{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 " " 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 13 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 13 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 259 "" 1 13 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 13 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 12 0 0 0 0 1 0 0 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 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT 261 6 "Quelle" }}{PARA 0 "" 0 " " {TEXT -1 408 "Dateiname: funkbest.mws\nDateigr\366\337e: 12 KB\nName : Andreas Pf\344ffle\nSchule: Isolde-Kurz-Gymnasium\nKlasse: 11 d\nDat um: 04.05.97\nFach: Mathematik\nThema: Funktionsbesimmung \nStichw\366 rter: Funktionsbestimmung, n-ter Grad, n+1 Angaben\nKurzbeschreibung: \+ Zuerst wird das Problem an einem Bsp erkl\344rt, dann mit Maple durchg erechnet. Danach wird es verallgemeinert. Am Schlu\337 wird das Ganze \+ mit Zufallsgenerator gespielt.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Andreas Pf\344ffle Gomaringen, 21.04.97" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 256 19 "Funktionsbestimmung" }}{PARA 0 "" 0 "" {TEXT 257 8 "B ekannt:" }{TEXT -1 16 " geg: n+1 Punkte" }}{PARA 0 "" 0 "" {TEXT -1 42 " ges: Polynom n-ten Grades" }}{PARA 0 "" 0 "" {TEXT 258 4 "Neu:" }{TEXT -1 48 " geg: Anzahl von Punkten und Steigung in Punkten" }}{PARA 0 "" 0 "" {TEXT -1 35 " ges: Polynom n-t en Grades" }}{PARA 0 "" 0 "" {TEXT 259 5 "oder:" }{TEXT -1 52 " geg: F unktionswert, 1. Ableitung, 2. Ableitung, ..." }}{PARA 0 "" 0 "" {TEXT -1 36 " ges: Polynom n-ten Grades" }}{PARA 0 "" 0 "" {TEXT 260 9 "Beispiel:" }{TEXT -1 2 " " }{XPPEDIT 18 0 " f(x)=a[3]*x^ 3+a[2]*x^2+a[1]*x+a[0] " "/-%\"fG6#%\"xG,**&&%\"aG6#\"\"$\"\"\"*$F&\" \"$F-F-*&&F*6#\"\"#F-*$F&\"\"#F-F-*&&F*6#\"\"\"F-F&F-F-&F*6#\"\"!F-" } {TEXT -1 21 " \n " }{XPPEDIT 18 0 " fs(x)=3*a[3]*x^2 +2*a[2]*x+a[1] " "/-%#fsG6#%\"xG,(*(\"\"$\"\"\"&%\"aG6#\"\"$F*F&\"\"# F**(\"\"#F*&F,6#\"\"#F*F&F*F*&F,6#\"\"\"F*" }{TEXT -1 21 " \n \+ " }{XPPEDIT 18 0 " fss(x)=6*a[3]*x+2*a[2] " "/-%$fssG6#%\"xG ,&*(\"\"'\"\"\"&%\"aG6#\"\"$F*F&F*F**&\"\"#F*&F,6#\"\"#F*F*" }{TEXT -1 115 " \n1. Punkt [1,2] --> f(1)=2\n2. Punkt [2,3] --> f(2)=3\n3. Pu nkt [-1,-1] --> fs(-1)=-1\n4. Punkt [-2,1] --> fss(-2)=1\n" }{XPPEDIT 18 0 " a[3]+a[2]+a[1]+a[0]=2 " "/,*&%\"aG6#\"\"$\"\"\"&F%6#\"\"#F(&F%6 #\"\"\"F(&F%6#\"\"!F(\"\"#" }{TEXT -1 1 "\n" }{XPPEDIT 18 0 " 8*a[3]+4 *a[2]+2*a[1]+a[0]=3 " "/,**&\"\")\"\"\"&%\"aG6#\"\"$F&F&*&\"\"%F&&F(6# \"\"#F&F&*&\"\"#F&&F(6#\"\"\"F&F&&F(6#\"\"!F&\"\"$" }{TEXT -1 1 "\n" } {XPPEDIT 18 0 " 3*a[3]-2*a[2]+a[1]=-1 " "/,(*&\"\"$\"\"\"&%\"aG6#\"\"$ F&F&*&\"\"#F&&F(6#\"\"#F&!\"\"&F(6#\"\"\"F&,$\"\"\"F0" }{TEXT -1 1 "\n " }{XPPEDIT 18 0 " -12*a[3]+2*a[2]=1 " "/,&*&\"#7\"\"\"&%\"aG6#\"\"$F& !\"\"*&\"\"#F&&F(6#\"\"#F&F&\"\"\"" }{TEXT -1 18 "\nGleichungen nach \+ " }{XPPEDIT 18 0 " a[i] " "&%\"aG6#%\"iG" }{TEXT -1 10 " aufl\366sen. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 37 "Funktionsbestimmumg an einem Beispiel" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "f:=x->a[3]*x^3+a[2]*x^2+a[1]*x+a[0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrowGF(,**&&%\"aG 6#\"\"$\"\"\"9$F1F2*&&F/6#\"\"#F2F3F7F2*&&F/6#F2F2F3F2F2&F/6#\"\"!F2F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "fs:=D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fsG:6#%\"xG6\"6$%)operatorG%&arrowGF(,(*&&% \"aG6#\"\"$\"\"\"9$\"\"#F1*&&F/6#F4F2F3F2F4&F/6#F2F2F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "fss:=D(fs);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$fssG:6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&&%\"aG6#\" \"$\"\"\"9$F2\"\"'&F/6#\"\"#F7F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "gl1:=f(1)=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl 1G/,*&%\"aG6#\"\"$\"\"\"&F(6#\"\"#F+&F(6#F+F+&F(6#\"\"!F+F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "gl2:=f(2)=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl2G/,*&%\"aG6#\"\"$\"\")&F(6#\"\"#\"\"%&F(6#\" \"\"F.&F(6#\"\"!F2F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gl3 :=fs(-1)=-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl3G/,(&%\"aG6#\"\" $F*&F(6#\"\"#!\"#&F(6#\"\"\"F1!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gl4:=fss(-2)=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $gl4G/,&&%\"aG6#\"\"$!#7&F(6#\"\"#F.\"\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 25 "solve(\{gl1,gl2,gl3,gl4\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/&%\"aG6#\"\"$#!\"\"\"#o/&F&6#\"\"!#\"#f\"#M/&F&6#\" \"\"#!\"*F+/&F&6#\"\"##\"\"(\"#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y=f(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,**$%\"xG\"\"$#! \"\"\"#o*$F'\"\"##\"\"(\"# " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 "Funktionsbestimmung Allgemein" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots ):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Bei Grad den gew\374nschten Grad des Polynoms eingeben!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Grad:=3: \n`Information: Es gibt `. `Grad` .` verschiedene Ablei tungen`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%PInformation:~Es~gibt~3~v erschiedene~AbleitungenG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Hier \+ nun die gew\374nschte Ableitungenanzahl eingeben!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "Ableitungenanzahl:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%2AbleitungenanzahlG\"\"#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 205 "Liste:=([seq(a[i]*x^i, i=0..Grad)]):\nTerm:=sort(c onvert(Liste,`+`),x):\nf:=unapply(Term,x):\n`f(x)`=f(x);\nfor i from 1 to Ableitungenanzahl do Ableitung[i]:=((D@@i)(f)) od;\n\n`ben\366tigt e Angaben`:=nops(Liste);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(x)G,* *&&%\"aG6#\"\"$\"\"\"%\"xGF*F+*&&F(6#\"\"#F+F,F0F+*&&F(6#F+F+F,F+F+&F( 6#\"\"!F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*AbleitungG6#\"\"\":6# %\"xG6\"6$%)operatorG%&arrowGF+,(*&&%\"aG6#\"\"$F'9$\"\"#F4*&&F26#F6F' F5F'F6&F2F&F'F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*AbleitungG6# \"\"#:6#%\"xG6\"6$%)operatorG%&arrowGF+,&*&&%\"aG6#\"\"$\"\"\"9$F5\"\" '&F2F&F'F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%2ben|aztigte~Angaben G\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 510 "Bei \"ben\366tigte Ang aben\" in der dar\374berliegenden Ausgabe sehen Sie, wieviele Angaben \+ Sie machen m\374ssen, damit man die Gleichungen l\366sen kann. Falls z uviele Angaben bereits vorhanden sind, entfernen Sie sie oder unterdr \374cken sie, indem sie ein # vor die Eingaben schreiben. Falls Sie ei nen Ableitung ben\374tzen wollen, schreiben Sie \"Ableitung\" und als \+ Index die wievielte Ableitung Sie wollen. x[i] ist die jeweilige Funkt ion ( oder Ableitung) mit dem x-Wert und y[i] mit was die Funktion gle ichgetzt werden soll." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "x [1]:=f(1):\ny[1]:=2:\nx[2]:=f(2):\ny[2]:=3:\nx[3]:=Ableitung[1](-1):\n y[3]:=-1:\nx[4]:=Ableitung[2](-2):\ny[4]:=1:\n#x[5]:=:\n#y[5]:=:\n#x[6 ]:=:\n#y[6]:=:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "for i fr om 1 to `ben\366tigte Angaben` do Gleichung[i]:=x[i]=y[i] od;\nLoesung en:=solve(\{seq(Gleichung[i],i=1..`ben\366tigte Angaben`)\});\nassign( Loesungen):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*GleichungG6#\"\"\"/ ,*&%\"aG6#\"\"$F'&F+6#\"\"#F'&F+F&F'&F+6#\"\"!F'F0" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%*GleichungG6#\"\"#/,*&%\"aG6#\"\"$\"\")&F+F&\"\"%& F+6#\"\"\"F'&F+6#\"\"!F3F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*Glei chungG6#\"\"$/,(&%\"aGF&F'&F+6#\"\"#!\"#&F+6#\"\"\"F2!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*GleichungG6#\"\"%/,&&%\"aG6#\"\"$!#7&F+6 #\"\"#F1\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*LoesungenG<&/&%\" aG6#\"\"$#!\"\"\"#o/&F(6#\"\"\"#!\"*F-/&F(6#\"\"##\"\"(\"# " 0 "" {MPLTEXT 1 0 84 "`f(x)`=f(x);\n for i from 1 to Ableitungenanzahl do `Ableitung`[i]=Ableitung[i](x) od ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(x)G,**$%\"xG\"\"$#!\"\"\"#o* $F'\"\"##\"\"(\"# " 0 "" {MPLTEXT 1 0 172 "k:=[seq(Ableitung[i](x),i=1..Ableitungenanzahl)]:\nfplot:=plot( f(x),x=-10..10,-50..50,color=magneta,thickness=2):\nablplot:=plot(k,x= -10..10,-50..50):\ndisplay(fplot,ablplot);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 42 "Funktions bestimmung durch Zufallsgenerator" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}}{EXCHG {PARA 0 "> " 0 "funk tionsbestimmung" {MPLTEXT 1 0 62 "`Gradm\366glichkeiten`:=rand(1..10): \nGrad:=`Gradm\366glichkeiten`();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%GradG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "Liste:=([s eq(a[i]*x^i, i=0..Grad)]):\nTerm:=sort(convert(Liste,`+`),x):\nf:=unap ply(Term,x):\n`f(x)`=f(x);\nfor i from 1 to Grad do Ableitung[i]:=((D@ @i)(f)) od;\n`ben\366tigte Angaben`:=nops(Liste):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(x)G,(*&&%\"aG6#\"\"#\"\"\"%\"xGF*F+*&&F(6#F+F+F,F+ F+&F(6#\"\"!F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*AbleitungG6#\"\" \":6#%\"xG6\"6$%)operatorG%&arrowGF+,&*&&%\"aG6#\"\"#F'9$F'F4&F2F&F'F+ F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*AbleitungG6#\"\"#:6#%\"xG6\" 6$%)operatorG%&arrowGF+,$&%\"aGF&F'F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 336 "k:=[seq(Ableitung[i](x),i=1..Grad),f(x)]: \nk wert:=nops(k):\nxfwert:=rand(1..kwert):\nzuwert:=rand(0..20):\nfor i f rom 1 to `ben\366tigte Angaben` do x[i]:=(subs(x=zuwert(), k[xfwert()] )) od:\nywert:=rand(0..100):\nfor i from 1 to `ben\366tigte Angaben` d o y[i]:=ywert() od:\nfor i from 1 to `ben\366tigte Angaben` do Gleichu ng[i]:=x[i]=y[i] od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*GleichungG 6#\"\"\"/!#e\"#e" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*GleichungG6#\" \"#/\"#Z\"#j" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*GleichungG6#\"\"$/ \"#@F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "Loesungen:=solve (\{seq(Gleichung[i],i=1..`ben\366tigte Angaben`)\});\nassign(Loesungen ):\n`f(x)`=f(x);\nfor i from 1 to Grad do `Ableitung`[i]=Ableitung[i]( x) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*LoesungenG<%/&%\"aG6#\"\" !\"$>'/&F(6#\"\"##\"#@F//&F(6#\"\"\"!$5$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(x)G,(*$%\"xG\"\"##\"#@F(F'!$5$\"$>'\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%*AbleitungG6#\"\"\",&%\"xG\"#@!$5$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%*AbleitungG6#\"\"#\"#@" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 36 "die Punkte einzeichnen mit xi und yi" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 210 "ks:=[seq(Ableitung[i](x),i=1..Grad )]:\nfplot:=plot(f(x),x,color=magneta,thickness=2):\nablplot:=plot(ks, x):\ndisplay(fplot,ablplot,axes=none,title=`Stammfunktion (schwarz) mi t Ableitungen`,view=[-10..10,-20..20]);" }}}{EXCHG {PARA 0 "" 0 "" {HYPERLNK 17 "Neue zuf\344llige Funktionsbestimmung" 1 "" "funktionsbe stimmung" }{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 1 "" {TEXT -1 0 "" }}}} {MARK "6" 0 }{VIEWOPTS 1 1 0 1 1 1803 }