{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "pol:=(x-(A+B)/2)*(x-B)/(A-B)^2*2*y (A)+(x-A)*(x-B)/(B-A)/(A-B)*4*y((A+B)/2)+\n(x-A)*(x-(A+B)/2)/(B-A)^2*2 *y(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,(*,\"\"#\"\"\",(%\"x GF(*&F'!\"\"%\"AGF(F,*&F'F,%\"BGF(F,F(,&F*F(F/F,F(,&F-F(F/F,!\"#-%\"yG 6#F-F(F(*.\"\"%F(,&F*F(F-F,F(F0F(,&F/F(F-F,F,F1F,-F46#,&*&F'F,F-F(F(*& F'F,F/F(F(F(F(*,F'F(F8F(F)F(F9F2-F46#F/F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "simplify(eval(pol,x=A)); simplify(eval(pol,x=(A+B) /2)); simplify(eval(pol,x=B));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\" yG6#%\"AG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"yG6#,&*&\"\"#!\"\"%\" AG\"\"\"F+*&F(F)%\"BGF+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"yG6#% \"BG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "factor(int(pol,x=A. .B));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"'F&*&,(*&\"\"% F&-%\"yG6#,&*&\"\"#!\"\"%\"AGF&F&*&F1F2%\"BGF&F&F&F&-F-6#F5F&-F-6#F3F& F&,&F3F&F5F2F&F&F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "seq([ x^i,(4*.5^i+1)/6,1/(i+1.)],i=1..6);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 (7%%\"xG$\"+++++]!#5F%7%*$)F$\"\"#\"\"\"$\"+MLLLLF'$\"+LLLLLF'7%*$)F$ \"\"$F,$\"+++++DF'F57%*$)F$\"\"%F,$\"+MLL$3#F'$\"+++++?F'7%*$)F$\"\"&F ,$\"++++v=F'$\"+nmmm;F'7%*$)F$\"\"'F,$\"+ML$3x\"F'$\"+H9dG9F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "Y:=mtaylor(y(xc+Delta),Delta,7);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"YG,0-%\"yG6#%#xcG\"\"\"*&--%\"DG6#F'F(F*%&DeltaGF *F**&#F*\"\"#F**&---%#@@G6$F.F3F/F(F*)F0F3F*F*F**&#F*\"\"'F**&---F86$F .\"\"$F/F(F*)F0FCF*F*F**&#F*\"#CF**&---F86$F.\"\"%F/F(F*)F0FMF*F*F**&# F*\"$?\"F**&---F86$F.\"\"&F/F(F*)F0FWF*F*F**&#F*\"$?(F**&---F86$F.F=F/ F(F*)F0F=F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "exact:=i nt(Y,Delta=-h/2..h/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&exactG,** &-%\"yG6#%#xcG\"\"\"%\"hGF+F+*&#F+\"#CF+*&---%#@@G6$%\"DG\"\"#6#F(F)F+ )F,\"\"$F+F+F+*&#F+\"%?>F+*&---F46$F6\"\"%F8F)F+)F,\"\"&F+F+F+*&#F+\"' gDKF+*&---F46$F6\"\"'F8F)F+)F,\"\"(F+F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 61 "(eval(Y,Delta=-h/2)+4*eval(Y,Delta=0)+eval(Y,Delta= h/2))/6*h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"'F&*&,**& F'F&-%\"yG6#%#xcGF&F&*&#F&\"\"%F&*&---%#@@G6$%\"DG\"\"#6#F,F-F&)%\"hGF 9F&F&F&*&#F&\"$#>F&*&---F66$F8F1F:F-F&)F " 0 "" {MPLTEXT 1 0 19 "simpson:=expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%(simpsonG,**&-%\"yG6#%#xcG\"\"\"%\"hGF+F+*&#F+\"#CF+*&---%#@@G6$% \"DG\"\"#6#F(F)F+)F,\"\"$F+F+F+*&#F+\"%_6F+*&---F46$F6\"\"%F8F)F+)F,\" \"&F+F+F+*&#F+\"'S#Q\"F+*&---F46$F6\"\"'F8F)F+)F,\"\"(F+F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "exact-simpson;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"%!)GF&*&---%#@@G6$%\"DG\"\"%6#%\"yG 6#%#xcGF&)%\"hG\"\"&F&F&!\"\"*&#F&\"'?>CF&*&---F,6$F.\"\"'F0F2F&)F5\" \"(F&F&F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "evalf((sin(0)+4*sin(Pi/4)+sin(Pi/2) )/6*Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+x)zA+\"!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f:=x->sin(x): A:=0: B:=Pi /2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "for k from 1 to 6 d o n:=2^k:\nIn[k]:=evalf( (B-A)*(\nf(A)+f(B)+\n2*sum(f(A+2*(B-A)*i/n), i=1..n/2-1)+\n4*sum(f(A+(2*i-1)*(B-A)/n),i=1..n/2)\n)/3/n); end do;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#InG6#\"\"\"$\"+x)zA+\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#InG6 #\"\"#$\"+&eM,+\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#InG6#\"\"$$\"+&H3++\"!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#InG6#\"\"%$\"+<0++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#InG6# \"\"&$\"+K+++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#k" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#InG6#\"\"'$\"+-+++5!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "for i from 1 to 5 do J[i]:=( 16*In[i+1]-In[i])/15 end do; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\" JG6#\"\"\"$\"+bc\"*****!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6 #\"\"#$\"+g()******!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6#\" \"$$\"+$)********!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6#\"\"% $\"+**********!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6#\"\"&$\" +++++5!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "for i from 1 \+ to 4 do K[i]:=(64*J[i+1]-J[i])/63 end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"KG6#\"\"\"$\"+3+++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"KG6#\"\"#$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"KG6#\"\"$$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"KG6#\"\"%$\"+++++5!\"*" }}}}{MARK "4 0 0" 9 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }