘3' man/6:: Ca: liq/c; Era-.Hj Tim“ FK¢J:{% 5,3,1 7T1. ¢f¢/ _ i f 0 [tit-4 2, {fir saw-H 34-13 \$3 0 3¢£¢ff ﬂit) (Camsmmt) a} féq’J-T-x‘ﬂpag pﬁr‘ “'83” 11-4" M wow“) + mam/m = o _ =7 By = C) :‘b (’3’ : 0 =9 Fa}: Aims (PX) win-3:0 =2 Agjfkpj lo |_ FCH. VJJECGJ V 59-5 MJ (-65 WEI-i1 M) SKI-,1 M3 Oéqi'ZTr- (JE- Lu: 3' L ﬁt; ; [‘Cas Vsr'h 5-4" £95 Vac-,5 of] 03 5. r1; "' [H5551 Vin: LA" "‘ 55*: Vﬁ‘h £4... 12¢; 1/] .:/{’= n. arr... :. .5 J' j; -—¢¢J PIE-H I... Cosucm L; C} “‘5’?! “curt-4 “57". VII-51 it do: If n.— 1— .. C: (CdE'L’I-i’ Gail-1.) ‘J'{*CQ§1V\$H1 a.) r- {*5 (Ca; MINI-a VIr'h 1' Lg *Srhwcugycgjlq) - f H 1. ~ C95 Massif] Ccflh’IrﬂE/f} CGJVS‘I'J-q V] 1'55 ﬁﬁ-hu : If M 34 w j; mags: i; _ . 5: 51 #1“ 11. 5; : I’Qp :34: jpjeuft. I! = F0) -A/ 824 J daft-we?” 3'“ amivss'ir‘q .rL. cm 12' Ir'h‘v’ J}... c/c, H. *‘r '11-! a: {‘551/ “"095 1/5173” arc/c,- Gr I C05 I! JV 0);, _= [afﬁx/53H ;@ XE:- _ﬁr5'-'-h (9": A}? '-‘- —£'C¢pﬁ’= .. gr .. Efﬁe-'- CD\$_0J-)f’ Mi). =7 gal-a t" ﬁg V2" ‘61“)! ’3')“ “a” “@4- ‘V +16; r; + em = at cm») + army ~J 164:? "'“ w)[f1"yz) _ 8w“ J’i‘y-‘L: Ezrﬁa51¢‘*ﬁzrﬁﬁ10’¢ :1” =2} 1'“ng air-{gm ,2 2%., zmét OE- 15-1 056 La: (3;: Mm»): inf—aw) = 0 IC' £46110): Sr” Cir/r“ Ear/‘5': Cap/=35: or? 25: 1- 2 tag = 5% fﬁfwfazﬁ) - eta/3f 3.5x; =- 5IJ~ 5' rm»: Ex) 5} ca;— 55 = gyngx) m) £30153:- Aomcpﬁwﬂsaqs Sg/u-xm. 1‘" quhqur IQH, 7. ﬂarixf—Bgu‘éx +C Ir'ﬁ/g-f) gr Csr'ﬁ{.§)r’( it. raf-rw‘} ("I"), L 1.. "Ug‘j \$r‘h(gx) “ “2% C 943*) = ‘gsr'wg‘w .3". L =5 73'" r1 _ C E *1 —.'> “I ‘5- — C- _ L . ...
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FinalExam_Review - \$5M BIT—Final Review Problems 1 Using...

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