{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 " Arial Black" 1 18 128 128 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "Helvetica" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "Helvetica" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "Helvetica" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "Helvetica" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "Helvetica" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "Helvetica" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 } {CSTYLE "" -1 277 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 255 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 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 }{PSTYLE "" 0 257 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 }{PSTYLE "" 0 258 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 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {BITMAP 33 32 32 1 "?TMgGJNjJJJB:=J>J: ::R:r:Ar:>rVAR[ilGoSJmjFK`C:;rFV`mJmH=mvF^smj yI=;bS;jST@GeSFm`K`U@yiS>ZS@:aS`nfSlFaCSX`vySL:lV:V`FMmlFmFm^sFmymFasy nfymFyISxy>Z:V`:V@nFakFW@SpSvYaK:HmSnfmV@mvFaK`ImSvymV@;bSaC:acSaKmTpS Fm`W@ShSakyUpS>ZSX`:V`SX@GU`akFasS^sSX@yY`aK:lvSZ:nf:JmZyqf:V`yqFGuyGmFyYm^syqFyyyGM:SpFwYmN:HmF=jSHmFofmFMmvFmN`ImFwymFM;bSmF:acSmNmTpFGm`GMShSmnyUpF?Z SHm:V`SHMGU`mN`asFwySHM;BmmF:aCmmNmlvFGmFIMSHmmnymvF?ZyIm:V`yIMGuymnFy yF_syIMyyymN:Z: vy:>ZyM:vy:vy:Z:vYxi:vyyyYyay=:::::::Z:>Z::mQ:>:ryvY::::oaAbxoixVYqixmAvYZ::ty=dYy=ZAB:;:hYwiy wayv[y=;:nYoa:r;dY:>Z:v:qyxqyxmAvY<:bydIwI:bxIZArxVY`Iry:qyxqqvwYxIB:NyxeydYw=ZAVyt YytYyuuxjv[y=ZsQY;jw;;B:`IZ sAZyAZsQYNYqqwaiyM:vYyA:>Z:vY;RxqaAVyuux`I>:xyy;:;ryRxoArx`IryvY::>ZsY Y>:qAjy;::>:oyx>ZAVY:yA::J:VysYyAvZuYysYysA:vY:::;jv=jviywii:FysuyvY:: :;J:>:qYxxI;jywY:::;B:>ZsYYJ:ryyA::J:xIyI:mI:ry;ryvY:::Z:FYry:::::;ryv Y::::::::3:" }}{PARA 256 "" 0 "" {TEXT 256 32 "Meine Hilfe zu Maple Re lease V.4" }}{PARA 257 "" 0 "" {TEXT 257 46 "(c) 1996-1997 by Fabian H ust; VHumorus@aol.com" }}{PARA 258 "" 0 "" {TEXT -1 22 "Last updated: \+ 26.01.97" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT 258 7 "Themen:" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Algebra" 1 "" "A lgebra" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Diagramme und Funktionen mit M aple" 1 "" "diafu" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Differentialrechnun g" 1 "" "Differentialrechnung" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Tips un d Tricks" 1 "" "tipsutricks" }{HYPERLNK 17 "" 1 "" "triogonometrie" }} {PARA 0 "" 0 "" {HYPERLNK 17 "Trigonometrie" 1 "" "triogonometrie" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "Algebra" {TEXT 259 8 "Algebra:" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Ausmultiplizieren (ex pand)" 1 "" "expand" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Dezimalstellen da rstellen (evalf)" 1 "" "Dezimal" }}{PARA 0 "" 0 "" {HYPERLNK 17 "" 1 " " "expand" }{HYPERLNK 17 "Faktorisieren (factor)" 1 "" "factor" }} {PARA 0 "" 0 "" {HYPERLNK 17 "L\366sen von Gleichungen/Gleichungssyste men (solve)" 1 "" "solve" }{HYPERLNK 17 "" 1 "" "simplify" }}{PARA 0 " " 0 "" {HYPERLNK 17 "Terme vereinfachen (simplify)" 1 "" "simplify" }} {PARA 0 "" 0 "" {HYPERLNK 17 "Wurzeln ziehen (sqrt/root)" 1 "" "wurzel " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "_____ ______________________________________________________________________ _____________________" }}{PARA 0 "" 0 "wurzel" {TEXT -1 61 "Um mit Map le mit Wurzeln zu Rechnen braucht man zwei Befehle:" }}{PARA 0 "" 0 " " {TEXT -1 35 "Die Quadratwurzel berechnet man so:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "sqrt(9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 48 "Die n-te Wurzel berechnet man m it diesem Befehl:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "root(27 ,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 170 "Das geht nach \+ folgendem Schema: root (Zahl unter der Wurzel, n-te Wurzel) __________ ______________________________________________________________________ ________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "solv e" {TEXT -1 37 "L\366sen von Gleichungen mit dem Befehl " }{TEXT 267 5 "solve" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " solve(x+7-y=3,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&!\"%\"\"\"%\"yG F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(3*y+2/x=45,y); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&!\"#\"\"\"%\"xG\"#XF'F(!\"\" #F'\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 85 "Das geht nach folgendem Prin zip: solve(Gleichung mit Variablen=Wert, aufl\366sen nach?);" }}{PARA 0 "" 0 "" {TEXT -1 40 "Und Gleichungssysteme kann man so l\366sen:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "solve(\{x+y+z=1,x-y+z=2,2*x- y-z=0\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"zG#\"\"(\"\"'/%\"xG #\"\"\"\"\"$/%\"yG#!\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________ _________________________________________________________________" }} {PARA 0 "" 0 "simplify" {TEXT -1 43 "Terme kann man vereinfachen mit d em Befehl " }{TEXT 266 8 "simplify" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "9^(1/2)+3;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,&*$\"\"*#\"\"\"\"\"#F'\"\"$F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" '" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________________________ _______________________________________" }}{PARA 0 "" 0 "factor" {TEXT -1 38 "Faktorisieren kann man mit dem Befehl " }{TEXT 263 6 "fac tor" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(a+b)^ 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&%\"aG\"\"\"%\"bGF&\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"aG\"\"#\"\"\"*&F%F'%\"bGF'F&*$F)F&F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&%\"aG\"\"\"%\"bGF&\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 96 "__________________________________________________ ______________________________________________" }}{PARA 0 "" 0 "expand " {TEXT -1 33 "Ausmultiplizieren mit dem Befehl " }{TEXT 262 6 "expand " }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(a+b)^2; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&%\"aG\"\"\"%\"bGF&\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"aG\"\"#\"\"\"*&F%F'%\"bGF'F&*$F)F&F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________________________________________ _________________________________" }}{PARA 0 "" 0 "Dezimal" {TEXT -1 104 "So stellt man Dezimalzahlen dar, die z. B. von Maple als Bruch in vereinfachter Form dargestellt wurden:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "37/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#P\"\"$" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLL7!\")" }}}{PARA 0 "" 0 "" {TEXT -1 21 "Sch neller geht es so:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf( 37/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLL7!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 59 "An wenden kann man evalf nat\374rlich auch bei Hochzahlen, etc." }}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________________________ _________________________________________________" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{SECT 0 {PARA 3 "" 0 "diafu" {TEXT 260 35 "Diagramme und Funktione n mit Maple:" }}{PARA 0 "" 0 "" {HYPERLNK 17 "" 1 "" "3dplots" }} {PARA 0 "" 0 "" {HYPERLNK 17 "3D-Plots mit Maple (plot3d)" 1 "" "3dplo ts" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Animieren von Plots mit Maple (ani mate)" 1 "" "animate" }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Bereichsangaben" 1 "" "plot3" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Besc hriften von Linien (textplot)" 1 "" "Beschriften" }{MPLTEXT 1 0 0 "" } }{PARA 0 "" 0 "" {HYPERLNK 17 "" 1 "" "plot1" }{HYPERLNK 17 "Mehrere P lots in einem Fenster darste" 1 "" "plot2" }{TEXT 269 4 "llen" }} {PARA 0 "" 0 "" {HYPERLNK 17 "Parabel" 1 "" "Parabel" }}{EXCHG }{PARA 0 "" 0 "plot2" {HYPERLNK 17 "" 1 "" "plot3" }{HYPERLNK 17 "Plotten mit Maple (plot)" 1 "" "plot1" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Steigungsd reieck zeichnen" 1 "" "Steigungsdreieck" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Steigungsformen der Gerade" 1 "" "steigungsformen" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Textplot mit variablen Werten (convert)" 1 "" "conver t" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "____________________ ______________________________________________________________________ ______" }}{PARA 0 "" 0 "" {TEXT -1 123 "Bei bestimmten Plots ist die 1 :1-Ansicht immer n\366tig. Man spart sich den Klick auf das 1:1-Symbol mit dem folgenden Syntax:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(x^2,x,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "____________________ ______________________________________________________________________ ______" }}{PARA 0 "" 0 "convert" {TEXT -1 114 "Oftmals ist es n\366tig , Werte die sich \344ndern in einen Textplot zu bringen. Dies kann man auf folgende Weise machen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " Wert:=27:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "textplot([12,1 1,convert(evalf(Wert),string,` (Text)`)]);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "__________________ ______________________________________________________________________ ________" }}{PARA 0 "" 0 "Beschriften" {TEXT -1 53 "So kann man einzel ne Linien in Plots beschriften mit " }{TEXT 274 8 "textplot" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plo ts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y1:=x->(x-3)^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G:6#%\"xG6\"6$%)operatorG%&arrowG F(*$,&9$\"\"\"!\"$F/\"\"#F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y2:=x->(x+2)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G:6#%\"x G6\"6$%)operatorG%&arrowGF(*$,&9$\"\"\"\"\"#F/F0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "y3:=x->x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y3G:6#%\"xG6\"6$%)operatorG%&arrowGF(*$9$\"\"#F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Parabeln:=plot(\{y1(x),y2(x) ,y3(x)\},x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "t1:= textpl ot([-6,27,`(x-3)^2`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "t 2:= textplot([-4,27,`x^2`]):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "t3:= textplot([-1,27,`(x+2)^2`]):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(\{Parabeln,t1,t2,t3\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "________ ______________________________________________________________________ __________________" }}{PARA 0 "" 0 "animate" {TEXT -1 37 "So animiert \+ man Plots mit dem Befehl " }{TEXT 272 7 "animate" }{TEXT -1 1 ":" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f:=x->x^2+a:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "animate(f(x),x=-2..2,a=-2..2,view=[ -4..4,-4..4]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT 273 4 "view" }{TEXT -1 30 " steht hierbei f\374r den Bereich" }}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________ ______________________________________________________________________ _" }}{PARA 0 "" 0 "steigungsformen" {TEXT -1 90 "Die Steigungsformen d er Gerade: Zweipunkteform (ZPF), Punktsteigungsform (PSF), Hauptform: " }}{PARA 0 "" 0 "" {TEXT -1 15 "Allgemein gilt:" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "delta(y)/delta(x)=y2-y1/x2-x1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%&deltaG6#%\"yG\"\"\"-F&6#%\"xG!\"\",(%#y2GF)* &%#y1GF)%#x2GF-F-%#x1GF-" }{TEXT -1 3 "= m" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "y=m*(x-x1)+y1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ %\"yG,&*&%\"mG\"\"\",&%\"xGF(%#x1G!\"\"F(F(%#y1GF(" }}}{PARA 3 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y=m*x-m*x1 +y1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,(*&%\"mG\"\"\"%\"xGF(F( *&F'F(%#x1GF(!\"\"%#y1GF(" }}}{PARA 0 "" 0 "" {TEXT -1 19 "Die Zweipun kteform:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y-y1/x-x1=y2-y1/ x2-x1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(%\"yG\"\"\"*&%#y1GF&%\"xG !\"\"F*%#x1GF*,(%#y2GF&*&F(F&%#x2GF*F*F+F*" }}}{PARA 0 "" 0 "" {TEXT -1 23 "Die Punktsteigungsform:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "y-y1/x-x1=m;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(%\"yG\"\"\"*& %#y1GF&%\"xG!\"\"F*%#x1GF*%\"mG" }}}{PARA 0 "" 0 "" {TEXT -1 14 "Die H auptform:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "y=m*x+b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&*&%\"mG\"\"\"%\"xGF(F(%\"bGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________ _______________________________________________________" }}{PARA 0 "" 0 "3dplots" {TEXT -1 32 "So macht man 3D-Plots mit Maple:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 34 "plot3d(x^2+y^3,x=-10..10,y=-3..3);" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________________________________________ _________________________________" }}{PARA 0 "" 0 "plot1" {TEXT -1 40 "So plottet man mit Maple mit dem Befehl " }{TEXT 261 4 "plot" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "plot(x,x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "plot(x^2,x);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "plot2" {TEXT -1 56 "Man kann auch m ehrere Plots in einem Fenster darstellen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(\{sin,cos\});" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "plot3" {TEXT -1 97 "Falls eine Funktion an einer Stell e \"gestaucht\" wird, kann man mit einer Bereichsangabe schaffen:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(tan,-5..5,-2..2);" }}} {PARA 0 "" 0 "" {TEXT -1 57 " x y" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________ _______________________________________________________" }}{PARA 0 "" 0 "Steigungsdreieck" {TEXT -1 48 "So kann man ein Steigungsdreieck ein fach machen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: wit h(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "x1:=2: y1:=4: \+ x2:=5: y2:=8:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "zweipunkte :=[[x1,y1],[x2,y2]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+zweipunkteG 7$7$\"\"#\"\"%7$\"\"&\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "strecke:=plot(zweipunkte,0..8,0..8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "punkte:=plot(zweipunkte,0..8,0..8,style=point,symbol= circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "dreix:=plot([[x 1,y1],[x2,y1]],color=green,thickness=3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "dreiy:=plot([[x2,y1],[x2,y2]],color=blue,thickness=3) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "display(strecke,punkte ,dreix,dreiy);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________ _______________________________________________________" }}{PARA 0 "" 0 "Parabel" {TEXT -1 30 "Funktion der Parabel: ax\262+bx+c" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y:=a*x^2+b*x+c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"yG,(*&%\"aG\"\"\"%\"xG\"\"#F(*&%\"bGF(F)F(F(%\"cGF(" }}}{PARA 0 "" 0 "" {TEXT -1 41 "Jetzt soll die Funktion geplottet werden:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "a:=1: b:=2: c:=3: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(a*x^2+b*x+c,x=-2..2);" }}} {PARA 0 "" 0 "" {TEXT -1 53 "Und schlie\337lich wird noch eine Werteta belle erstellt:" }}{EXCHG {PARA 0 "> " 0 "fordo" {MPLTEXT 1 0 34 "for \+ x from -2 to 2 by 1 do x,y od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"# \"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"\"\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$\"\"!\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\" \"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#\"#6" }}}{PARA 0 "" 0 "s ubs" {TEXT -1 29 "Auch kann amn mit dem Befehl " }{TEXT 271 4 "subs" } {TEXT -1 44 " arbeiten, wobei hier das x erhalten bleibt:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "for i from -2 to 2 by 1 do i ,subs( x=i,y) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"#\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"\"\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"! \"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"#=" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$\"\"#\"#=" }}}{PARA 0 "" 0 "funktionen" {TEXT -1 58 " Die dritte M\366glichkeit ist die Aufstellung einer Funktion:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "y:=x->a*x^2+b*x+c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG:6#%\"xG6\"6$%)operatorG%&arrowGF(,(*&%\"aG\"\"\" 9$\"\"#F/*&%\"bGF/F0F/F/%\"cGF/F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 55 "M an sagt jetzt, wie bei einer Funktion y von x -> y(x):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "y(KarlOtto);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"aG\"\"\"%)KarlOttoG\"\"#F&*&%\"bGF&F'F&F&%\"cGF& " }}}{PARA 0 "" 0 "" {TEXT -1 74 "Jetzt kann man Werte zuweisen und gl eich den neuen y-Wert ausgeben lassen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a:=1: b:=2: c:=99: y(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"xG\"\"#\"\"\"F%F&\"#**F'" }}}{PARA 0 "" 0 "" {TEXT -1 43 "Und zum Schlu\337 kann man noch alles plotten:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(y(x), x=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "__ ______________________________________________________________________ ________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "Differentialrechnung" {TEXT 275 20 "Di fferentialrechnung" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Ableiten/Differenz ieren (diff)" 1 "" "ableiten" }{HYPERLNK 17 "" 1 "" "diffschr" }} {PARA 0 "" 0 "" {HYPERLNK 17 "Graphisches Differenzieren" 1 "" "diffgr " }}{PARA 0 "" 0 "" {HYPERLNK 17 "Schreibweise der Differentialrechnun g" 1 "" "diffschr" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Trigonometrische Fu nktionen ableiten" 1 "" "difftrigo" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "_________ ______________________________________________________________________ _________________" }}{PARA 0 "" 0 "difftrigo" {TEXT -1 121 "Vorsicht i st bei der Ableitung von trigonometrischen Funktionen geboten. Folgend e Schreibweise ist dabei verbindlich (x):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(sin(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-% $cosG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________________________ _________________________________________________" }}{PARA 0 "" 0 "dif fschr" {TEXT -1 26 "Geg.: f(x) Differ" }{TEXT 279 6 "ential" }{TEXT -1 20 "qu. Differ" }{TEXT 278 3 "enz" }{TEXT -1 8 "qu otient" }}{PARA 0 "" 0 "" {TEXT -1 22 "1. Ableitung: f'(x) = " } {XPPEDIT 18 0 "diff(f(x),x)" "-%%diffG6$-%\"fG6#%\"xGF(" }{TEXT -1 11 " kommt von " }{XPPEDIT 18 0 "Delta f/Delta x" "**%&DeltaG\"\"\"%\"fGF $F#!\"\"%\"xGF$" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "d/dx" "*&%\"dG\"\" \"%#dxG!\"\"" }{TEXT -1 12 " sprich: \"d " }{TEXT 276 4 "nach" }{TEXT -1 26 " dx\" -> Integration nach x" }}{PARA 0 "" 0 "" {TEXT -1 23 "2. \+ Ableitung: f''(x) = " }{XPPEDIT 18 0 "diff(diff(f(x),x),x)" "-%%diffG6 $-F#6$-%\"fG6#%\"xGF*F*" }{TEXT -1 33 " sprich: \"d zwei nach dx Quadr at\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 23 " Integral/Stammfunktion:" }}{PARA 0 "" 0 "" {TEXT -1 8 " F(x) = " } {XPPEDIT 18 0 "int(f(x),x)" "-%$intG6$-%\"fG6#%\"xGF(" }{TEXT -1 49 " \+ sprich: \"Integral f(x) dx\" -> Integration \374ber x" }}{PARA 0 "" 0 "" {TEXT -1 11 "kommt von: " }{XPPEDIT 18 0 "Sum(f(x)*Delta x)" "-%$Su mG6#*(-%\"fG6#%\"xG\"\"\"%&DeltaGF*F)F*" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "____________________________________ ____________________________________________________________" }}{PARA 259 "" 0 "diffgr" {TEXT 280 3 "Rot" }{TEXT -1 20 " = Ausgangspolynom; \+ " }{TEXT 281 4 "Blau" }{TEXT -1 20 " = erste Ableitung; " }{TEXT 282 4 "Gr\374n" }{TEXT -1 19 " = zweite Ableitung" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{PARA 0 "" 0 "" {TEXT -1 15 "Erstes Polynom:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Po l1:=(x^3-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Pol1G,&*$%\"xG\"\"$ \"\"\"F'!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 49 "Ableitung 1 mittels des Befehls diff() durf\374hren:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a1:=diff(Pol1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a1G,&*$% \"xG\"\"#\"\"$!\"\"\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 12 "Ableitung 2 :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a2:=diff(a1,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a2G,$%\"xG\"\"'" }}}{PARA 0 "" 0 " " {TEXT -1 16 "Plots erstellen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Pl1a:=plot(Pol1,x=-1.1..1.1):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Pl2a:=plot(a1,x=-1.1..1.1,color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "Pl3a:=plot(a2,x=-0.4..0.4,color=green):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "display(Pl1a,Pl2a,Pl3a,scaling=constrained); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________________________ _______________________________________" }}{PARA 0 "" 0 "ableiten" {TEXT -1 50 "Differenzieren (Ableiten) kann man mit dem Befehl " } {TEXT 283 4 "diff" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pol1:=a*x^3+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% Pol1G,&*&%\"aG\"\"\"%\"xG\"\"$F(\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(Pol1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*& %\"aG\"\"\"%\"xG\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________________ _______________________________________________________________" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "triogonometr ie" {TEXT 264 14 "Trigonometrie:" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Trig onometrische Umformungen (combine)" 1 "" "combine" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Darstellen griechischer Buchstaben:" 1 "" "griech" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "____________________ ______________________________________________________________________ ______" }}{PARA 0 "" 0 "combine" {TEXT -1 44 "Trigonometrische Umformu ngen mit dem Befehl " }{TEXT 265 7 "combine" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "expand(sin(alpha+beta));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$sinG6#%&alphaG\"\"\"-%$cosG6#%%betaGF )F)*&-F+F'F)-F&F,F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "co mbine(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#,&%&alphaG\"\" \"%%betaGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________________ _______________________________________________" }}{PARA 0 "" 0 "griec h" {TEXT -1 35 "Darstellen griechischer Buchstaben:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sin(alpha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%&alphaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " cos(beta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%%betaG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sin(gamma);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%&gammaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sin(delta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sin G6#%&deltaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________________ _______________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 " tipsutricks" {TEXT 268 16 "Tips und Tricks:" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Arbeiten mit dem Speicher von Maple" 1 "" "speicher" }} {PARA 0 "" 0 "" {HYPERLNK 17 "Aufstellen von Funktionen (->)" 1 "" "fu nktionen" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Beweisen, da\337 zwei Gleich ungen gleich sind" 1 "" "" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Definieren \+ von Variablen ohne Ver\344nderung der Variable (subs)" 1 "" "subs" }} {PARA 0 "" 0 "" {HYPERLNK 17 "Dreick: Drei Punkte gegeben, zeichnen" 1 "" "Dreieck" }}{PARA 0 "" 0 "" {HYPERLNK 17 "For...do...by...od - Sc hleifen mit Maple" 1 "" "fordo" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Funkti onen oder Werte mit Namen benennen" 1 "" "namen" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Gerade: Zwei Punkte gegeben, zeichnen" 1 "" "zweip" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "_________ ______________________________________________________________________ _________________" }}{PARA 0 "" 0 "Dreieck" {TEXT -1 125 "Drei Punkte \+ sind gegeben und es soll ein Dreieck gezeichnet werden. Man mu\337 bea chten, da\337 Maple einen vierten Punkt ben\366tigt!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart: with (plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A:=[5,1]: B:=[2,6]: C:=[-3,-2]: A1:=[5,1] :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dreieck:=[A,B,C,A1]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Punkte:=plot(dreieck,style=point, color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Strecken:=p lot(dreieck):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "display(Pu nkte,Strecken);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________ _______________________________________________________" }}{PARA 0 "" 0 "beweis" {TEXT -1 62 "So beweist man ganz einfach, da\337 zwei Gleic hungen gleich sind:" }}{PARA 0 "" 0 "" {TEXT -1 20 "1. Gleichung: (a+b )\262" }}{PARA 0 "" 0 "" {TEXT -1 27 "2. Gleichung: (a\262+2*a*b+b\262 )" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "(a+b)^2-(a^2+2*a*b+b^2) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$,&%\"aG\"\"\"%\"bGF'\"\"#F'*$ F&F)!\"\"*&F&F'F(F'!\"#*$F(F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }}{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 17 "Oder ganz a nders:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalb(expand((a+b) ^2)=a^2+2*a*b+b^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________________________________________ _________________________________" }}{PARA 0 "" 0 "namen" {TEXT -1 41 "Funktionen oder Werte mit Namen benennen:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "a:=30: b:=60:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "MeineRechnung:=a-b:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "MeineRechnung;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#I " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_________________________________________________________ _______________________________________" }}{PARA 0 "" 0 "speicher" {TEXT -1 22 "So kann man speichern:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=12; b:=13; c:=14;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"#9" }}}{PARA 0 "" 0 "" {TEXT -1 39 " L\366schen einer bestimmten Zahl/Variable:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 7 "a:='a':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a;b;c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#9" }}}{PARA 0 "" 0 "" {TEXT -1 33 "L\366schen des kompletten Speichers:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 6 "a;b;c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"cG" }}}{PARA 0 "" 0 "" {TEXT -1 88 "Wenn man wissen will, welche Variablen man schon vergeben hat, braucht man dern Befehl " }{TEXT 270 6 "anames" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=12; b:=13; c:=14;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "anames();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%\"aG%\"bG%\"cG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "_______________________________________________________________ _________________________________" }}{PARA 0 "" 0 "zweip" {TEXT -1 74 "Zwei Punkte einer Gerade sind gegeben, die Gerade soll gezeichnet we rden:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x1:=1: y1:=2: x2:=4: \+ y2:=5: " }}}{PARA 0 "" 0 "" {TEXT -1 34 "So kann man die Punkte darste llen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "P1:=[x1,y1]:P2:=[x2 ,y2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "Punkte:=plot([P1,P 2],style=point, symbol=circle, color=green):" }}}{PARA 0 "" 0 "" {TEXT -1 45 "Und schlie\337lich auch die Gerade dazuzeichnen:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Linie:=plot([P1,P2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "with(plots):display(\{Linie, Punkte\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 " " 0 "" {TEXT -1 96 "__________________________________________________ ______________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "5 0 0" 5 }{VIEWOPTS 1 1 0 1 1 1803 }