{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 } {CSTYLE "" -1 256 "" 1 36 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{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 }{PSTYLE "War ning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{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 }{PSTYLE " Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 84 "R\351mi SOUVETON - A1\n Math\351matiques Assist\351es par Ordinateur\n(MAO)\nTh\350me 04 - 28/ 02/07\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 26 "Programmation d'une boucle" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "suite := proc(u0,n,f)\nloca l u,compteur;\n\nu := u0;\nfor compteur from 1 to n do\n u := f(u); \nod;\nu;\nend;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&suiteGR6%%#u0G %\"nG%\"fG6$%\"uG%)compteurG6\"F-C%>8$9$?(8%\"\"\"F49%%%trueG>F0-9&6#F 0F0F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := x-> sqrt( 1+x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operator G%&arrowGF(-%%sqrtG6#,&\"\"\"F09$F0F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "evalf(suite(1,10,f));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(fG!=;!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 36 "R\351solution d'\351quation par dichotomie" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 262 "Dichotomie : = proc(a0,b0,f,erreur)\nlocal a,b,c;\n\n# Initialisation\na := a0;\nb \+ := b0;\nc := (a+b)/2.0;\n\n# Corps de la proc\351dure\nwhile b-a > err eur do\n c := (a+b)/2.0;\n if evalf(f(c)) > 0 \n then a := c; \n else b := c;\n fi;\nod;\n#fin du programme\nc;\nend;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+DichotomieGR6&%#a0G%#b0G%\"f G%'erreurG6%%\"aG%\"bG%\"cG6\"F/C'>8$9$>8%9%>8&,&F2$\"+++++]!#5*&F:\" \"\"F5F>F>?(F/F>F>F/29',&F5F>F2!\"\"C$>F8F9@%2\"\"!-%&evalfG6#-9&6#F8> F2F8>F5F8F8F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Dichot omie(3,4,sin,0.0001);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+F0aTJ!\"* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 328 "\nDichotomie := proc(a 0,b0,f,erreur)\nlocal a,b,c,resultat;\n\n# Initialisation\na := a0;\nb := b0;\nc := (a+b)/2.0;\nresultat := NULL;\n\n# Corps de la proc\351d ure\nwhile b-a > erreur do\n c := (a+b)/2.0;\n if evalf(f(c)) > \+ 0 \n then a := c;\n else b := c;\n fi;\n resultat := resul tat , c;\nod;\n#fin du programme\nresultat;\nend;\n" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%+DichotomieGR6&%#a0G%#b0G%\"fG%'erreurG6&%\"aG%\"bG %\"cG%)resultatG6\"F0C(>8$9$>8%9%>8&,&F3$\"+++++]!#5*&F;\"\"\"F6F?F?>8 '%%NULLG?(F0F?F?F029',&F6F?F3!\"\"C%>F9F:@%2\"\"!-%&evalfG6#-9&6#F9>F3 F9>F6F9>FA6$FAF9FAF0F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Dichotomie(3,4,sin,0.0001);" }}{PARA 12 "" 1 "" {XPPMATH 20 "60$\"+++ ++N!\"*$\"++++]KF%$\"++++DJF%$\"+++](=$F%$\"+++DcJF%$\"++]iSJF%$\"++vV [JF%$\"+]7`WJF%$\"+D\"yD9$F%$\"+i:gTJF%$\"+\"G869$F%$\"+@uNTJF%$\"+\" \\z99$F%$\"+F0aTJF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "with (plots);\nlistplot([Dichotomie(3,4,sin,0.0001)]);" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7U%(animateG%*animate3dG%-animatecurve G%-changecoordsG%,complexplotG%.complexplot3dG%*conformalG%,contourplo tG%.contourplot3dG%*coordplotG%,coordplot3dG%-cylinderplotG%,densitypl otG%(displayG%*display3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradpl ot3dG%-implicitplotG%/implicitplot3dG%(inequalG%-listcontplotG%/listco ntplot3dG%0listdensityplotG%)listplotG%+listplot3dG%+loglogplotG%(logp lotG%+matrixplotG%(odeplotG%'paretoG%*pointplotG%,pointplot3dG%*polarp lotG%,polygonplotG%.polygonplot3dG%4polyhedra_supportedG%.polyhedraplo tG%'replotG%*rootlocusG%,semilogplotG%+setoptionsG%-setoptions3dG%+spa cecurveG%1sparsematrixplotG%+sphereplotG%)surfdataG%)textplotG%+textpl ot3dG%)tubeplotG" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6#-%'CURVESG6#707$$\"\"\"\"\"!$\"+++++N!\"*7$$\"\"#F*$\"++++]KF-7$$ \"\"$F*$\"++++DJF-7$$\"\"%F*$\"+++](=$F-7$$\"\"&F*$\"+++DcJF-7$$\"\"'F *$\"++]iSJF-7$$\"\"(F*$\"++vV[JF-7$$\"\")F*$\"+]7`WJF-7$$\"\"*F*$\"+D \"yD9$F-7$$\"#5F*$\"+i:gTJF-7$$\"#6F*$\"+\"G869$F-7$$\"#7F*$\"+@uNTJF- 7$$\"#8F*$\"+\"\\z99$F-7$$\"#9F*$\"+F0aTJF-" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "M\351thode d'it\351ration" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 269 "Iteration : = proc(x0,g,rho,erreur)\nlocal x,compteur,resultat;\n\nx := x0;\ncompt eur := 0;\nresultat := NULL;\n\nwhile evalf(abs(g(x))) > erreur and co mpteur < 100 do\n x := evalf(x+rho*g(x));\n compteur := compte ur + 1;\n resultat := resultat , x;\nod;\nresultat;\nend;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%*IterationGR6&%#x0G%\"gG%$rhoG%'erreurG6%%\"xG%)compteurG%)resultatG 6\"F/C'>8$9$>8%\"\"!>8&%%NULLG?(F/\"\"\"F;F/329'-%&evalfG6#-%$absG6#-9 %6#F22F5\"$+\"C%>F2-F@6#,&F2F;*&9&F;FEF;F;>F5,&F5F;F;F;>F86$F8F2F8F/F/ F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "listplot([Iteration(3 ,sin,1.1,0.0001)]);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6#-%'CURVESG6#7&7$$\"\"\"\"\"!$\"+4?BbJ!\"*7$$\"\"#F*$\"+ $=H-9$F-7$$\"\"$F*$\"++!H<9$F-7$$\"\"%F*$\"+>!z:9$F-" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "M \351thode de Newton" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 317 "Newt on := proc(x0,f,erreur)\nlocal x,compteur,resultat;\n\nx := x0;\ncompt eur := 0;\nresultat := NULL;\n\nwhile evalf(abs(f(x))) > erreur and co mpteur < 100 do\n x := evalf(x - f(x) / D(f)(x));\n compteur := \+ compteur +1;\n resultat := resultat , x;\nod;\nresultat;\nend;\nIte ration(3,sin,0.5,0.0001);\nNewton(3,sin,0.0001);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'NewtonGR6%%#x0G%\"fG%'erreurG6%%\"xG%)compteurG%)res ultatG6\"F.C'>8$9$>8%\"\"!>8&%%NULLG?(F.\"\"\"F:F.329&-%&evalfG6#-%$ab sG6#-9%6#F12F4\"$+\"C%>F1-F?6#,&F1F:*&FDF:--%\"DG6#FEFF!\"\"FS>F4,&F4F :F:F:>F76$F7F1F7F.F.F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6-$\"+/+cqI!\" *$\"+pk/1JF%$\"+>e\"Q7$F%$\"+oPqKJF%$\"+_\"[r8$F%$\"+&Rq$RJF%$\"+B:[SJ F%$\"+)3P59$F%$\"+r[JTJF%$\"+iPXTJF%$\"+3K_TJF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+VlaUJ!\"*$\"+`EfTJF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "5 0 0" 17 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }