(*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 0, 0] NotebookDataLength[ 319571, 8332] NotebookOptionsPosition[ 266852, 7635] NotebookOutlinePosition[ 267488, 7658] CellTagsIndexPosition[ 267445, 7655] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Einf\[UDoubleDot]hrung in Mathematica", "Title", CellChangeTimes->{{3.529736694722261*^9, 3.5297367195705547`*^9}, 3.529773051349444*^9},ExpressionUUID->"26c95577-b717-4594-871c-\ fded58151949"], Cell[TextData[{ "Dieses ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebook ist dazu gedacht, Sie mit der Arbeitsweise dieses \"Systems\" an \ sich und den grundlegendsten Funktionen vertraut zu machen. 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komplexe Zahlen definierbar sind (", StyleBox["Sqrt", "Input"], ", ", StyleBox["Exp", "Input"], ", ", StyleBox["Log", "Input"], ", ", StyleBox["Sin", "Input"], ", ", StyleBox["...", "Input"], "), k\[ODoubleDot]nnen wie zu erwarten ausgewertet werden, solche f\ \[UDoubleDot]r die das nicht gilt (", StyleBox["Min", "Input"], ", ", StyleBox["Max", "Input"], ", ", StyleBox["...", "Input"], ") aber nicht." }], "ItemNumbered", PageWidth->PaperWidth, CellChangeTimes->{{3.529774203854248*^9, 3.529774329588429*^9}, { 3.529774365864402*^9, 3.529774377937664*^9}, {3.780041638170609*^9, 3.780041639050167*^9}},ExpressionUUID->"f77e699d-63e4-4387-9438-\ f75941f943e6"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["1.3 Ausdr\[UDoubleDot]cke & Symbole", "Subsubtitle", PageWidth->PaperWidth, CellChangeTimes->{{3.529742826018319*^9, 3.529742836434126*^9}, { 3.5297437366473293`*^9, 3.5297437447916517`*^9}, {3.52975867492907*^9, 3.529758675758161*^9}, 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Ein Ausdruck wird durch \ einen Zeilenumbruch oder ein \[OpenCurlyDoubleQuote]", StyleBox[";", "Input"], "\[CloseCurlyDoubleQuote] (Semikolon/Strichpunkt) beendet, wobei letzteres \ die Ausgabe des Ergebnisses unterdr\[UDoubleDot]ckt. (Mehrere Befehle k\ \[ODoubleDot]nnen also in einer Zeile oder Zelle untergebracht werden.)" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.52975063640701*^9, 3.529750827187196*^9}, { 3.529750858328718*^9, 3.529750951298003*^9}, {3.529750996865749*^9, 3.529751019081653*^9}, 3.5297533287692757`*^9, {3.529753392508995*^9, 3.529753393832539*^9}, {3.529753436160894*^9, 3.5297534732114143`*^9}, 3.5297730513697577`*^9, {3.530336754125355*^9, 3.5303367733917294`*^9}, { 3.685339023667675*^9, 3.685339024419153*^9}},ExpressionUUID->"2d66ec92-6d20-4f3b-bca5-\ 98c2c261e8e7"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"E", "^", RowBox[{"(", RowBox[{"I", "*", RowBox[{"(", RowBox[{"Pi", "/", "3"}], ")"}]}], ")"}]}], "]"}]], "Input", CellChangeTimes->{{3.529751030705175*^9, 3.529751052973456*^9}, 3.529773051369937*^9},ExpressionUUID->"a456f355-b3a7-4ccd-948e-\ cf7af36aeb09"], Cell[BoxData[ RowBox[{ RowBox[{"N", "[", RowBox[{"E", "^", RowBox[{"(", RowBox[{"I", "*", RowBox[{"(", RowBox[{"Pi", "/", "3"}], ")"}]}], ")"}]}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.529751030705175*^9, 3.5297510706821203`*^9}, 3.529773051370302*^9},ExpressionUUID->"d80bbdaf-262d-451d-bdc1-\ 060b676fbb13"], Cell[TextData[{ "Nicht ausgegebene Ausdr\[UDoubleDot]cke k\[ODoubleDot]nnen beispielsweise \ durch Verwendung des \[OpenCurlyDoubleQuote]History-Operators\ \[CloseCurlyDoubleQuote] \[OpenCurlyDoubleQuote]", StyleBox["%", "Input"], "\[CloseCurlyDoubleQuote] angezeigt werden. (Nicht zu verwechseln mit ", StyleBox["Out[]", "Input"], ", bzw. ", StyleBox["%", "Input"], "!) Auch ", StyleBox["%%", "Input"], ", ", StyleBox["%%%", "Input"], ", usw. sind m\[ODoubleDot]glich aber nicht zu empfehlen!" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{ 3.5297491018836737`*^9, {3.5297515137234163`*^9, 3.529751590618545*^9}, { 3.529751656236456*^9, 3.5297516634917383`*^9}, {3.529751825729393*^9, 3.52975187396362*^9}, {3.529751922826226*^9, 3.5297519476000023`*^9}, 3.529773051370422*^9, {3.5303368215870523`*^9, 3.530336839449131*^9}, 3.530336893833918*^9},ExpressionUUID->"9a7c4b51-7366-4b8a-9125-\ 08d715e4462b"], Cell[BoxData["%"], "Input", CellChangeTimes->{3.529751666505785*^9, 3.529773051370544*^9},ExpressionUUID->"bba0c657-79c6-417c-8b8c-\ af27c2fca18c"], Cell[TextData[{ "Mit ", StyleBox["Print", "Input"], " l\[ADoubleDot]sst sich beliebig zusammengesetzter Text ausgeben. Strings m\ \[UDoubleDot]ssen in Anf\[UDoubleDot]hrungszeichen geschrieben werden." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.5297519843483047`*^9, 3.5297520428770742`*^9}, { 3.529752084176421*^9, 3.529752133242957*^9}, 3.5297730513708153`*^9, { 3.530335333432892*^9, 3.5303353346804543`*^9}, 3.780041672626192*^9},ExpressionUUID->"cf4d7698-5ec6-4de9-9128-\ 85716f37e1cb"], Cell[BoxData[ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", "%%"}], "]"}]], "Input", CellChangeTimes->{{3.529752046105338*^9, 3.529752073224515*^9}, { 3.529752137714521*^9, 3.529752153804515*^9}, 3.529773051371003*^9},ExpressionUUID->"2587beb2-c48f-46c3-b9ac-\ 2ce75695d7af"], Cell[TextData[StyleBox["Ausdr\[UDoubleDot]cke lassen sich auch in Variablen \ oder Symbolen speichern. Hierzu gibt es zwei M\[ODoubleDot]glichkeiten:", FontWeight->"Bold"]], "ItemParagraph", PageWidth->PaperWidth, CellChangeTimes->{{3.529752325101363*^9, 3.52975242958362*^9}, { 3.529752492060771*^9, 3.529752521481395*^9}, 3.529773051371277*^9, 3.685339138503825*^9},ExpressionUUID->"3962a002-37c9-4905-ba7d-\ a4580e3e44c4"], Cell[TextData[{ StyleBox["Set", "Input"], ", bzw. \[OpenCurlyDoubleQuote]", StyleBox["=", "Input"], "\[CloseCurlyDoubleQuote] (Shortcut)" }], "Item", CellChangeTimes->{{3.529752450881103*^9, 3.529752510369131*^9}, 3.5297730513714237`*^9, 3.68533913850404*^9},ExpressionUUID->"907ee581-0ade-46e7-92e3-\ f94d08d97054"], Cell[CellGroupData[{ Cell[TextData[{ "und ", StyleBox["SetDelayed", "Input"], ", bzw. \[OpenCurlyDoubleQuote]", StyleBox[":=", "Input"], "\[CloseCurlyDoubleQuote]." }], "Item", CellChangeTimes->{{3.529752525117017*^9, 3.529752565162279*^9}, 3.529773051371573*^9, 3.685339138504199*^9},ExpressionUUID->"f33e1577-77e3-4207-844a-\ da9a5da2e34e"], Cell[BoxData[ RowBox[{"a", "=", RowBox[{"N", "[", RowBox[{"Exp", "[", "44", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.5297526251059847`*^9, 3.5297526327432423`*^9}, 3.5297730513717527`*^9},ExpressionUUID->"5d9ffe72-1b8c-472d-87c8-\ 154c5a94664a"], Cell[BoxData[ RowBox[{"b", ":=", RowBox[{"N", "[", RowBox[{"Log", "[", "44", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.529752641349326*^9, 3.529752653811602*^9}, 3.52977305137212*^9},ExpressionUUID->"df9afedb-717a-4288-a18d-\ f165c17f53ea"] }, Open ]], Cell[TextData[{ "Hierbei f\[ADoubleDot]llt auf, dass f\[UDoubleDot]r \[OpenCurlyDoubleQuote]", StyleBox["b", "Input"], "\[CloseCurlyDoubleQuote] keine Ausgabe erscheint. Grund hierf\[UDoubleDot]r \ ist folgendes: Bei ", StyleBox["Set", "Input"], " wird die rechte Seite sofort ausgewertet und das Ergebnis im Symbol auf \ der linken Seite gespeichert (Wertzuweisung wie bspw. in ", StyleBox["C++)", "Input"], ". Bei ", StyleBox["SetDelayed", "Input"], " wird nicht das Ergebnis der Auswertung der rechten Seite, sondern die \ Eingabe selbst im Symbol abgelegt (Anlegen einer Definition)." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.5297529918497562`*^9, 3.529753266580289*^9}, 3.529773051372243*^9, {3.5303370973676243`*^9, 3.530337101393215*^9}, { 3.530337133679701*^9, 3.5303371362851667`*^9}},ExpressionUUID->"b5844e8b-814f-4d83-8d3e-\ 6077ba22cede"], Cell[TextData[{ "Hierzu ein kleines Beispiel (Kommentare m\[UDoubleDot]ssen in \ \[OpenCurlyDoubleQuote]", StyleBox["(*", "Input"], "\[CloseCurlyDoubleQuote] und \[OpenCurlyDoubleQuote]", StyleBox["*)", "Input"], "\[CloseCurlyDoubleQuote] eingeschlossen werden):" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529753679045218*^9, 3.529753791707284*^9}, 3.529773051372348*^9},ExpressionUUID->"24ea38c4-6662-4bff-b929-\ 587f422d3e23"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", "Wertzuweisung", " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a", "=", RowBox[{"RandomReal", "[", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"(*", " ", "Definitionszuweisung", " ", "*)"}], "\[IndentingNewLine]", RowBox[{"b", ":=", RowBox[{"RandomReal", "[", "]"}]}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"mehrfacher", " ", "Aufruf"}], " ", "*)"}], "\[IndentingNewLine]", "a", "\[IndentingNewLine]", "a", "\[IndentingNewLine]", "a", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"a", " ", "konstant"}], " ", "*)"}], "\[IndentingNewLine]", "b", "\[IndentingNewLine]", "b", "\[IndentingNewLine]", "b", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"b", " ", "variabel"}], " ", "*)"}]}]}]], "Input", CellChangeTimes->{{3.529753531377174*^9, 3.529753538814619*^9}, { 3.5297535937727127`*^9, 3.529753654451997*^9}, {3.5297537569955673`*^9, 3.5297537624789057`*^9}, {3.5297538010999403`*^9, 3.5297538132759666`*^9}, {3.52975392708714*^9, 3.529754002194806*^9}, { 3.5297540446943407`*^9, 3.5297540595740957`*^9}, 3.529773051372636*^9, 3.530426679311956*^9},ExpressionUUID->"dbe91b50-105d-4750-a57b-\ 6f82e4a3d103"], Cell[TextData[{ "Bei der Auswahl von Symbolnamen kann die farbliche Syntax-Hervorhebung \ helfen: Bereits vergebene/gesetzte Namen werden schwarz, alle anderen blau \ dargestellt. Eingebaute ", StyleBox["Mathematica", FontSlant->"Italic"], " Funktionen oder Konstanten beginnen in der Regel mit einem \ Gro\[SZ]buchstaben (auch zur Trennung von Wortteilen im Funktionsnamen). Man \ ist folglich auf der sicheren Seite, wenn man eigene Symbolnamen immer mit \ einem Kleinbuchstaben beginnt (Symbolnamen sind \[OpenCurlyDoubleQuote]Case \ sensitive\[CloseCurlyDoubleQuote])." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.52975707496774*^9, 3.52975709148726*^9}, { 3.529757262562008*^9, 3.52975741599712*^9}, {3.5297578701313677`*^9, 3.529757990336257*^9}, {3.529758026946002*^9, 3.52975808506255*^9}, 3.5297730513737507`*^9, {3.5303340645573683`*^9, 3.530334089396057*^9}, { 3.530334129801613*^9, 3.5303341301881123`*^9}, {3.530337235264893*^9, 3.5303372404342403`*^9}, {3.685336773952606*^9, 3.6853367967223883`*^9}, { 3.780041697299312*^9, 3.7800416985554543`*^9}},ExpressionUUID->"266efd42-63a3-472b-9961-\ 93e1fbc58727"], Cell[BoxData[{ RowBox[{"a", ";", "b", ";"}], "\[IndentingNewLine]", RowBox[{"c", ";"}]}], "Input", CellChangeTimes->{{3.529758557868072*^9, 3.52975862104111*^9}, 3.529773051373962*^9, {3.712564793706382*^9, 3.712564794890285*^9}},ExpressionUUID->"8385fedd-aab0-49ab-af06-\ 434ec50c97ab"], Cell[TextData[{ "Die Verwendung von ", StyleBox["Mathematica", FontSlant->"Italic"], "-internen Sonderzeichen wie ", StyleBox["\[Alpha]", "Input"], ", ", StyleBox["\[Beta]", "Input"], ", ", StyleBox["\[Gamma]", "Input"], " usw. sollte aus Gr\[UDoubleDot]nden der Lesbarkeit, Benutzung anderer \ Editoren und Portierbarkeit von Code vermieden werden." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529758133789613*^9, 3.5297584627490253`*^9}, { 3.529770435119555*^9, 3.52977043613139*^9}, 3.529773051374085*^9},ExpressionUUID->"6bf703bc-4980-480d-9ac3-\ 6e70de6261bb"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.53034407273593*^9, 3.5303440769222097`*^9}},ExpressionUUID->"e3905d2e-cbfc-43f3-b2dc-\ 9958ef152ebc"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Aufgabe", FontSlant->"Italic"]], "Subsubsection", PageWidth->PaperWidth, CellChangeTimes->{{3.5297747600942793`*^9, 3.52977476232712*^9}},ExpressionUUID->"acb8e1f4-7850-4211-8ea0-\ 14158835a35a"], Cell[TextData[{ "Probieren Sie \[OpenCurlyDoubleQuote]", StyleBox["d", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["D", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["e", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["E", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["0D", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["d0d", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["Im", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["d_", "Input"], "\[CloseCurlyDoubleQuote] als Variablennamen aus. Welche davon lassen sich \ verwenden und welche nicht? Warum ist das so?" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529774779213578*^9, 3.529774922915406*^9}, { 3.530337344825742*^9, 3.5303373515042667`*^9}},ExpressionUUID->"f62c8823-a1b5-4937-9f36-\ cd1820a104fd"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["L\[ODoubleDot]sung", FontSlant->"Italic"]], "Subsubsection", PageWidth->PaperWidth, CellChangeTimes->{{3.5297749274270687`*^9, 3.529774937606641*^9}},ExpressionUUID->"2b45bfde-22d5-4de6-a8ae-\ 1a04f1d58161"], Cell[BoxData[{ RowBox[{"d", "=", "123"}], "\[IndentingNewLine]", RowBox[{"D", "=", "123"}], "\[IndentingNewLine]", RowBox[{"e", "=", "123"}], "\[IndentingNewLine]", RowBox[{"E", "=", "123"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"0", "D"}], "=", "123"}], "\[IndentingNewLine]", RowBox[{"d0d", "=", "123"}], "\[IndentingNewLine]", RowBox[{"Im", "=", "123"}], "\[IndentingNewLine]", RowBox[{"d_", "=", "123"}]}], "Input", CellChangeTimes->{{3.5297749423931437`*^9, 3.529774973526827*^9}},ExpressionUUID->"e2d98a7a-fbd7-435f-b11d-\ 3de634537187"], Cell[TextData[{ "Zul\[ADoubleDot]ssig (oder nicht \[OpenCurlyDoubleQuote]", StyleBox["Protected", "Input"], "\[CloseCurlyDoubleQuote]) sind nur \[OpenCurlyDoubleQuote]", StyleBox["d", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["e", "Input"], "\[CloseCurlyDoubleQuote] und \[OpenCurlyDoubleQuote]", StyleBox["d0d", "Input"], "\[CloseCurlyDoubleQuote]. \[OpenCurlyDoubleQuote]", StyleBox["D", "Input"], "\[CloseCurlyDoubleQuote] ist die Ableitungsfunktion, \ \[OpenCurlyDoubleQuote]", StyleBox["E", "Input"], "\[CloseCurlyDoubleQuote] die Euler Konstante, \[OpenCurlyDoubleQuote]", StyleBox["0d", "Input"], "\[CloseCurlyDoubleQuote] beginnt mit einer Ziffer, \ \[OpenCurlyDoubleQuote]", StyleBox["Im", "Input"], "\[OpenCurlyDoubleQuote] ist die Funktion f\[UDoubleDot]r den Imagin\ \[ADoubleDot]rteil und \[OpenCurlyDoubleQuote]", StyleBox["d_", "Input"], "\[CloseCurlyDoubleQuote] ist ein Pattern (kein g\[UDoubleDot]ltiger \ Symbolname)." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529775027482527*^9, 3.529775191841564*^9}, { 3.53033741187504*^9, 3.53033742722546*^9}},ExpressionUUID->"d49769fe-bb6d-4685-9dec-\ 760755e0d96c"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", RowBox[{"d", ",", "e", ",", "d0d"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.530344099428894*^9, 3.5303441107468863`*^9}},ExpressionUUID->"00b03492-f8fe-45da-b4be-\ 96265fdedc76"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["1.4 Der \[OpenCurlyDoubleQuote]Kernel\[CloseCurlyDoubleQuote]", \ "Subsubtitle", PageWidth->PaperWidth, CellChangeTimes->{{3.5297590979861727`*^9, 3.5297591021145573`*^9}, { 3.529759440074375*^9, 3.529759442451075*^9}, 3.5297730513742743`*^9},ExpressionUUID->"cd37168f-aab3-40b2-a23e-\ 4245a22c1732"], Cell[TextData[{ "Sobald Sie ", StyleBox["Mathematica", FontSlant->"Italic"], " starten, sei es durch \[CapitalODoubleDot]ffnen eines Notebooks oder durch \ Aufruf in einem Konsolenfenster, wird ein \[OpenCurlyDoubleQuote]Kernel\ \[CloseCurlyDoubleQuote] gestartet. Jeder Aufruf einer Funktion, jede \ Auswertung, das Speichern von Werten oder Definitionen usw. wird vom Kernel (\ \[OpenCurlyDoubleQuote]Backend\[CloseCurlyDoubleQuote]) \ \[UDoubleDot]bernommen. Das Interface in dem Sie sich gerade dieses Notebook \ anschauen ist das sog. \ \[OpenCurlyDoubleQuote]Frontend\[CloseCurlyDoubleQuote], es dient lediglich \ zur angenehmeren Darstellung von Ergebnissen und der \ \[CapitalUDoubleDot]bergabe von Eingaben an den Kernel." }], "Text", PageWidth->PaperWidth,ExpressionUUID->"0fde5169-43d2-4d37-8221-00e5cde07982"], Cell[TextData[{ "Wenn Sie eine Definition oder einen Wert aus dem aktuellen Zustand des \ Kernels l\[ODoubleDot]schen wollen, helfen Ihnen die Befehle ", StyleBox["Clear[]", "Input"], " oder", StyleBox[" ClearAll", "Input"], "." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.5297599056284437`*^9, 3.529760195330166*^9}, 3.52976079716825*^9, {3.529770464079427*^9, 3.529770465032073*^9}, 3.529773051374507*^9},ExpressionUUID->"b0c53b7a-ec65-4de2-9944-\ 2692e956005d"], Cell[BoxData[{ RowBox[{ RowBox[{"a", ":=", "11"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "=", "10"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"c", ":=", RowBox[{"a", "+", "b"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"a", ",", "\"\< \>\"", ",", "b", ",", "\"\< \>\"", ",", "c"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "b", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"a", ",", "\"\< \>\"", ",", "b", ",", "\"\< \>\"", ",", "c"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "a", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"a", ",", "\"\< \>\"", ",", "b", ",", "\"\< \>\"", ",", "c"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "c", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"a", ",", "\"\< \>\"", ",", "b", ",", "\"\< \>\"", ",", "c"}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.529760226141128*^9, 3.5297604807772703`*^9}, { 3.529760666841454*^9, 3.529760667039885*^9}, 3.529773051374908*^9},ExpressionUUID->"fcf0e4a9-abee-4e83-b0aa-\ 0d35ab459396"], Cell[BoxData[{ RowBox[{ RowBox[{"a", ":=", "11"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "=", "10"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"c", ":=", RowBox[{"a", "+", "b"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"a", ",", "\"\< \>\"", ",", "b", ",", "\"\< \>\"", ",", "c"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "c", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"a", ",", "\"\< \>\"", ",", "b", ",", "\"\< \>\"", ",", "c"}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.529760226141128*^9, 3.529760547475607*^9}, { 3.529760673489504*^9, 3.529760673680419*^9}, 3.5297730513758297`*^9},ExpressionUUID->"88a6ea7d-4520-43a1-9e96-\ cc770274999a"], Cell[TextData[{ "Um ganz sicher zu gehen, mit einem \[OpenCurlyDoubleQuote]frischen\ \[CloseCurlyDoubleQuote] Kernel zu arbeiten, l\[ADoubleDot]sst sich dieser \ \[UDoubleDot]ber \[OpenCurlyDoubleQuote]Evaluation -> Quit Kernel -> Local\ \[CloseCurlyDoubleQuote] beenden. Alternativ kann auch der Befehl ", StyleBox["Quit[]", "Input"], " eingegeben werden. Eine neue Instanz des Kernels startet dann bei Ausf\ \[UDoubleDot]hren des n\[ADoubleDot]chsten Befehls. ", StyleBox["Achtung", FontSlant->"Italic"], ": alle bis dahin gespeicherten Ausdr\[UDoubleDot]cke verschwinden dadurch \ aus dem Speicher!" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.5297609135101767`*^9, 3.529761234871277*^9}, 3.529773051376254*^9, {3.530337616747136*^9, 3.530337618611779*^9}},ExpressionUUID->"a2adc759-c20c-4a0c-afd1-\ e13b2d6f54be"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.53034413926096*^9, 3.530344145319668*^9}},ExpressionUUID->"9c7837b8-da03-475d-8c0a-\ b6125f9e8f41"] }, Open ]], Cell[CellGroupData[{ Cell["1.5 Listen", "Subsubtitle", PageWidth->PaperWidth, CellChangeTimes->{{3.529770574437111*^9, 3.529770579221714*^9}, 3.529773051376411*^9},ExpressionUUID->"fc99ccb3-35fe-4463-acfb-\ 93ffeb8f3714"], Cell[TextData[{ "Ausdr\[UDoubleDot]cke haben in ", StyleBox["Mathematica", FontSlant->"Italic"], " keinen festen Datentyp sondern sind Typ-frei. Variablen \ k\[ODoubleDot]nnen also ohne Einschr\[ADoubleDot]nkung Zahlen- oder \ Stringwerte, Definitionen oder Ausdr\[UDoubleDot]cke zugewiesen werden. Ein \ wichtigstes Konstrukt sind Listen, die in \[OpenCurlyDoubleQuote]", StyleBox["{", "Input"], "\[OpenCurlyDoubleQuote] und \[OpenCurlyDoubleQuote]", StyleBox["}", "Input"], "\[CloseCurlyDoubleQuote] eingefasst und deren Elemente durch Komma \ \[OpenCurlyDoubleQuote]", StyleBox[",", "Input"], "\[CloseCurlyDoubleQuote] voneinander getrennt werden. Listenelemente k\ \[ODoubleDot]nnen nun wiederum beliebig kompliziert konstruiert werden. \ Insbesondere k\[ODoubleDot]nnen die einzelnen Listenelemente unterschiedlich \ aufgebaut werden, was den wichtigsten Unterschied zu einfachen Arrays \ darstellt, deren Elemente immer desselben Typs sind." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.52982996966669*^9, 3.529830050661449*^9}, { 3.5298301256976347`*^9, 3.529830179346147*^9}, {3.529830212232257*^9, 3.529830404898897*^9}, {3.529830445741592*^9, 3.529830503875929*^9}, { 3.5298305378828583`*^9, 3.529830558986567*^9}, {3.52983060035525*^9, 3.5298307325036983`*^9}, 3.530337697223444*^9, 3.712570369563452*^9, { 3.712570400195032*^9, 3.712570418803028*^9}},ExpressionUUID->"1c16812e-0a86-46af-8b84-\ ff2d92306f8d"], Cell[BoxData[{ RowBox[{"liste1", "=", RowBox[{"{", RowBox[{"1", ",", "3", ",", "2", ",", "4"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"liste2", "=", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"liste3", "=", RowBox[{"{", RowBox[{"1", ",", "a", ",", "\"\\""}], "}"}]}], "\[IndentingNewLine]", RowBox[{"liste4", "=", RowBox[{"{", RowBox[{"d", ",", "liste3"}], "}"}]}]}], "Input", CellChangeTimes->{{3.529830760262662*^9, 3.529830859937476*^9}, { 3.5304267333579597`*^9, 3.5304267481658773`*^9}},ExpressionUUID->"5453458d-13b1-4448-bc9a-\ 6c3dbb0ffced"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " bietet zahlreiche Funktionen f\[UDoubleDot]r den Umgang mit Listen, siehe ", Cell[BoxData[ FormBox[ ButtonBox[ RowBox[{"List", " ", "Manipulation"}], BaseStyle->"Link", ButtonData->"paclet:guide/ListManipulation"], TextForm]],ExpressionUUID-> "d8ea9805-a37a-4dc9-8702-0024dd101969"], "." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.5298315427010107`*^9, 3.5298315817198553`*^9}, { 3.529831621966662*^9, 3.52983165389819*^9}, {3.529831688110125*^9, 3.529831689468412*^9}, {3.5298334250117693`*^9, 3.529833440358917*^9}},ExpressionUUID->"1fe157ec-ea60-4316-80b9-\ c69de71cc2c7"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Generierung", " ", "von", " ", "Listen"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"10", "-", "i"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "10"}], "}"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"i", "*", "j"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.5298316953616257`*^9, 3.529831771961241*^9}},ExpressionUUID->"02aec85f-5de7-4297-a2c7-\ 6975ab765d07"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Operationen", " ", "auf", " ", "Listen"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"liste1", "=", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"liste2", "=", RowBox[{"{", 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Formal wird das durch die Anwendung einer \ Ersetzungsregel auf einen Ausdruck erreicht. Ersetzungsregeln sowie nat\ \[UDoubleDot]rlich Ergebnisse einer Substitution k\[ODoubleDot]nnen in \ Variablen/Symbolen gespeichert werden. Syntax:" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.5298346584805307`*^9, 3.529834795868228*^9}, { 3.529835333121469*^9, 3.52983553555931*^9}, {3.5298355805755463`*^9, 3.529835778861347*^9}, {3.530338340013083*^9, 3.530338361977755*^9}, { 3.7125706033473167`*^9, 3.712570635971167*^9}, 3.780041846002613*^9},ExpressionUUID->"f674a3cb-229e-4163-a157-\ fc6c322f34f0"], Cell[TextData[{ StyleBox[" = -> ", "Input"], "\nwobei\n", StyleBox[" /. 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\ (", StyleBox["Hinweis", FontSlant->"Italic"], ": formulieren Sie Ihre Regel geschickt und verwenden Sie ", StyleBox["Expand", "Input"], "!)" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529836787055979*^9, 3.5298368227585907`*^9}, { 3.5298370453687963`*^9, 3.5298370515686607`*^9}, {3.529837524132135*^9, 3.529837529079043*^9}, {3.5298378469193068`*^9, 3.529837863462945*^9}, { 3.529837930026115*^9, 3.52983800457614*^9}, {3.529839380390664*^9, 3.5298393803934717`*^9}, {3.5298394163466597`*^9, 3.529839500442215*^9}, { 3.529839726312224*^9, 3.529839783586006*^9}},ExpressionUUID->"68eb734b-cbc9-4909-b7f0-\ ff1512a185e5"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["L\[ODoubleDot]sung", FontSlant->"Italic"]], "Subsubsection", PageWidth->PaperWidth, CellChangeTimes->{{3.529836772224371*^9, 3.529836774852188*^9}},ExpressionUUID->"3e499ef4-d422-4a77-83e5-\ c5590d9e4449"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "p"}], "}"}], "=", RowBox[{"{", RowBox[{"2", ",", "1", ",", "7"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"poly", "=", RowBox[{"Expand", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"a", "*", RowBox[{"Sin", "[", "x", "]"}]}], "+", RowBox[{"b", "*", RowBox[{"Cos", "[", "x", "]"}]}]}], ")"}], "^", "p"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"%", "/.", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "x", "]"}], "\[Rule]", RowBox[{"Sqrt", "[", RowBox[{"1", "-", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "^", "2"}]}], "]"}]}], "}"}]}]}], "Input", CellChangeTimes->{{3.52983951143327*^9, 3.529839707248439*^9}, 3.52983980919147*^9, {3.530426842879424*^9, 3.530426859359603*^9}},ExpressionUUID->"976d877e-36a2-4855-90f9-\ 7d861d5a8c06"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", RowBox[{"a", ",", "b", ",", "p", ",", "poly"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.530344283042199*^9, 3.530344291371413*^9}},ExpressionUUID->"517cce23-f2fe-4d80-9379-\ 5bfaccc6d067"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["2. Anwendungen", "Subtitle", CellChangeTimes->{{3.5297425543763027`*^9, 3.529742557910366*^9}, { 3.5297426316137447`*^9, 3.52974264182384*^9}, 3.529742708591662*^9, { 3.529743601950033*^9, 3.5297436189959297`*^9}, 3.529773051376731*^9},ExpressionUUID->"bbb2bcf6-7083-47a1-84d6-\ 252f830ec055"], Cell["2.1 Gleichungen", "Subsubtitle", PageWidth->PaperWidth, CellChangeTimes->{{3.5297414250588303`*^9, 3.529741426879901*^9}, { 3.5297586825012903`*^9, 3.529758683048922*^9}, {3.529771218788065*^9, 3.529771220221965*^9}, 3.529773051376895*^9},ExpressionUUID->"01c3c816-7364-4667-a572-\ f7b624e54a66"], Cell[TextData[{ "Gleichungen werden mit \[OpenCurlyDoubleQuote]", StyleBox["==", "Input"], "\[CloseCurlyDoubleQuote] notiert und wieder, soweit m\[ODoubleDot]glich, \ ausgewertet. (Es existieren weitere Vergleichsoperatoren \ \[CloseCurlyDoubleQuote]", StyleBox["!=", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["<", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox[">", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox["<=", "Input"], "\[CloseCurlyDoubleQuote], \[OpenCurlyDoubleQuote]", StyleBox[">=", "Input"], "\[CloseCurlyDoubleQuote].)" }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529770823301293*^9, 3.529770852369877*^9}, { 3.529771276792819*^9, 3.529771304122431*^9}, 3.529773051377132*^9, { 3.529773417634728*^9, 3.5297735848018093`*^9}},ExpressionUUID->"2fc2bc7e-ae22-48d7-85ce-\ 4091f4b348df"], Cell[BoxData[ RowBox[{"1", "\[Equal]", "0"}]], "Input", CellChangeTimes->{{3.52977085471239*^9, 3.529770855536456*^9}, 3.529773051377304*^9},ExpressionUUID->"310fac0c-f7b0-480b-9294-\ 330f73947ee5"], Cell[BoxData[ RowBox[{"1", "\[Equal]", "1"}]], "Input", CellChangeTimes->{{3.52977123387621*^9, 3.52977123420462*^9}, 3.529773051381428*^9},ExpressionUUID->"d95dfe3c-1d89-404d-ad1b-\ 12e02da93b9d"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", "124"}], "+", RowBox[{"345234", "/", "354"}]}], "\[GreaterEqual]", RowBox[{"3", "^", "7"}]}]], "Input", CellChangeTimes->{{3.529773336579412*^9, 3.529773391753715*^9}},ExpressionUUID->"f64bcdb2-f413-41c7-82fb-\ 30f485abca45"], Cell["Ist das nicht der Fall ...", "Text", CellChangeTimes->{{3.529771314548194*^9, 3.529771329526422*^9}, 3.529773051386767*^9},ExpressionUUID->"d75d70a3-e6e9-41c4-86ba-\ 80eb1c957406"], Cell[BoxData[ RowBox[{"gln", "=", RowBox[{"(", RowBox[{"y", "\[Equal]", RowBox[{ RowBox[{"a", "*", RowBox[{"x", "^", "2"}]}], "+", RowBox[{"b", "*", "x"}], "+", "c"}]}], ")"}]}]], "Input", CellChangeTimes->{{3.5297712442769833`*^9, 3.5297712520232983`*^9}, { 3.529771337417548*^9, 3.529771341426229*^9}, {3.529771517785946*^9, 3.529771537685425*^9}, 3.5297730513903837`*^9},ExpressionUUID->"d3c2bd9b-e98b-4170-82cc-\ f4999d74b132"], Cell[TextData[{ "... hilft der Befehl ", StyleBox["Solve[,]", "Input"], ". ", StyleBox["", "Input"], " und ", StyleBox["", "Input"], " k\[ODoubleDot]nnen jeweils auch Listen sein." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529771351932129*^9, 3.5297714882428493`*^9}, 3.5297730513930798`*^9, 3.530339349534217*^9, {3.5303394193434343`*^9, 3.530339420030011*^9}},ExpressionUUID->"974b5c44-5c0f-42c7-83a6-\ e9df961eb3f4"], Cell[BoxData[ RowBox[{"lsg", "=", RowBox[{"Solve", "[", RowBox[{"gln", ",", "x"}], "]"}]}]], "Input", CellChangeTimes->{{3.529749680906555*^9, 3.5297496838250713`*^9}, { 3.5297715116355247`*^9, 3.529771544270914*^9}, {3.52977158561487*^9, 3.529771592504961*^9}, 3.529773051393305*^9, {3.530339443127781*^9, 3.530339443760988*^9}},ExpressionUUID->"45eb664e-478e-4958-85db-\ 01c113b2fd35"], Cell["\<\ Der Output erfolgt als Liste von Ersetzungsregeln (mehrere Listeneintr\ \[ADoubleDot]ge bedeuten mehrere m\[ODoubleDot]gliche L\[ODoubleDot]sungen).\ \>", "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529771621300481*^9, 3.529771637160696*^9}, 3.529773051396237*^9, {3.530191722565606*^9, 3.53019175378104*^9}, 3.530334920476159*^9, {3.530334981427575*^9, 3.530334982351969*^9}},ExpressionUUID->"52202a78-5093-46f8-bce5-\ 1a27c31fdc57"], Cell[BoxData[ RowBox[{"lsg1", "=", RowBox[{"x", "/.", RowBox[{"lsg", "[", RowBox[{"[", "1", "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.529771562134741*^9, 3.529771594923847*^9}, 3.5297730513965*^9},ExpressionUUID->"d854af76-1412-4bea-b279-8ffe70a442bf"], Cell[BoxData[ RowBox[{"lsg2", "=", RowBox[{"x", "/.", RowBox[{"lsg", "[", RowBox[{"[", "2", "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.5297715968459997`*^9, 3.529771604098432*^9}, 3.52977305139935*^9},ExpressionUUID->"18bd5e03-3f50-4ed7-b86f-\ 9c3b9972fb00"], Cell[TextData[{ "Ist keine analytische L\[ODoubleDot]sung m\[ODoubleDot]glich, kann man es \ mit ", StyleBox["N", "Input", FontWeight->"Bold"], StyleBox["Solve", "Input"], " oder ", StyleBox["FindRoot ", "Input"], "versuchen." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.529772051819387*^9, 3.5297720956238413`*^9}, { 3.529772198512426*^9, 3.529772198825835*^9}, 3.529773051402281*^9, { 3.530339491806239*^9, 3.530339497051845*^9}},ExpressionUUID->"44f04a1c-5c48-4361-b454-\ 4fe35f7ac2cb"], Cell[BoxData[ RowBox[{ RowBox[{"gln", "=", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", "x", "]"}], "\[Equal]", "x"}], ")"}]}], ";"}]], "Input", PageWidth->PaperWidth, CellChangeTimes->{{3.5297721252374153`*^9, 3.5297721572156773`*^9}, { 3.5297722326444483`*^9, 3.529772259863913*^9}, 3.5297730514025593`*^9},ExpressionUUID->"1ef2970f-b755-464b-b471-\ 469765c6f39d"], Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{"gln", ",", "x"}], "]"}]], "Input", PageWidth->PaperWidth, CellChangeTimes->{{3.52977214311467*^9, 3.529772147461681*^9}, 3.529773051404071*^9},ExpressionUUID->"6f60c259-6f0d-4dba-aea1-\ 614b887683fe"], Cell[BoxData[ RowBox[{"NSolve", "[", RowBox[{"gln", ",", "x", ",", "Reals"}], "]"}]], "Input", PageWidth->PaperWidth, CellChangeTimes->{{3.5297721714623623`*^9, 3.529772254296051*^9}, 3.5297730514099207`*^9},ExpressionUUID->"a4cd1dfa-9c81-448d-bb65-\ 0efe90f9695c"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "0", " ", "ist", " ", "die", " ", "Vorgabe", " ", "f\[UDoubleDot]r", " ", "einen", " ", "Startwert", " ", "bei", " ", "der", " ", "Suche", " ", "nach", " ", "Nullstellen"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"FindRoot", "[", RowBox[{"gln", ",", RowBox[{"{", RowBox[{"x", ",", "0"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.5297722766666803`*^9, 3.529772314394628*^9}, 3.529773051412561*^9, {3.5299041172433977`*^9, 3.529904145181005*^9}, { 3.5299146795570803`*^9, 3.529914685115509*^9}, {3.780041918025955*^9, 3.780041918610057*^9}},ExpressionUUID->"2637eaec-9190-4598-9148-\ e5e2c43f263d"], Cell[TextData[{ "H\[ADoubleDot]ufig haben ", StyleBox["Mathematica", FontSlant->"Italic"], " Funktionen mehrere m\[ODoubleDot]gliche Schreibweisen, das bedeutet, sie \ lassen sich mit unterschiedlicher Anzahl an Argumenten oder Optionen aufrufen \ (oder auch mit Argumenten unterschiedlicher Bedeutung!). Optionen \ unterscheiden sich von Argumenten dadurch, dass sie als Ersetzungsregel \ \[UDoubleDot]bergeben werden." }], "Text", PageWidth->PaperWidth, CellChangeTimes->{{3.52977238868574*^9, 3.529772748713258*^9}, { 3.5297729753504*^9, 3.5297729787330437`*^9}, 3.529773051414941*^9, { 3.530339565450218*^9, 3.530339565701507*^9}, 3.780041934418714*^9},ExpressionUUID->"a3a24e91-0483-43d9-b720-\ b52bf887d54b"], Cell[TextData[StyleBox["[,(,<\ optionales_Argument>(,