{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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }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 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }0 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 0 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Stephan Simon, LK Mathe 12 , 6.10.1997" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 256 6 "Quelle" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 258 "Dateiname: intrvall.mws\nDateigr\366\337e: 8.41 KB\nName: Step han J. Simon\nSchule: Isolde-Kurz-Gymnasium\nKlasse: 12\nDatum: 06.10. 1997\nFach: Mathematik (LK)\nThema: Algebra\nStichw\366rter: Intervall schachtelung\nKurzbeschreibung: Rechenveorgang einer Intervallschachte lung" }{MPLTEXT 1 0 1 "\n" }{TEXT -1 44 "Update auf Maple 8: 07.05.04 \+ David Ausl\344nder" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 28 "Mathe: I ntervallschachtelung" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart;\nwith(plots):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 7 "Bsp 1.:" }{TEXT -1 1 " " }{XPPEDIT 18 0 "sqrt(2)" "6#-%%s qrtG6#\"\"#" }{TEXT -1 11 " berechnen:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 28 "Bereich immer halbieren (m):" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "m:= (l+ r)/2;\n" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 31 "Festlegen des Start- Intervalls:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "l:=1:\nr:=2:" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 64 "Starten der Intervallschachtelung nach dem Halbierungsverfahren:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "for i to 10 do\n if m^2 > 2 then r:= m\nelse l:= m fi;\n\nprint(evalf([l,m,r]));\nod;\n \nm;\n" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 26 "Ausgeben des L\366sun gswerts:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Lsg[1]:=evalf(m,25);\n" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 64 " \"Hi-Lo\"-Prinzip: Ein kleines Spiel in der Intervallschachtelung:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart ;\nwith(plots):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 5 "Idee:" } {TEXT -1 258 " Man denkt sich einen Intervallbereich aus (z.B.: 1..100 ). Jetzt geht es darum, wo man den n\344chsten Intervallbereich w\344h len soll, wie z.B.: 1..50: \"Ja !\" und 50..100: \"Nein !\", usw. Folg lich bestimmt man den Verlauf der Intervallhalbierung durch Ja und Nei n." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "mt:= (l+r)/2;\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "l:= 1: r:= 100: Bereich:= [l ..r];\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "m:= trunc(mt);\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "\nantwort:= ja;\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "if antwort = ja then r:= m\n else l:= m fi:\nBereich:= [l..r];\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "\nm:= trunc(mt):\nantwort:= ja;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "if antwort = ja then r:= m\nelse l:= m fi: \ntrunc(mt): Bereich:= [l..r];\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "\nm:= trunc(mt):\nantwort:= nein;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "if antwort = ja then r:= m\nelse l:= m fi :\ntrunc(mt): Bereich:= [l..r];\n" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 23 "2. Konvergenzkriterium:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 22 "restart;\nwith(plots):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Allgemeine L\366sung der Rekursions-Beziehung:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rsolve( x(n) = 1/2*(x(n-1)+x(n-2)), x(n));\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "L\366sung durch Angabe der Werte:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "rsolve(\{x(n) = 1/2*(x(n-1)+ x(n-2)),x(0)=0,x(1)=1\}, x(n));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "func:= rsolve(\{x(n) = 1/2*(x(n-1)+x(n-2)),x(0)=0,x(1 )=1\}, x(n),makeproc);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "plot(func);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "func(n);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Stephan Simon, 15.10.1997" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "2 1 0 2" 44 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }