From 33613a85afc4b1481367fbe92a17ee59c240250b Mon Sep 17 00:00:00 2001 From: Sven Eisenhauer Date: Fri, 10 Nov 2023 15:11:48 +0100 Subject: add new repo --- Bachelor/Numerische Mathematik/Num05Aufg4B.nb | 1437 +++++++++++++++++++++++++ 1 file changed, 1437 insertions(+) create mode 100644 Bachelor/Numerische Mathematik/Num05Aufg4B.nb (limited to 'Bachelor/Numerische Mathematik/Num05Aufg4B.nb') diff --git a/Bachelor/Numerische Mathematik/Num05Aufg4B.nb b/Bachelor/Numerische Mathematik/Num05Aufg4B.nb new file mode 100644 index 0000000..e9223fd --- /dev/null +++ b/Bachelor/Numerische Mathematik/Num05Aufg4B.nb @@ -0,0 +1,1437 @@ +(************** Content-type: application/mathematica ************** + CreatedBy='Mathematica 5.0' + + Mathematica-Compatible Notebook + +This notebook can be used with any Mathematica-compatible +application, such as Mathematica, MathReader or Publicon. The data +for the notebook starts with the line containing stars above. + +To get the notebook into a Mathematica-compatible application, do +one of the following: + +* Save the data starting with the line of stars above into a file + with a name ending in .nb, then open the file inside the + application; + +* Copy the data starting with the line of stars above to the + clipboard, then use the Paste menu command inside the application. + +Data for notebooks contains only printable 7-bit ASCII and can be +sent directly in email or through ftp in text mode. Newlines can be +CR, LF or CRLF (Unix, Macintosh or MS-DOS style). + +NOTE: If you modify the data for this notebook not in a Mathematica- +compatible application, you must delete the line below containing +the word CacheID, otherwise Mathematica-compatible applications may +try to use invalid cache data. + +For more information on notebooks and Mathematica-compatible +applications, contact Wolfram Research: + web: http://www.wolfram.com + email: info@wolfram.com + phone: +1-217-398-0700 (U.S.) + +Notebook reader applications are available free of charge from +Wolfram Research. +*******************************************************************) + +(*CacheID: 232*) + + +(*NotebookFileLineBreakTest +NotebookFileLineBreakTest*) +(*NotebookOptionsPosition[ 49607, 1336]*) +(*NotebookOutlinePosition[ 50269, 1359]*) +(* CellTagsIndexPosition[ 50225, 1355]*) +(*WindowFrame->Normal*) + + + +Notebook[{ +Cell[BoxData[ + StyleBox[\(\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Numerik\ - \ + Aufgabe\ \ +4\ \ B\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ SS\ \ +2005\ \ \ \ \ *) \)\(\ \)\), + "Subtitle", + FontColor->RGBColor[1, 0, 0]]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{ + RowBox[{ + StyleBox["(*", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[\(\(Interpolation\)\(:\)\), + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Section"], + + StyleBox[ + " \ + ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section"]}]], + StyleBox["*)", + "Section", + FontColor->RGBColor[1, 0, 0]]}], "\n", + RowBox[{ + StyleBox["(*", + "Section", + FontColor->RGBColor[1, 0, 0]], + RowBox[{ + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + RowBox[{ + RowBox[{ + StyleBox["Parametrische", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox["Darstellung", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], + StyleBox["x", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox["=", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + RowBox[{ + RowBox[{ + StyleBox["\[CurlyPhi]", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[\((x)\), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["und", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["y", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["=", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + RowBox[{ + StyleBox["\[Psi]", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[\((x)\), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]}]}], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[")", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]]}]], + StyleBox["*)", + "Section", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", + RowBox[{ + StyleBox["(*", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[ + RowBox[{" ", + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]]}]], + RowBox[{ + StyleBox["(", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[\(f\[UDoubleDot]r\ geschlossene\ Kurven\), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[")", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox["*)", + "Section", + FontColor->RGBColor[1, 0, 0]]}], "\[IndentingNewLine]", + RowBox[{ + StyleBox["(*", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], + RowBox[{ + StyleBox["1.", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox["Klassische", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["Interpolation", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[\((\ Newton\ )\), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], " "}]], + StyleBox["*)", + "Section", + FontColor->RGBColor[1, 0, 0]]}], "\n", + RowBox[{ + StyleBox["(*", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + RowBox[{ + RowBox[{ + StyleBox["2.", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], + StyleBox["Nat\[UDoubleDot]rliche", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["kubische", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["Spline", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox["-", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]], + StyleBox["Funktion", + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Section", + FontColor->RGBColor[1, 0, 0]], " "}]], + StyleBox["*)", + "Section", + FontColor->RGBColor[1, 0, 0]]}]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + \(\(\(\(\(Off[General::spell]\)\(\ \)\) \)\(;\)\(\ \ \ \ \ \ \)\(Off[ + General::spell1]\)\(\ \)\)\)], "Input"], + +Cell[BoxData[ + RowBox[{\(lauf = 1\), ";", " ", + StyleBox[\( (*\ \ Lauf\ mit\ der\ Nummer\ lauf\ \ , \ + alle\ vorhergehenden\ L\[ADoubleDot]ufe\ bleiben\ \(erhalten\ !\)\ *) \ +\), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ Vorgeben\ \(("\")\)\ der\ m + + 1\ St\[UDoubleDot]tzpunkte\ , \[IndentingNewLine]\ \ \ \ \ \ \ L\ +\[ODoubleDot]schen\ \(("\< L \>")\)\ , \ \ Einf\[UDoubleDot]gen\ \(("\< E \ +\>")\)\ \ oder\ \ \[CapitalADoubleDot]ndern\ \(("\< K\>")\)\ eines\ Punktes\ \ +\ ?\ \ \ \ \ \ \ \ nichts\ \[CapitalADoubleDot]ndern\ \ \(("\< N \>")\)\ \ \ \ +\ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{" ", + RowBox[{\(sch = \ "\"\), ";", + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontSize->16, + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ \ \ Erster\ Lauf\ mit\ vorgegebenen\ \(Werten\ \ +!\)\ \ \ \ *) \), + FontSize->16, + FontColor->RGBColor[0, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[0, 0, 1]], "\[IndentingNewLine]", + StyleBox[" ", + FontSize->14, + FontColor->RGBColor[1, 0, 0]], + StyleBox[\( (*\ + Hier\ \[CapitalADoubleDot]nderungen\ \((L, E, + K)\)\ eingeben\ und\ direkt\ ausf\[UDoubleDot]hren\ \ +\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ oder\ N\ f\[UDoubleDot]r\ nicht\ \ +\[ADoubleDot]ndern\ bei\ einem\ neuen\ Lauf\ *) \), + FontSize->16, + FontColor->RGBColor[1, 0, 0]], + StyleBox[" ", + FontSize->16, + FontColor->RGBColor[1, 0, 0]]}]}]], "Input"], + +Cell[BoxData[ + \(If[sch \[Equal] "\", + If[index \[GreaterEqual] 0\ And\ index \[LessEqual] + m\ \ , \ \ \ \[IndentingNewLine]TableForm[ + Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>", + PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>", + ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}], + TableSpacing \[Rule] {1, 0}]]]\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[ + RowBox[{ + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + "Subsection", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\(St\[UDoubleDot]tzpunkte\ 0, .. , m\ \ eingeben\), + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[ + RowBox[{ + StyleBox[" ", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(\(If[\ + sch == "\", {\ \ m = + 20, \[IndentingNewLine]xp[0] = \(-4. \); \ \ \ yp[0] = + 0. ; \ \ \ xp[1] = \(-3.95\); \ \ \ \ \ yp[1] = + 0.5; \ \ \ \ \ \ xp[2] = \(-3.5\); \ \ \ \ \ \ yp[2] = + 1.5; \ \ \ \ \ xp[3] = \(-3. \); \ \ \ yp[3] = + 2. ; \ \ \ xp[4] = \ \(-2\); \ \ \ \ \ \ \ \ \ \ yp[4] = + 2.6; \ \ \ \ \ \ xp[5] = \ \(-1\); \ \ \ \ \ \ \ \ \ yp[5] = + 2.9; \ \ \ \ \ \ \ \ xp[6] = \ \ \ 0. ; \ \ \ yp[6] = + 3. ; \ \ xp[7] = \ \ \ 2; \ \ \ \ \ \ \ \ \ \ \ yp[7] = + 2.6; \ \ \ \ \ \ \ xp[8] = \(+3. \); \ \ \ \ \ \ \ \ yp[8] = + 2. ; \nxp[9] = \ 3.75; \ \ \ \ \ \ yp[9] = + 1; \ \ \ \ \ \ \ \ \ \ xp[10] = \(+4. \); \ \ \ \ \ \ \ yp[10] = + 0. ; \ \ \ \ \ \ \ \ xp[11] = + 3.5; \ \ \ \ \ yp[11] = \(-1.5\); \ \ \ \ \ \ \n + xp[12] = \(+3. \); \ \ \ \ \ \ yp[12] = \(-2. \); \ \ \ \ xp[ + 13] = \ \ \ 1; \ \ \ \ \ \ \ \ \ yp[13] = \(-2.9\); \ \ xp[ + 14] = \ \ \ 0. ; \ \ \ yp[14] = \(-3. \); \[IndentingNewLine]xp[ + 15] = \ \(-2\); \ \ \ \ \ \ \ \ yp[15] = \(-2.6\); \ + xp[16] = \(-3. \); \ \ \ \ \ yp[16] = \(-2. \); \ \ \ \ \ xp[ + 17] = \(-3.5\); \ \ \ yp[ + 17] = \(-1.5\); \ \ \ \ \ \ \[IndentingNewLine]xp[ + 18] = \(-3.75\); \ + yp[18] = \(-1. \); \ \ xp[19] = \(-3.95\); \ \ \ \ yp[ + 19] = \(-0.5\); \ \ xp[20] = \(-4. \); \ \ \ yp[20] = + 0. ;}];\)\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(Vorgegebene\ St\[UDoubleDot]tzpunkte\ 0, .. , m\), + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(If[sch == "\", + TableForm[ + Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>", + PaddedForm[xp[i], {3, 2}], "\< yp[\>", ind, "\<] = \>", + PaddedForm[yp[i], {3, 2}]}, {i, 0, m}], + TableSpacing \[Rule] {1, 0}]]\)], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ +L\[ODoubleDot]schen\ \ eines\ \ Punktes\ \ mit\ \ der\ \ Nummer\ \ index\ \ \ \ +*) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{" ", + RowBox[{\(index\ = 9\), " ", ";", " ", + StyleBox[\( (*\ + Nummer\ des\ zu\ entfernenden\ Punktes\ \((\ + index\ )\)\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]], " ", "\n", + " ", \(If[sch \[Equal] "\", + If[index \[GreaterEqual] 0\ And\ index \[LessEqual] + m\ , {m = + m - 1; \n\ \ \ \ \ \ \ \ \ Do[{\ xp[j] = xp[j + 1], + yp[j] = yp[j + 1]}, {j, index, m}]}]]\), ";", + " "}]}]], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[ + RowBox[{ + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + "Subsection", + FontColor->RGBColor[1, 0, 1]]}]], + RowBox[{ + StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\), + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox["..", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox["m", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(nach\ dem\ Entfernen\ von\ Punkten\), + FontColor->RGBColor[1, 0, 1]]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(If[sch \[Equal] "\", + If[index \[GreaterEqual] 0\ And\ index \[LessEqual] + m\ \ , \ \ \ \[IndentingNewLine]TableForm[ + Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>", + PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>", + ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}], + TableSpacing \[Rule] {1, 0}]]]\)], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ \ \ \ +Einf\[UDoubleDot]gen\ \ eins\ \ Punktes\ \ mit\ \ der\ \ Nummer\ i\ ndex\ \ \ \ +\ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{" ", + RowBox[{ + RowBox[{\(index\ = \ \ 1\ ;\), " ", + + StyleBox[\( (*\ + Nummer\ des\ einzuf\[UDoubleDot]genden\ Punktes\ \((\ + index\ )\)\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]]}], " ", + "\[IndentingNewLine]", + RowBox[{ + RowBox[{"If", "[", + RowBox[{\(sch \[Equal] "\"\), ",", + RowBox[{"If", "[", + + RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual] + m\), ",", + RowBox[{"{", + + RowBox[{\(m = m + 1\), + ";", \(Do[{xp[j], yp[j]}, {j, 0, index - 1}]\), ";", + "\[IndentingNewLine]", + " ", \(Do[{xp[j] = xp[j - 1], yp[j] = yp[j - 1]}, {j, + m, index + 1, \(-1\)}]\), ";", + "\[IndentingNewLine]", + " ", \(xp[index] = \ \ \(-\ 3.75\)\), + " ", + StyleBox[\( (*\ xp[i]\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]], + StyleBox[";", + FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", + " ", \(yp[index] = \ \ \ 1.0\)}], + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 0]]}]], + StyleBox[\( (*\ yp[i]\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]], + StyleBox["}", + FontColor->RGBColor[1, 0, 0]]}]}], + StyleBox["]", + FontColor->RGBColor[1, 0, 0]]}]}], + StyleBox["]", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[";", + FontColor->RGBColor[1, 0, 0]]}]}]}]], "Input"], + +Cell[BoxData[ + \(\(nummer[lauf] = m;\)\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[ + RowBox[{ + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + "Subsection", + FontColor->RGBColor[1, 0, 1]]}]], + RowBox[{ + StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\), + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox["..", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox["m", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\), + FontColor->RGBColor[1, 0, 1]]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(If[sch \[Equal] "\", + If[index \[GreaterEqual] 0\ And\ index \[LessEqual] + m, \ \ \ \[IndentingNewLine]TableForm[ + Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>", + PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>", + ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}], + TableSpacing \[Rule] {1, 0}]]]\)], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ \ \[CapitalADoubleDot]ndern\ des\ Punktes\ mit\ \ +der\ Nummer\ index\ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{" ", + RowBox[{ + RowBox[{\(index\ = \ \ 19\ ;\), " ", + + StyleBox[\( (*\ + Nummer\ des\ zu\ \[ADoubleDot]ndernden\ Punktes\ \((\ + index\ )\)\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]]}], " ", "\n", " ", + RowBox[{ + RowBox[{"If", "[", + RowBox[{\(sch \[Equal] "\"\), ",", + RowBox[{"If", "[", + + RowBox[{\(index \[GreaterEqual] 0\ And\ index \[LessEqual] + m\), ",", + RowBox[{"{", " ", + + RowBox[{\(xp[index] = \ \ \ \(-3.90\)\), + " ", + StyleBox[\( (*\ xp[i]\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]], + StyleBox[";", + FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", + " ", \(yp[index] = \ \ \ \(-0.5\)\)}], + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 0]]}]], + StyleBox[\( (*\ yp[i]\ eingeben\ *) \), + FontColor->RGBColor[1, 0, 0]], + StyleBox["}", + FontColor->RGBColor[1, 0, 0]]}]}], + StyleBox["]", + FontColor->RGBColor[1, 0, 0]]}]}], + StyleBox["]", + FontColor->RGBColor[1, 0, 0]]}], + StyleBox[";", + FontColor->RGBColor[1, 0, 0]]}]}]}]], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[ + RowBox[{ + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + "Subsection", + FontColor->RGBColor[1, 0, 1]]}]], + RowBox[{ + StyleBox[\(St\[UDoubleDot]tzpunkte\ \ \ 0\), + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox["..", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox["m", + "Subsection", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[",", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(nach\ dem\ Einf\[UDoubleDot]gen\ von\ Punkten\), + FontColor->RGBColor[1, 0, 1]]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(If[sch \[Equal] "\", + If[index \[GreaterEqual] 0\ And\ index \[LessEqual] + m, \ \ \ \[IndentingNewLine]TableForm[ + Table[{ind = PaddedForm[i, 2], "\< xp[\>", ind, "\<] = \>", + PaddedForm[xp[i], {3, 2}], \[IndentingNewLine]"\< yp[\>", + ind, "\<] = \>", PaddedForm[yp[i], {3, 2}]}, {i, 0, m}], + TableSpacing \[Rule] {1, 0}]]]\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ \ \ \ \ Bereitstellen\ des\ Parameters\ tp\ f\ +\[UDoubleDot]r\ die\ m\ St\[UDoubleDot]tzpunkte\ \ \ \ \ \ \ \ \ *) \), + "Subsection", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + \(\(\(\ \)\(\(tp[0] = 0;\)\[IndentingNewLine] + Do[{Delt[k - 1] = + Sqrt[\((xp[k] - xp[k - 1])\)^2 + \((yp[k] - yp[k - 1])\)^2], + tp[k] = tp[k - 1] + Delt[k - 1]}, {k, 1, m}]\)\)\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ \ \ \ \ St\[UDoubleDot]tzstellen\ f\[UDoubleDot]r\ +\ die\ Parameterdarstellung\ der\ Ellipse\ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]", + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ und\ Bereitstellen\ des\ Parameters\ +\ tj, \ \((\ j, \ 0, \ nd\ )\)\ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(\(nd = 400;\)\)], "Input"], + +Cell[BoxData[ + \(Do[{tj[j] = tp[0] + j*\((tp[m] - tp[0])\)/nd, \ + tel[j] = + 8. *ArcTan[1]/nd* + j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xel[j] = \(-\ 4\)*Cos[tel[j]], + yel[j] = 3*Sin[tel[j]]}, {j, 0, nd}]\)], "Input"], + +Cell[BoxData[ + \(<< Graphics`Colors`\)], "Input"], + +Cell[BoxData[ + \(\(liste1 = {Red, HotPink, Green, Apricot, Brown, DarkGreen, Cobalt, + Brick, Orange, Magenta, IndianRed, ForestGreen};\)\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ \ Plotten\ der\ Ellipse\ \ x\ = \ \(4* + cos \((t)\)\ \ und\ \ y\ = \ + 3*sin \((t)\)\)\ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(ellipsplot = + ListPlot[Table[{xel[j], yel[j]}, {j, 0, nd}], + PlotJoined\ -> \ True, \n\t + PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Brown, + AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], + +Cell[BoxData[ + \(punktplot = + ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ False, \t + PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue, + Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5, + AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], + +Cell[BoxData[ + \(linienplot = + ListPlot[Table[{xp[k], yp[k]}, {k, 0, m}], PlotJoined\ -> \ True, \t + PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue, + Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5, + AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], + +Cell[BoxData[ + \(Show[ellipsplot, linienplot, punktplot, + Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Newton\ - \ + Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\ \ \ \ *) \), + "Section", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \ +der\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]", + " ", + StyleBox[\( (*\ \ \ \ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ \ +Newton - Interpolation\ \ \ \ \ \ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 1]], " "}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(FunkDivDiff[xpform_, + ypform_] := \ \((\[IndentingNewLine]Do[ + DivDiffret[k, + 1] = \((ypform[k + 1] - ypform[k])\)/\((xpform[k + 1] - + xpform[k])\), {k, 0, m - 1}]; \[IndentingNewLine]Do[ + Do[DivDiffret[k, + j] = \((DivDiffret[k + 1, j - 1] - + DivDiffret[k, j - 1])\)/\((xpform[k + j] - + xpform[k])\), {k, 0, m - j}], {j, 2, m}]; + DivDiffmatret = + Table[DivDiffret[0, j], {j, 1, m}]; {DivDiffmatret})\)\)], "Input"], + +Cell[BoxData[ + \(\(DivDiffxmat = FunkDivDiff[tp, xp]\ ;\)\)], "Input"], + +Cell[BoxData[ + RowBox[{\(DivDiffx = DivDiffxmat[\([1]\)];\), + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ x - + Werte\ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(DivDiffymat = FunkDivDiff[tp, yp]\ ;\), + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(DivDiffy = DivDiffymat[\([1]\)];\), " ", + StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ y - + Werte\ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ xj\ und\ yj\ f\ +\[UDoubleDot]r\ den\ Graph\ der\ Newton - Interpolation\ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(Do[{xnew[j] = xp[0], + prox = tj[j] - + tp[0], \[IndentingNewLine]Do[{xnew[j] = + xnew[j] + prox*DivDiffx[\([i]\)], + prox = prox*\((tj[j] - tp[i])\)}, {i, 1, + m}], \[IndentingNewLine]ynew[j] = yp[0], + proy = tj[j] - tp[0], \n\t + Do[{ynew[j] = ynew[j] + proy*DivDiffy[\([i]\)], + proy = proy*\((tj[j] - tp[i])\)}, {i, 1, m}]}, {j, 0, + nd}]\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ Parametrische\ Darstellung\ der\ Newton - + Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(newtonplot = + ListPlot[Table[{xnew[j], ynew[j]}, {j, 0, nd}], + PlotJoined\ -> \ True, \n\t + PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Red, + AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], + +Cell[BoxData[ + \(\(\(Show[newtonplot, ellipsplot, linienplot, punktplot, + Prolog\ -> \ AbsolutePointSize[5]]\)\(\[IndentingNewLine]\) + \)\)], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Nat\[UDoubleDot]rliche\ Spline - + Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \ +\), + "Section", + FontColor->RGBColor[1, 0, 0]]}]], "Input", + Background->RGBColor[0, 1, 0]], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ \ \ \ \ Funktionsunterprogramm\ zur\ Berechnung\ \ +der\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]", + " ", + StyleBox[\( (*\ \ \ \ \ Koeffizienten\ f\[UDoubleDot]r\ die\ nat\ +\[UDoubleDot]rlichen\ Spline - Interpolation\ \ \ \ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 1]], " "}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + RowBox[{\(FunkNatSpl[xpform_, ypform_]\), ":=", " ", + RowBox[{ + "(", "\[IndentingNewLine]", " ", + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Erstellen\ \ +der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 1]], "\n", + " ", + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \((\ + Haupt - \ und\ Nebendiagonale\ )\)\ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]", + RowBox[{\(Du[0] = xpform[1] - xpform[0]\), ";", "\n", + " ", \(Do[{Du[k] = xpform[k + 1] - xpform[k], + Dh[k] = 2 \((Du[k - 1] + Du[k])\)}, {k, 1, m - 1}]\), ";", + "\[IndentingNewLine]", " ", + + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Cholesky - + Zerlegung\ der\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ *) \), + "Subsubtitle", + FontColor->RGBColor[1, 0, 1]], + "\[IndentingNewLine]", \(Ch[1] = Sqrt[Dh[1]]\), ";", "\n", + " ", \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1], + Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2]}, {k, 2, m - 1}]\), ";", + "\[IndentingNewLine]", " ", + + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Vorw\[ADoubleDot]rtsrechnung\ \ +"\"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], + StyleBox["\n", + FontColor->RGBColor[1, 0, 1]], " ", + + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ und\ Erstellen\ der\ rechten\ \ +Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], + "\[IndentingNewLine]", \(Dv[0] = ypform[1] - ypform[0]\), ";", + " ", \(Dv[1] = ypform[2] - ypform[1]\), ";", "\n", + " ", \(Dr[1] = 3 \((Dv[1]/Du[1] - Dv[0]/Du[0])\)\), ";", "\n", + " ", \(Z[1] = Dr[1]/Ch[1]\), ";", "\n", + " ", \(Do[{Dv[k] = ypform[k + 1] - ypform[k], \n\t\tDr[k] = + 3 \((Dv[k]/Du[k] - Dv[k - 1]/Du[k - 1])\), \n\t\tZ[ + k] = \((Dr[k] - Z[k - 1]*Cn[k - 1])\)/Ch[k]}, \n\ \ \ {k, + 2, m - 1}]\), ";", "\[IndentingNewLine]", + " ", + + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R\[UDoubleDot]ckw\ +\[ADoubleDot]rtsrechnung\ "\"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], + StyleBox["\n", + FontColor->RGBColor[1, 0, 1]], " ", + + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \tBerechnung\ der\ \ +Koeffizienten\ B\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], + "\[IndentingNewLine]", \(B[m] = 0\), ";", + " ", \(B[m - 1] = Z[m - 1]/Ch[m - 1]\), ";", "\n", + " ", \(Do[ + B[k] = \((Z[k] - B[k + 1]*Cn[k])\)/Ch[k], {k, m - 2, + 1, \(-1\)}]\), ";", " ", \(B[0] = 0\), ";", + "\[IndentingNewLine]", " ", + + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ Berechnung\ der\ \ +Koeffizienten\ A\_\(\(k\)\(\ \)\), \ C\_k\ , \ + D\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]], + "\[IndentingNewLine]", \(Do[{A[ + k] = \((B[k + 1] - B[k])\)/\((3 + Du[k])\), \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ Cc[k] = + Dv[k]/Du[k] - Du[k]*\((B[k + 1] + 2 B[k])\)/3, \ + Dc[k] = ypform[k]}, {k, 0, m - 1}]\), ";", + "\[IndentingNewLine]", + " ", \(Aret = Table[A[k], \ {k, 0, m - 1}]\), ";", + " ", \(Bret = Table[B[k], {k, 0, m}]\), ";", " ", + "\[IndentingNewLine]", " ", \(Cret = Table[Cc[k], {k, 0, m - 1}]\), + ";", " ", \(Dret = Table[Dc[k], {k, 0, m - 1}]\), ";", + "\[IndentingNewLine]", \({Aret, Bret, Cret, Dret}\)}], + ")"}]}]], "Input"], + +Cell[BoxData[ + \(\(ABCDxmat = FunkNatSpl[tp, xp]\ \ ;\)\)], "Input"], + +Cell[BoxData[ + RowBox[{\(Anatx = ABCDxmat[\([1]\)]\ ;\), " ", + StyleBox[\( (*\ + Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x - Werte\ *) \), + FontColor->RGBColor[1, 0, 1], + Background->None]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(Bnatx = ABCDxmat[\([2]\)];\), " ", + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + RowBox[{ + RowBox[{ + StyleBox["Koeffizienen", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["Bk", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(f \[UDoubleDot]r\), + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["die", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["x", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox["-", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["Werte", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(Cnatx = ABCDxmat[\([3]\)];\), " ", + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + RowBox[{ + RowBox[{ + StyleBox["Koeffizienen", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["Ck", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(f \[UDoubleDot]r\), + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["die", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["x", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox["-", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["Werte", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(Dnatx = ABCDxmat[\([4]\)];\), " ", + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + RowBox[{ + RowBox[{ + StyleBox["Koeffizienen", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["Dk", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(f \[UDoubleDot]r\), + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["die", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["x", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox["-", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["Werte", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], + +Cell[BoxData[ + \(\(ABCDymat = FunkNatSpl[tp, yp]\ ;\)\)], "Input"], + +Cell[BoxData[ + RowBox[{\(Anaty = ABCDymat[\([1]\)];\), " ", + StyleBox[\( (*\ + Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x - Werte\ *) \), + FontColor->RGBColor[1, 0, 1], + Background->None]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(Bnaty = ABCDymat[\([2]\)];\), " ", + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + RowBox[{ + RowBox[{ + StyleBox["Koeffizienen", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["Bk", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(f \[UDoubleDot]r\), + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["die", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["x", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox["-", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["Werte", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(Cnaty = ABCDymat[\([3]\)];\), " ", + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + RowBox[{ + RowBox[{ + StyleBox["Koeffizienen", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["Ck", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(f \[UDoubleDot]r\), + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["die", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["x", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox["-", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["Werte", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], + +Cell[BoxData[ + RowBox[{\(Dnaty = ABCDymat[\([4]\)]\ ;\), " ", + RowBox[{ + StyleBox["(*", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + RowBox[{ + RowBox[{ + StyleBox["Koeffizienen", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["Dk", + FontColor->RGBColor[1, 0, 1]], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox[\(f \[UDoubleDot]r\), + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["die", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["x", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox["-", + FontColor->RGBColor[1, 0, 1], + Background->None], + StyleBox["Werte", + FontColor->RGBColor[1, 0, 1], + Background->None]}], + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]], + StyleBox["*)", + FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], + +Cell[BoxData[ + RowBox[{" ", + StyleBox[\( (*\ \ \ \ St\[UDoubleDot]tzstellen\ xj\ und\ yj\ f\ +\[UDoubleDot]r\ den\ Graph\ der\ Spline - Interpolation\ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(Do[{tint = tp[0], \n\t + Do[{Dnt[k] = tp[k + 1] - tp[k], + If[\((tj[j] \[GreaterEqual] + tint\ )\)\ \[And] \ \ \((tj[j] \[LessEqual] + tint + Dnt[k]\ )\), {knt = k, Break[]}\ , + tint = tint + Dnt[k]]}, {k, 0, m - 1}], \n\t + Dntmj = tj[j] - tp[knt], \[IndentingNewLine]\ \ \ \ \ xnat[j] = + Anatx[\([knt + 1]\)]*Dntmj^3 + Bnatx[\([knt + 1]\)]*Dntmj^2 + + Cnatx[\([knt + 1]\)]*Dntmj + Dnatx[\([knt + 1]\)]\ , \n\t + ynat[j] = + Anaty[\([knt + 1]\)]*Dntmj^3 + Bnaty[\([knt + 1]\)]*Dntmj^2 + + Cnaty[\([knt + 1]\)]*Dntmj + \ \ Dnaty[\([knt + 1]\)]\ }, \n\t{j, + 0, nd}]\)], "Input"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{" ", + StyleBox[" ", + FontColor->RGBColor[1, 0, 1]]}]], + StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ Graph\ der\ nat . \ Spline - + Funktion\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \), + FontColor->RGBColor[1, 0, 1]]}]], "Input", + Background->RGBColor[1, 1, 0]], + +Cell[BoxData[ + \(natsplplot = + ListPlot[Table[{xnat[j], ynat[j]}, {j, 0, nd}], + PlotJoined\ -> \ True, \n\t + PlotRange -> {{\(-5\), 5}, {\(-4\), 4}}, \tPlotStyle -> Green, + AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"], + +Cell[BoxData[ + \(graf[lauf] = + Show[natsplplot, newtonplot, ellipsplot, linienplot, punktplot, + Prolog\ -> \ AbsolutePointSize[5]]\)], "Input"], + +Cell[BoxData[ + \(Do[{Print["\< Lauf Nummer \>", l\ , "\< mit \>", + nummer[l], "\< St\[UDoubleDot]tzpunkten \>"\ ], Show[graf[l]]}, {l, + 1, lauf}]\)], "Input"] +}, +FrontEndVersion->"5.0 for Microsoft Windows", +ScreenRectangle->{{0, 1024}, {0, 685}}, +WindowSize->{1016, 651}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, +Magnification->1 +] + +(******************************************************************* +Cached data follows. If you edit this Notebook file directly, not +using Mathematica, you must remove the line containing CacheID at +the top of the file. The cache data will then be recreated when +you save this file from within Mathematica. +*******************************************************************) + +(*CellTagsOutline +CellTagsIndex->{} +*) + +(*CellTagsIndex +CellTagsIndex->{} +*) + +(*NotebookFileOutline +Notebook[{ +Cell[1754, 51, 318, 7, 59, "Input"], +Cell[2075, 60, 7848, 236, 137, "Input"], +Cell[9926, 298, 133, 2, 30, "Input"], +Cell[10062, 302, 294, 6, 30, "Input"], +Cell[10359, 310, 527, 10, 69, "Input"], +Cell[10889, 322, 1032, 26, 70, "Input"], +Cell[11924, 350, 434, 7, 70, "Input"], +Cell[12361, 359, 724, 23, 46, "Input"], +Cell[13088, 384, 1583, 26, 170, "Input"], +Cell[14674, 412, 450, 13, 46, "Input"], +Cell[15127, 427, 305, 6, 70, "Input"], +Cell[15435, 435, 292, 7, 46, "Input"], +Cell[15730, 444, 565, 12, 70, "Input"], +Cell[16298, 458, 1235, 39, 46, "Input"], +Cell[17536, 499, 434, 7, 70, "Input"], +Cell[17973, 508, 300, 7, 46, "Input"], +Cell[18276, 517, 2079, 45, 110, "Input"], +Cell[20358, 564, 54, 1, 30, "Input"], +Cell[20415, 567, 1246, 39, 46, "Input"], +Cell[21664, 608, 430, 7, 70, "Input"], +Cell[22097, 617, 292, 6, 49, "Input"], +Cell[22392, 625, 1728, 38, 70, "Input"], +Cell[24123, 665, 1246, 39, 46, "Input"], +Cell[25372, 706, 430, 7, 70, "Input"], +Cell[25805, 715, 405, 10, 46, "Input"], +Cell[26213, 727, 228, 4, 50, "Input"], +Cell[26444, 733, 700, 16, 66, "Input"], +Cell[27147, 751, 46, 1, 30, "Input"], +Cell[27196, 754, 324, 6, 50, "Input"], +Cell[27523, 762, 52, 1, 30, "Input"], +Cell[27578, 765, 162, 2, 30, "Input"], +Cell[27743, 769, 411, 10, 46, "Input"], +Cell[28157, 781, 275, 5, 50, "Input"], +Cell[28435, 788, 307, 5, 50, "Input"], +Cell[28745, 795, 307, 5, 50, "Input"], +Cell[29055, 802, 115, 2, 30, "Input"], +Cell[29173, 806, 337, 7, 49, "Input"], +Cell[29513, 815, 570, 11, 66, "Input"], +Cell[30086, 828, 566, 11, 90, "Input"], +Cell[30655, 841, 73, 1, 30, "Input"], +Cell[30731, 844, 346, 8, 30, "Input"], +Cell[31080, 854, 143, 3, 30, "Input"], +Cell[31226, 859, 244, 4, 30, "Input"], +Cell[31473, 865, 285, 5, 46, "Input"], +Cell[31761, 872, 460, 10, 90, "Input"], +Cell[32224, 884, 380, 9, 46, "Input"], +Cell[32607, 895, 275, 5, 50, "Input"], +Cell[32885, 902, 163, 3, 50, "Input"], +Cell[33051, 907, 333, 7, 49, "Input"], +Cell[33387, 916, 585, 11, 66, "Input"], +Cell[33975, 929, 4213, 77, 552, "Input"], +Cell[38191, 1008, 71, 1, 30, "Input"], +Cell[38265, 1011, 262, 5, 30, "Input"], +Cell[38530, 1018, 1452, 41, 30, "Input"], +Cell[39985, 1061, 1453, 41, 30, "Input"], +Cell[41441, 1104, 1453, 41, 30, "Input"], +Cell[42897, 1147, 69, 1, 30, "Input"], +Cell[42969, 1150, 262, 5, 30, "Input"], +Cell[43234, 1157, 1452, 41, 30, "Input"], +Cell[44689, 1200, 1453, 41, 30, "Input"], +Cell[46145, 1243, 1454, 41, 30, "Input"], +Cell[47602, 1286, 285, 5, 46, "Input"], +Cell[47890, 1293, 728, 13, 150, "Input"], +Cell[48621, 1308, 350, 9, 46, "Input"], +Cell[48974, 1319, 277, 5, 50, "Input"], +Cell[49254, 1326, 161, 3, 30, "Input"], +Cell[49418, 1331, 185, 3, 30, "Input"] +} +] +*) + + + +(******************************************************************* +End of Mathematica Notebook file. +*******************************************************************) + -- cgit v1.2.3