{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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Outpu t" -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 "Fixed Width" 0 17 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 17 0 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Au thor" -1 19 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 8 8 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 256 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 2 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 19 "Einf\374hrung in MAPLE" } }{PARA 19 "" 0 "" {TEXT -1 35 "\334bung, 8.9.2002, Martin Gr\374ttm \374ller" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 0 "" }{TEXT -1 21 "Inhalt der Vorlesung:" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 " Wissenswertes \374ber MAPLE" }}{PARA 0 "" 0 "" {TEXT -1 60 "Entwickelt an der Universit\344t Waterloo in Kanada (seit 1980) " }}{PARA 0 "" 0 "" {TEXT -1 73 "Zusammen mit Mathematica eines der le istungsst\344rksten Mathematikprogramme" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 " Was kann MAPLE ?" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 169 "Symbolisches Rechnen (wie mit \"Papier und Bleistift\") f\374r exakte L\366sungen, z.B. Differential- und Integralrechnung, Differentialgle ichungen, L\366sen von Gleichungssystemen" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Numerisches Rechnen (Gleit punktzahlen) mit gro\337er Genauigkeit" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Vielzahl graphischer Routinen zur Visualisierung" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Sehr gro\337e Bibliothek an Routinen aus allen \+ Bereichen der Mathematik und verwandter Gebiete" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Programmiersprach e zur Erstellung neuer Routinen " }}{PARA 0 "" 0 "" {TEXT -1 66 "mit E xportm\366glichkeiten in andere Programmiersprachen (C, FORTRAN)" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "A usgabem\366glichkeiten im HTML- oder LaTeX-Format" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Einsatz in der Vo rlesung zur Veranschaulichung mathematischer Konzepte" }}{PARA 0 "" 0 "" {TEXT -1 40 "L\366sen oder \334berpr\374fen der \334bungsaufgaben" }}{PARA 0 "" 0 "" {TEXT -1 76 "n\374tzlich f\374r Pr\374fungsvorbereit ung, aber keine Relevanz in der Pr\374fung selber" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 " Hilfefunktion " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "ausf\374hrliche Online-Hilfe: " }}{PARA 0 "" 0 "" {TEXT -1 17 "- New User\264s Tour" }}{PARA 0 "" 0 "" {TEXT -1 44 "- Suche nach einem Sachgebiet (Topic Search)" }}{PARA 0 "" 0 "" {TEXT -1 47 "- Suche nach einem Stichwort (Full Text Search) " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "- Erl\344uterungen zur Syntax eines Kommandos" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?Matrix;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Strg-F1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(x^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 " MAPLE als Taschenrechner " }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 14 "Arbeitsbl\344tter" }}{PARA 0 "" 0 "" {TEXT -1 32 "dienen der Interaktion mit MAPLE" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "Excecution Group zur E ingabe berechenbarer Ausdr\374cke" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Terme abschlie\337en mit Semikolon oder Doppelpunkt" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "76785238726326 * 8378483874 \+ - 61235513514;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "3 * 33:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "% + 1;" }{TEXT -1 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "Ergebniss e einer Variablen zuordnen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:= 100!;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:= a/45474; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "b mod 53;" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "Zusammenfassen von Excecution Groups unter Edit - Split or Join" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:= 100!;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b := a/45474;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "b mod 53;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 31 " Rechn en in den Zahlenbereichen" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 16 "Rationale Zahlen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "a:=1/3 + 1/4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "b:=evalf(7/12,5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "a*12; b*12;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Reelle Zahlen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pi; sqrt(2)/4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf (Pi, 50);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "Komplexe Zahlen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "a: = 3+5*I: b:= 7+6*I:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a*b;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "a:= sqrt(2)+sqrt(3)*I: b:= s qrt(2)-sqrt(3)*I:\nc:= a/b;\nevalc(c);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "convert(2+2*I, polar);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "Boolsche Ausdr\374cke" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalb(a*12 = b*12);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 25 " Mathematis che Funktionen" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "Wurzel-, Logarithmus-, Exponentialfunktion " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(8);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "ln(200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify( ln(200) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "exp(1); exp(5);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Trigonometrische Funktionen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "a:= sin(x)^2+cos(x)^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simpl ify(a);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Zahlentheorie" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ifactor (100!);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "isprime(53);" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "Eigene F unktionen definieren:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:= x->x^3+2*x^2-3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(1); f( 3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "g:=(x,y)->x^2+y^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(2,3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 14 "Mengen, Listen" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Mengen:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "\{x,z,y\}; \{x,y,y,z\};" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "nops(\{x,y,y,z\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "op(3, \{x,y,y,z\});" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Listen:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "liste:= [x,y,y,z,x];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "sliste:= sort(liste);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "op(2, sliste); sliste[2];" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 40 " Probleme aus der Linearen Algebra l\366sen" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 35 "Problem 1: L\366s ungen einer Gleichung" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Man finde alle L\366sungen der folgenden Gleichung:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "glg:= x^2 - 2*x - q = 0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(glg); solve(glg,x); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "lsg:= [solve(glg,x)];\n x1:= lsg[1];\nx2:= lsg[2];" }}}{PARA 0 "" 0 "" {TEXT -1 90 "Probe: Ein setzen(Substituieren) von x1 in die Gleichung und \374berpr\374fen des Wahrheitswertes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "einsetze n:= subs(x=x1,glg);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalb(simpli fy(einsetzen));" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 43 "Problem 2: L\366s ungen eines Gleichungssystems" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 55 "Man finde alle L\366sungen des folgendenG leichungssystems:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "glg1:= \+ x-y+2*z+2*u=0;\nglg2:= 2*y-z+4*u=3;\nglg3:= 3*x+4*y+2*z+13*u=8;\nglg4: = 2*x+y+2*z+4*u=2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve ( \{glg1,glg2,glg3,glg4\} );" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 19 "Andere M\366glichkeit:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 62 "M1:= Matrix(4,4,[[1,-1,2,2],[0,2,-1,4],[3,4,2, 13],[2,1,2,4]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "glg_en: = [glg1,glg2,glg3,glg4];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "(M1,b) := GenerateMatrix( glg_en, [x,y,z,u]);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "Determinant(M1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "M3:= MatrixInverse(M1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "b:= Vector(<0,3,8,2>);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "x_lin:= M3.b;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 29 "Falls keine Inverse existiert" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "M2:=Matrix(4,5,[<1,0,3,2>,<-1,2,4,1 >,<2,-1,2,2>,<2,4,13,4>,<2,-1,3,1>]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "x_lin:= LinearSolve(M2,b);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 32 " Probleme aus der Analysis l\366sen" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 " Differentialrech nung" }}{PARA 0 "" 0 "" {TEXT -1 17 "Man bestimme von " }{XPPEDIT 18 0 "x^2*sin(x);" "6#*&%\"xG\"\"#-%$sinG6#F$\"\"\"" }{TEXT -1 31 " die e rste und zweite Ableitung" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fkt_1:= x^2 * sin(x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(fkt_ 1, x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff(fkt_1, x,x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fkt_2:= x^(tan(x^2-v^2));" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(fkt_2, x);" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 16 "Integralrechnung" }}{PARA 0 "" 0 "" {TEXT -1 43 "Man bestimme das unbestimmte Integral von " }{XPPEDIT 18 0 "x^2*sin(x); " "6#*&%\"xG\"\"#-%$sinG6#F$\"\"\"" }{TEXT -1 30 " und das bestimmte \+ Integral " }{XPPEDIT 18 0 "int(x^2*sin(x),x = 0 .. Pi);" "6#-%$intG6$ *&%\"xG\"\"#-%$sinG6#F'\"\"\"/F';\"\"!%#PiG" }{TEXT -1 2 " " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fkt_1:= x^2 * sin(x);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fkt_3:= int(fkt_1, x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(fkt_1, x=0..Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eval(fkt_3, x=Pi) - eval(fkt_3, x=0 );" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 11 " Grenzwerte" }}{PARA 0 "" 0 "" {TEXT -1 32 "Man bestimme den Grenzwert von " }{XPPEDIT 18 0 "sin(x)/ x;" "6#*&-%$sinG6#%\"xG\"\"\"F'!\"\"" }{TEXT -1 38 " an der Stelle x= 0 und im Unendlichen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fkt_ 4:= sin(x)/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "limit(fkt_ 4, x=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(fkt_4, x= infinity);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 " Visualisieren" }} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 "2D-Graphiken" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "Zweidimensionale Graphike n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(\{sin(x), sin(5*x) \}, x=-Pi..Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot([t/ 5*cos(t),t/5*sin(t), t=0..10*Pi]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "with(plots):\nimplicitplot(x^2 + y^2 = 1,x=-1..1,y=-1 ..1, scaling= constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "with(student):\nshowtangent(x^2+5, x = 2);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Kontextmen\374" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "fkt_1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"#\"\"\"-%$sinG6#F%F'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 "3D-Graphiken" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "Dreidimensionale Gra phiken" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "fkt_5:= x^2-y^2;\n with(plots):\nplot3d( fkt_5, x=-3..3, y=-3..3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 " Packages" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "Hier sind die in Maple 6 verf\374gbaren Bibliotheken aufgelistet " }}{PARA 0 " " 0 "" {TEXT -1 42 "Aufrufe erfolgen mit with(package_name);" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 17 "" 0 "" {HYPERLNK 17 "algcurves" 2 "algcurves" "" }{TEXT -1 62 " \+ Algebraic Curves \n" } {HYPERLNK 17 "codegen" 2 "codegen" "" }{TEXT -1 64 " Code Gener ation \n" }{HYPERLNK 17 "combin at" 2 "combinat" "" }{TEXT -1 63 " combinatorial functions \+ \n" }{HYPERLNK 17 "combstruct" 2 "combstruct " "" }{TEXT -1 61 " combinatorial structures \+ \n" }{HYPERLNK 17 "context" 2 "context" "" }{TEXT -1 64 " \+ context sensitive menus \n" } {HYPERLNK 17 "DEtools" 2 "DEtools" "" }{TEXT -1 64 " differenti al equations tools \n" }{HYPERLNK 17 "diffal g" 2 "diffalg" "" }{TEXT -1 64 " differential algebra \+ \n" }{HYPERLNK 17 "diffalg" 2 "diffalg[differ ential_ideals]" "" }{TEXT -1 64 " differential algebra - differ ential ideals \n" }{HYPERLNK 17 "diffalg" 2 "diffalg[diffe rential_polynomial_rings]" "" }{TEXT -1 64 " differential algeb ra - differential polynomial rings \n" }{HYPERLNK 17 "difforms" 2 "d ifforms" "" }{TEXT -1 63 " differential forms \+ \n" }{HYPERLNK 17 "Domains" 2 "Domains" "" }{TEXT -1 64 " create domains of computation \+ \n" }{HYPERLNK 17 "finance" 2 "finance" "" }{TEXT -1 64 " finan cial mathematics \n" }{HYPERLNK 17 "G aussInt" 2 "GaussInt" "" }{TEXT -1 63 " Gaussian Integers \+ \n" }{HYPERLNK 17 "genfunc" 2 "genfunc " "" }{TEXT -1 64 " rational generating functions \+ \n" }{HYPERLNK 17 "geom3d" 2 "geom3d" "" }{TEXT -1 65 " \+ Euclidean three-dimensional geometry \n" } {HYPERLNK 17 "geometry" 2 "geometry" "" }{TEXT -1 63 " Euclidean geometry \n" }{HYPERLNK 17 "GF" 2 "GF" "" }{TEXT -1 69 " Galois Fields \+ \n" }{HYPERLNK 17 "Groebner" 2 "Groebner" "" } {TEXT -1 63 " Groebner basis calculations in skew algebras \+ \n" }{HYPERLNK 17 "group" 2 "group" "" }{TEXT -1 66 " pe rmutation and finitely-presented groups \n" }{HYPERLNK 17 "inttrans" 2 "inttrans" "" }{TEXT -1 63 " integral transforms \n" }{HYPERLNK 17 "liesymm" 2 "lie symm" "" }{TEXT -1 64 " Lie symmetries \+ \n" }{HYPERLNK 17 "linalg" 2 "linalg" "" }{TEXT -1 65 " linear algebra package based on array data structures \n" } {HYPERLNK 17 "LinearAlgebra" 2 "LinearAlgebra" "" }{TEXT -1 58 " line ar algebra package based on rtable data structures \n" }{HYPERLNK 17 " LREtools" 2 "LREtools" "" }{TEXT -1 63 " manipulate linear recur rence relations \n" }{HYPERLNK 17 "Matlab" 2 "Matlab" "" }{TEXT -1 65 " Matlab Link \+ \n" }{HYPERLNK 17 "networks" 2 "networks" "" }{TEXT -1 63 " graph networks \n" } {HYPERLNK 17 "numapprox" 2 "numapprox" "" }{TEXT -1 62 " numerica l approximation \n" }{HYPERLNK 17 "numt heory" 2 "numtheory" "" }{TEXT -1 62 " number theory \+ \n" }{HYPERLNK 17 "Ore_algebra" 2 "Ore_al gebra" "" }{TEXT -1 60 " basic calculations in algebras of linear o perators \n" }{HYPERLNK 17 "orthopoly" 2 "orthopoly" "" }{TEXT -1 62 " orthogonal polynomials \n" } {HYPERLNK 17 "padic" 2 "padic" "" }{TEXT -1 66 " p-adic numbe rs \n" }{HYPERLNK 17 "PDEtools " 2 "PDEtools" "" }{TEXT -1 63 " tools for solving partial diffe rential equations \n" }{HYPERLNK 17 "plots" 2 "plots" "" }{TEXT -1 66 " graphics package \+ \n" }{HYPERLNK 17 "plottools" 2 "plottools" "" }{TEXT -1 62 " b asic graphical objects \n" }{HYPERLNK 17 "polytools" 2 "polytools" "" }{TEXT -1 62 " Polynomial tools \+ \n" }{HYPERLNK 17 "powseries" 2 " powseries" "" }{TEXT -1 62 " formal power series \+ \n" }{HYPERLNK 17 "process" 2 "process" "" }{TEXT -1 64 " (Unix)-multi-processing \+ \n" }{HYPERLNK 17 "simplex" 2 "simplex" "" }{TEXT -1 64 " linea r optimization \n" }{HYPERLNK 17 "S pread" 2 "Spread" "" }{TEXT -1 65 " Spreadsheets \+ \n" }{HYPERLNK 17 "stats" 2 "stats" "" } {TEXT -1 66 " statistics \+ \n" }{HYPERLNK 17 "student" 2 "student" "" }{TEXT -1 64 " \+ student calculus \n" } {HYPERLNK 17 "sumtools" 2 "sumtools" "" }{TEXT -1 63 " indefinit e and definite sums \n" }{HYPERLNK 17 "tenso r" 2 "tensor" "" }{TEXT -1 65 " tensor computations and Genera l Relativity " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }