m201_l8 - Ob’é‘z‘fffl/e: T5 fi‘fld, aw I...

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Unformatted text preview: Ob’é‘z‘fffl/e: T5 fi‘fld, aw I fiffwwimaje value 4.2/9}; : mix a? 95,} war 2Q, , L81" fix (756%0'2‘6» at [DOSffiva [flafléwzfmf— [V1 351/ (Lu/'6? 1/67” x};360+!® 7%‘6545 x! xi If M assume; fax, y) Vchigs S/mflg M 7426 in?“va z e 36 e: .75, [m “- éfimafiiw iMfi‘i/fifgmfifl‘fl 1W): :2 jfié’x, y) I) \/[x'5):=>i6 L_______________ ~€><a6f Vflué (dig y a“? 9:2, 3/1—53/ wumw- gm imam. Ema i Waflymwvfi/W I EXWMEM 3 ng M€T££10Cf 25.3 {151% EV? fif:2%%y} yi’ffi}:/- fiapfay Wifv’ifxzazf fi/pmaima & $44M yaw; {£5 gflufim If at ya: {9.23 0.4) 4%», 52.2? flmd :1 52533 \g’ 9,) %;@‘2 ama‘f an?pr . {ampma wz‘f-é‘. W @wa?’ Vfi/iaé’.\$. Qzuhm; Wé {53% 867% “ff/LEE {Wt}? exam??? {/nflfe.’ MKS {fiéfimfiyfi M07" ('96 *5“? @fifia whém nwmgm‘wx’ WW5 42m age/035a?) Ling/25, éfumm wr’ffiu a Mfr/DJJQWTW 2% 69in5 y: ’Zg’xH) 4" 66"” yg’0)9j 33> a =3 f0 y: «2 {in3 +36%. ~ .. _ =_ a £4}. I, Figwi 91.1.. / (a) X1 = Xo + h = 0.2, f(xo,yo) = f(0,1) = 1.000, ,Vl = yo "1‘ hf(x0,y0) = 1.000 + 0.20.000) = 1.200. (1)) X2 = X1 + h = 0.4, f(x1,y1) = f(0.2,1.200) = 1.600, yz = M + hf(x1,y1) = 1.200 + O.2(1.600) = 1.520. (C) X3 = X2 + h = 0.6, f(X2,y2) = f(0.4,1.520) = 2.320, Y3 = yz + hf(X2,y2) = 1.520 + 0.2(2.320) = 1.984. (‘1) X4 = xs + h = 0.8, f(xa,y3) = f(0.6,1.984) = 3.184, M = ya + hf(xs,y3) =, 1.984 + 0.2(3.184) = 2.621, (e) x5 = x4 + h = 1.0, f(X4,y4) = f(0.8,2.621) = 4.221, ys = y4 + h f(x4,y4) = 2.621 + 0.2(4221) = 3.465. (a) X] = xo +11 = 0.1, f(xo.y0) = f(0,1) = 1.000, YI = yo ‘1' hf(X0,J’0) = 1.000 + 0.10.000) = 1.100. (b) x; = x1+ h = 0.2, f(xl,y1) = f(0.1,1.100) = 1.300, yz = y1 + hf(x1,y1) = 1.100 + O.1(1.300) = 1.230. (c) x; = x; +11 = 0.3, f(x2,y2) = f(0.2,1.230) = 1.630, ' y3 = y; + hf(x2,y2) = 1.230 + 0.1(1.630) = 1.393. (d) X4 = x3 + h = 0.4, f(X3,y3) = f(O.3,1.393) = 1.993, ' y4 = ya + hf(X3,y3) = 1.393 + O.1(1.993) = 1.592. (6) X5 = X4 + h = 0.5, f<X4,y4) = f(0.4,1.592) = 2.392, ys = 124 + hf(X4,y4) =. 1.592 + 0.1(2.392) = 1.831. (f) x5 = x5 + h = 0.6, f(xs,y5) = f(0.5,1.831) = 2.831, ya = y5 + hf(xs,y5) = 1.831 + 0.1(2.831) = 2.114. (g) X7 = X6 + h = 0.7, f(xs,y5) = f(0.6,2.114) = 3.314, y7 = ye + hf(xa,y6) = 2.114 + 0.1(3.314) = 2.445. (h) x8 2 X7 + h = 0.8, f(x7,y7) = f(0.7,2.445) = 3.845, ya = 177 + hf(X7,y7) =. 2.445 + 0.1(3.845) = 2.830. (1) x9 = xx + h = 0.9, f(xg,yg) = f(0.8,2.830) = 4.430, y9 = yg + hf(Xg,yg) = 2.830 + 0.1(4.430) = 3.273. (j) xro = X9 + h = 1.0, f(xQ,y9) = f(0.9,3.273) = 5.073, ylo = y9 + hf(XQ,y9) = 3.273 + 0.16.073) = 3.780. Cfi‘mqwmfimm 7113 43845165 Us; 1146 A, xn y" yn r y using Ii = 0.2 using h = 0.1 0.0 1.000 1.000 1.000 0.1 — 1.100 1.116 0.2 1.200 1.230 1.264 0.3 —— 1.393 1.450 0.4 1.520 1.592 1.675 0.5 —— 1.831 1.946 0.6 1.984 2.114 2.266 0.7 —— 2.445 2.641 0.8 2.621 2.830 3.076 0.9 — 3.273 3.579 1.0 3.465 3.780 4.155 Error Error x” using h = 0.2 using [1 = 0.1 0.2 0.064 0.034 0.4 0.155 0.083 0.6 0.282 0.152 0.8 0.455 0.246 1.0 0.690 0.375 ...
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This note was uploaded on 02/05/2011 for the course MATH 201 taught by Professor Steacy during the Spring '10 term at University of Victoria.

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m201_l8 - Ob’é‘z‘fffl/e: T5 fi‘fld, aw I...

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