\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\froman\fprq2 Times New Roman;}{\f4\fswiss\fprq2 Arial;}{\f5\fmodern\fprq1 Courier New;}{\f6\froman\fprq2\fcharset2 Symbol;}{\f7\froman Times New Roman;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue255;\red0\green128\blue0;\red0\green255\blue0;\red0\green128\blue128;} \deflang1031\pard\ri4\plain\f4\fs40\cf0 Folgen, Mengen, Listen und ihre Graphen \par \plain\f4\fs24\cf0 Prof. Dr. D\'f6rte Haftendorn: Mathematik mit MuPAD 3.1.1, \plain\f7\fs22\cf0 3.4.99, Jan 03\plain\f4\fs24\cf0 Update Sept.05 \par \plain\f4\fs22\cf3\b Web: www.uni-lueneburg.de/mathe-lehramt www.uni-lueneburg.de/ing-math\plain\f3\fs22\cf3\b \par \plain\f5\fs28\cf5\b Achtung: Menu ->Notebook->Evaluiere->Alle Eingaben\plain\f5\fs24\cf0 \par \plain\f4\fs28\cf0 1. Erzeugen und Zeichnen von Folgen ##### \par 2. Folgen, Listen, Mengen, Matrizen...,Verbinden##### \par 3. Erzeugen und Zeichnen von (Daten-)Punkten ##### \par 4. Datenpunkte aus Folgen und Funktionen ##### \par 5. Anf\'fcgen und Herausgreifen ##### \par 6. Rechnen mit Folgen #####\plain\f5\fs24\cf0 \par \plain\f4\fs28\cf0 ########## 1. 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01000004000000F00101001C000000FB021000070000000000BC02000000000102022253797374 656D0000F2140A3C34E71200B8A4F177C1A4F1772030F377D514666C040000002D010100040000 002701FFFF04000000F001020004000000F0010300040000002701FFFF030000000000 }\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\ri4\plain\f4\fs28\cf0 Listen haben Eckige Kammern [...] um Folgen herum.\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}[nummern] \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw3189\pich827\picwgoal1807\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\ri4\plain\f4\fs28\cf0 Mengen haben geschweifte Klammern\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}menge:=\{1,3,2,3,3,1\} \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw1919\pich827\picwgoal1087\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\ri4\plain\f4\fs24\cf0 Doppelte Elemente kann es in Mengen nicht geben, daher werden weniger Elemente \par angegeben. Die Reihenfolge ist nicht relevant. \par \plain\f4\fs28\cf0 Dagegen\plain\f4\fs24\cf0 bleibt bei Listen alles erhalten\plain\f4\fs28\cf0 .\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}myliste:=[1,3,2,3,3,1] \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw3189\pich827\picwgoal1807\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}ma:=matrix(myliste) \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw1517\pich3025\picwgoal860\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\ri4\plain\f5\fs28\cf2 {\pict\wmetafile8\picw1500\pich2992\picscalex98\picscaley98\picwgoal859\pichgoal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}\plain\f5\fs28\cf2 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}folge1:= 1,3,4,3,7; \par \pard\li600\ri1\fi-300\plain\f5\fs28\cf1\b folge2:= 2,2,6,8,5; \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw2427\pich827\picwgoal1375\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw2427\pich827\picwgoal1375\pichgoal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logisch!\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}liste1,liste2; \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw5348\pich827\picwgoal3031\pichgoal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Erzeugen und Zeichnen von (Daten-)Punkten ################### \par \plain\f4\fs24\cf0 Fasst man die erste Liste als x-Werte, die zweite als y-Werte auf, so kann man die Punkte \par so bekommen:\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}datenPunkte:=stats::unzipCol([liste1,liste2]); \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw6237\pich827\picwgoal3535\pichgoal468 010009000003B304000008001C0000000000050000000B0200000000050000000C023B035D1803 0000001E00030000001E00050000000C02D501D00D050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C0000001B120A6234E71200B8A4F177C1A4F1772030F3775F1766D7040000002D01 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\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab} \par \pard\ri4\plain\f4\fs28\cf0 5. Anf\'fcgen und Herausgreifen ###########################\plain\f5\fs24\cf0 \par \plain\f4\fs24\cf0 Durch eckige Klammern und Nummern greift man auf Elemente zu. \par Daber ver\'e4ndert man die Folge nicht. \par Genauso geht es f\'fcr Listen.\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}folge1; \par \pard\li600\ri1\fi-300\plain\f5\fs28\cf1\b liste1; \par folge1[3]; \par liste1[3]; \par folge1[2..4]; \par folge1; \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw2427\pich827\picwgoal1375\pichgoal468 0100090000034F01000005001C0000000000050000000B0200000000050000000C023B037B0903 0000001E00030000001E00050000000C02D5016005050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 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0000BC02000000000102022253797374656D0000F2140A4E34E71200B8A4F177C1A4F1772030F3 77A915667B040000002D010100040000002701FFFF04000000F001020004000000F00103000400 00002701FFFF030000000000 }\plain\f5\fs28\cf2\protect \par {\pict\wmetafile8\picw1496\pich827\picwgoal848\pichgoal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}\plain\f5\fs28\cf2\protect \par {\pict\wmetafile8\picw2427\pich827\picwgoal1375\pichgoal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}\plain\f5\fs28\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab} \par \pard\ri4\plain\f4\fs24\cf0 Will man aus eine Liste wieder eine Folge machen, so eignet sich\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}op(liste1) \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw2427\pich827\picwgoal1375\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\ri4\plain\f4\fs24\cf0 op ist eine wichtige sehr allgemeine Funktion, \par mit der man an die Operanden eines Ausdrucks herankommt.\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}op(a+b,0) \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw1274\pich827\picwgoal722\pichgoal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}\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect \par \pard\ri4\plain\f4\fs28\cf0 Anzahl der Elemente eine Folge oder Liste\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab}nops(folge1); \par \pard\li600\ri1\fi-300\plain\f5\fs28\cf1\b nops(liste1) \par \pard\li50\ri6\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal468 0100090000031701000005001C0000000000050000000B0200000000050000000C023B03340203 0000001E00030000001E00050000000C02D5014001050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C0000001B120A7634E71200B8A4F177C1A4F1772030F377D5146694040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E00B8A4F177C1A4F1772030F377D5146694040000002D0103000B0000 0026060F000C004D6174685479706500007B000500000009020000FF0007000000210501003500 3B01640008000000FA0200000000000000000000040000002D01040004000000F0010000070000 00FC020000FFFFFF000000040000002D01000004000000F00101001C000000FB02100007000000 0000BC02000000000102022253797374656D0000F2140A5334E71200B8A4F177C1A4F1772030F3 77D5146694040000002D010100040000002701FFFF04000000F001020004000000F00103000400 00002701FFFF030000000000 }\plain\f5\fs28\cf2\protect \par \pard\li50\ri2\plain\f5\fs28\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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}\plain\f5\fs28\cf2\protect \par \par \pard\ri4\plain\f4\fs24\cf0 Alles \'fcber Listen erf\'e4hrt man in der "Hilfe" mit dem \plain\f4\fs24\cf0\b Fernglas-Button. \par \plain\f4\fs24\cf0 Tragen Lesten bei "Suchen", nicht bei "Komandos" ein\plain\f5\fs24\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f5\fs28\cf1\b {\pntext\f1\'b7\tab} \par {\pntext\f1\'b7\tab} \par {\pntext\f1\'b7\tab} \par {\pntext\f1\'b7\tab} \par }