{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT 256 27 "NUMEERISEN ANALYYSIN DEMO T " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Perusasioita Maplesta" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Sijoitus := ,komennon p\344 \344tt\344minen ; tai : jolloin ei tulostusta" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A:=4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "B:= A:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "B;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Yht\344suuruus = " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "C:=symboli;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "C=4; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "symboli;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "C;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "symboli:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "C;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Yht\344suuruuden tarki stus evalb(x=y)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalb(C=4);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C:=4;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "evalb(C=4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Muuttujan nimi alkaa kirjaimella, lis\344ksi saa k\344ytt\344 \344 numeroita ja alaviivaa" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "W_78 wwQQ:=o;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3a:=3;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "Vinojen yl\344prikkojen ` v\344l iss\344 esitet\344\344n mik\344tahansa merkkijono, joka kelpaa my\366s muuttujan nimeksi" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "`22 \366\344 \+ !\244`:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Muuttujan A arvon poistaminen" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "A:='A';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Kaikkien mu uttujien nollaus" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "B;" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 53 "Laskennassa k\344ytettyjen merkitsevien numeroiden m \344\344r\344" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Digits;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "23.9/0.3578134532888;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Digits:=100;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 7 "exp(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "exp(1.);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(ex p(1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=10;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Maple pit\344\344 tarkat arvot, jo llei lausekkeissa esiinny liukulukuja" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sin(sqrt(2)*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sin(sqrt(2.)*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "% viittaa edellisen suoritetun laskutoimituksen tulokseen" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Kreikkalaiset p ja P" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=pi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "e valf(%);evalf(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "PI;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "lambda;Lambda;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Toistorakenteet" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "for - wh ile - lause" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "for i from 2 0 by -5 to 1 do print('i' = i); od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "i;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "while i<24 do lprint(i); i:=i+4; od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "i;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Maplen apusivut auke avat ?-merkki ja per\344\344n kyselt\344v\344 termi, tai viem\344ll \344 kursori" }}{PARA 0 "" 0 "" {TEXT -1 51 "kyselt\344v\344n termin p \344\344lle ja painamalla F1-n\344pp\344int\344" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "?for" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 48 "Suuren ja pienen luvun yhteen- ja v\344hennyslasku." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Digits:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "a:=0.10 00; b:=0.00004900;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a+b; \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "t:=a-b;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "t+t;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "t+a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%-b; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Edellisen toisto:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "s[0]:=0.00; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for i from 1 by 1 to 12 do s[i]:=s[i-1]+a-b; od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "for i to 12 do s[i]:=s[i-1]+t; od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Digits:=10:12*(a-b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 66 "Liit\344nt\344laki x+(y+z)=(x+y)+z ei voimassa l iukulukuaritmetiikassa!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "x :=0.5289;y:=0.8012;z:=0.6024;Digits:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:=x+y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b :=y+z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a+z=x+b;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Toinen esimerkki" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "x:=4.641;y:=-4.624;z:=-0.0159;Digits:=3:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:=x+y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "w1:=a+z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b:=y+z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "w 2:=x+b;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Digits:=10:w:=x+ y+z;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Suhteelliset virheet pros entteina:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "100*abs(w-w1)/ w;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "100*abs(w-w2)/w;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dx:=100*0.001/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dy:=100*0.004/abs(y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 67 "Osittelulaki x*(y+z)=x*y+x*z \+ ei voimassa liukulukuaritmetiikassa!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "x:=0.5289;y:=0.8012;z:=0.6024;Digits:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b:=y+z;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "xy:=x*y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xz:=x*z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "x*b=xy+xz;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Toinen esimerkki" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 41 "x:=4.2832;y:=-4.2821;z:=5.7632;Digits:=5;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:=x+y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "w1:=a*z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xz:=x*z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " yz:=y*z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "w2:=xz+yz;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Digits:=10:w:=(x+y)*z;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Suhteelliset virheet prosentteina: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "100*(w-w1)/w;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "100*(w-w2)/w;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "Virheen kasaantuminen." }} {EXCHG {PARA 0 "" 0 "" {TEXT 257 17 "M\344\344ritell\344\344n jono" } {TEXT -1 2 " " }{XPPEDIT 18 0 "t[0] = 1;" "6#/&%\"tG6#\"\"!\"\"\"" } {TEXT -1 4 " , " }{XPPEDIT 18 0 "t[1] = 1/3;" "6#/&%\"tG6#\"\"\"*&F'F '\"\"$!\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "t[k] = 10/3*t[k-1]-t[ k-2];" "6#/&%\"tG6#%\"kG,&*(\"#5\"\"\"\"\"$!\"\"&F%6#,&F'F+F+F-F+F+&F% 6#,&F'F+\"\"#F-F-" }{TEXT -1 3 ". " }{TEXT 258 18 "T\344m\344 on sama kuin " }{TEXT -1 7 " " }{XPPEDIT 18 0 "t[k] = 1/(3^k);" "6#/&% \"tG6#%\"kG*&\"\"\"F))\"\"$F'!\"\"" }{TEXT -1 12 " , " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Digits:=40;t[0]:=1.;t[1]:=1/ 3.;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "for k from 2 by 1 to 100 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " t[k]:=(10/3.)*t[k-1]- t[k-2];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " o[k]:=1./3^k;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " lprint('k'=k,t=t[k],o=o[k]);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 40 "Summausj\344rjestyksen vaikutus virheeseen." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "s:=Sum(sqrt( n^2+1.0)-n,n=0..200); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "D igits:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "s:=0: s1:=0: s 2:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "for n from 0 by 1 \+ to 200 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " apu1:=sqrt(n^2+1.0)- n; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " s1:=s1+apu1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " apu2:=1.0/(sqrt(n^2+1.0)+n);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 " s2:=s2+apu2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " s:=s+sqrt(n^2+1.0)-n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "o d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "print('s1'=s1,'s2'=s2 ,'s'=s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "n:=100; sqrt(n^ 2+1.0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "apu1:=sqrt(n^2+1 .0)-n; apu2:=1.0/(sqrt(n^2+1.0)+n);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Sama 10 merkitsev\344ll\344 numerolla" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }{MPLTEXT 1 0 11 "Digits:=10:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "s:=0: s1:=0: s2:=0:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "for n from 0 by 1 to 200 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " apu1:=sqrt(n^2+1.0)-n; apu2:=1/(sqrt(n^2+1.0)+n);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " s1:=s1+apu1; s2:=s2+apu2;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " s:=s+sqrt(n^2+1.0)-n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "print('s1'=s1,'s2'=s2,'s'=s);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Vaihdetaan summausj\344rjestys:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Digits:=4:n:='n':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "s:=Sum(sqrt(n^2+1.0)-n,n=200..0); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "s:=0: s1:=0: s2:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for n from 200 by -1 to 0 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " apu1:=sqrt(n^2+1.0)-n; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " s1:=s1+apu1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " apu2:=1.0/(sqrt(n^2+1.0)+n);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " s2:=s2+apu2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " s:=s+sqrt(n^ 2+1.0)-n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "print('s1'=s1,'s2'=s2,'s'=s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}}{MARK "6" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }