{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 1 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 257 0 "" }{TEXT 258 30 "Autour de la m\351thode de Newton" }{MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 12 "Dichotomie:\n" }{TEXT -1 122 "Entr\351e : une fonction f , les bornes de l'intervalles a < b et le nombre n d'iterations,\nSort ie : la n'ieme approximation.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 239 "dichot := proc(f,a,b,n)\n local x,y,z,i;\n x := a;\n y := \+ b;\n for i from 1 to n do\n z := (x+y)/2;\n if f(z) = 0 then \n break; RETURN(z);\n elif f(x)*f(z) < 0 then\n y := z;\n \+ else x := z;\n fi;\n od;\n RETURN(z);\nend;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 7 "Newton\n" }{TEXT 261 0 "" } {TEXT -1 121 "Entree : une fonction f, un point de depart x0 et un nom bre d'iteration n,\nSortie : le n-ieme de l'iteration newtonienne." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "newton := proc(f,x0,n)\n l ocal Nf,i,res;\n Nf := x -> x-f(x)/D(f)(x);\n res := x0;\n for i fr om 1 to n do\n res := Nf(res);\n od;\n RETURN(res);\nend; " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 262 0 "" } {TEXT 263 27 "Construction d'une fractale" }{TEXT 264 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 521 "Listing := proc(a,b,N,k,l)\n local A,alpha,f,Nf,i,j ,ii,ini,res;\n A := matrix(N+1,l-k+1);\n for i from 1 to N+1 do \n alpha := a+(i-1)*(b-a)/N;\n f := x-> x^3+alpha*x+1;\n \+ Nf := x -> x-(x^3+alpha*x+1)/(3*x^2+alpha);\n ini := 0;\n \+ for ii from 1 to k do\n ini := evalf(Nf(ini));\n od; \+ \n A[i,1] := ini;\n for j from 2 to l-k+1 do\n A[i,j] := evalf(Nf(A[i,j-1]));\n od;\n od;\n res := [seq(seq([A[i ,j],a+(i-1)*(b-a)/N],i=1..N+1),j=1..l-k+1)];\n RETURN(res);\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 233 "zoom := proc(s,inf,sup) \n local N,res,j,i;\n N := nops(s);\n j := 1; \n for i from 1 to N do\n if (inf <= s[i][1] and s[i][1] <= sup) then\n res[j] : = s[i];\n j := j+1;\n fi;\n od;\n RETURN([seq(res[i],i=1..j- 1)]);\nend;" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 12 "Un exemple :" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "whith(p lots);\nDigits := 100;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 " s := Listing(-2,-1,100,20,100):\nss := zoom(s,-2,2):\nplot(ss,style=po int,symbol=CROSS,axes=FRAMED,color=BLACK);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 122 "s := Listing(-1.30,-1.25,100,20,100):\nss := zoom( s,-0.19,0.22):\nplot(ss,style=point,symbol=CROSS,axes=FRAMED,color=BLA CK);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 34 "Dessin des it \351rations Newtoniennes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 577 "Graphnewton := proc(f,x0,n)\n local Nf,X,Y,P,Q,a,b,Gf,GP,GL,i,d;\n \+ Nf := x -> x-f(x)/D(f)(x);\n X := vector(n);\n X[1] := x0; \n for \+ i from 1 to n-1 do\n X[i+1] := evalf(Nf(X[i]));\n od;\n X := [seq (X[i], i=1..n)];\n Y := map(f,X);\n P := [seq([X[i],Y[i]],i=1..n)]; \+ \n Q := seq(op([[X[i],Y[i]],[X[i+1],0]]),i=1..n-1);\n Q := [Q,[X[n], Y[n]]];\n a := min(op(X)); b := max(op(X));\n d := 0.01*(b-a);\n a \+ := a-d; b := b+d;\n plot(f(x),x=a..b,linestyle=2,colour=black);\n pl ot(P,style=point,symbol=CIRCLE,colour=black);\n plots[display](\{%,%% ,plot(Q,x=a..b,colour=black)\});\nend;\n" }}}}}{MARK "5" 0 }{VIEWOPTS 1 1 0 1 1 1803 }