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Diffstat (limited to 'Bachelor/Numerische Mathematik/Num05Aufg4C.nb')
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diff --git a/Bachelor/Numerische Mathematik/Num05Aufg4C.nb b/Bachelor/Numerische Mathematik/Num05Aufg4C.nb new file mode 100644 index 0000000..1ba3a2b --- /dev/null +++ b/Bachelor/Numerische Mathematik/Num05Aufg4C.nb @@ -0,0 +1,1452 @@ +(************** Content-type: application/mathematica **************
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+ 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] "\<K\>",
+ 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[
+ \(\(nummer[lauf] = m;\)\)], "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\ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 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\ einer\ Acht\ \ \ \ \ \ \ *) \),
+ 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[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] = \(-3\)\ Cos[tach[j]] - 1.5,
+ yach[j] = 3*Sin[1.5 tach[j]]}, {j, \(-100\),
+ 100}]\), "\[IndentingNewLine]",
+ \(Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] = \(-6\) + \ 3*tach[j],
+ yach[j] = \(-1.5\) xach[j]}, {j, 101,
+ 150}]\), "\[IndentingNewLine]",
+ \(Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] = 6\ - \ 3*tach[251 + j],
+ yach[j] =
+ 1.5 xach[j]}, {j, \(-150\), \(-101\)}]\), "\[IndentingNewLine]",
+ \(\ Do[{\
+ tach[j] =
+ 8. *ArcTan[1]/nd*
+ j, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xach[j] =
+ 1.5 + \ 3*Cos[tach[\(-250\) + j]],
+ yach[j] = 3*Sin[1.5 tach[\(-250\) + j]]}, {j, 151, 360}]\)}], "Input"],
+
+Cell[BoxData[
+ \(\(\(\ \)\(Do[
+ tj[j] = tp[0] + j*\((tp[m] - tp[0])\)/nd, {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\ \
+Acht\ \ aus\ \ Kreisb\[ODoubleDot]gen\ \ x\ = \ \(3*
+ cos \((t)\)\ \ und\ \ y\ = \ \(3*
+ sin \((t)\)\ und\ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ \ linearen\ Teilen\ x\ = \ \(-6\) + 3*t\)\)\ , \
+ y\ = \ \(\(-1.5\)*x\ \ \ \ und\ \ x\ = \ 6 - 3*t\)\ , \
+ y\ = \ 1.5*x\ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ \(achtplot =
+ ListPlot[Table[{xach[j], yach[j]}, {j, \(-146\), 360}],
+ PlotJoined\ \[Rule] True, \n\t
+ PlotRange -> {{\(-6\), 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 -> {{\(-6\), 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 -> {{\(-6\), 5}, {\(-4\), 4}}, \n\tPlotStyle -> Blue,
+ Prolog\ -> \ AbsolutePointSize[5], AspectRatio -> 0.5,
+ AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(Show[achtplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)], "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[
+ RowBox[{
+ RowBox[{\(DivDiffxmat = FunkDivDiff[tp, xp]\ ;\), "\n",
+ 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]]}],
+ "\n", \(DivDiffymat = FunkDivDiff[tp, yp]\ ;\),
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ RowBox[{\(DivDiffy = DivDiffymat[\([1]\)];\), " ",
+
+ StyleBox[\( (*\ \ Dividierte\ Differenzen\ f\[UDoubleDot]r\ die\ y \
+- Werte\ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]]}]}],
+ "\[IndentingNewLine]"}]], "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 -> {{\(-6.0\), 5}, {\(-4\), 4}}, \tPlotStyle -> Red,
+ AspectRatio -> 0.5, AxesLabel -> {"\<> x\>", "\< ^ y\>"}]\)], "Input"],
+
+Cell[BoxData[
+ \(\(\(Show[achtplot, newtonplot, linienplot, punktplot,
+ Prolog\ -> \ AbsolutePointSize[5]]\)\(\[IndentingNewLine]\)
+ \)\)], "Input"],
+
+Cell[BoxData[
+ RowBox[{" ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ Periodische\ Spline -
+ Interpolation\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \
+\),
+ "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\ \
+periodischen\ Spline - Interpolation\ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], " "}]], "Input",
+ Background->RGBColor[1, 1, 0]],
+
+Cell[BoxData[
+ RowBox[{\(FunkPerSpl[xpform_, ypform_]\), ":=", " ",
+ RowBox[{
+ "(", "\[IndentingNewLine]", " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Erstellen\ der\ \
+"\<fast\>"\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]], "\n",
+ " ",
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \((\
+ Haupt - \ und\ Nebendiagonale\ )\)\ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ RowBox[{\(Du[0] = xpform[1] - xpform[0]\), ";",
+ " ", \(Du[m - 1] = xpform[m] - xpform[m - 1]\), ";",
+ "\[IndentingNewLine]", \(Dh[0] = 2*\((\ Du[m - 1] + Du[0]\ )\)\),
+ ";", "\n",
+ " ", \(Do[{Du[k] = xpform[k + 1] - xpform[k],
+ Dh[k] = 2 \((Du[k - 1] + Du[k])\), Dp[k] = 0}, {k, 1, m - 2}]\),
+ ";", "\[IndentingNewLine]", \(Dp[m - 2] = Du[m - 2]\), ";",
+ " ", \(Dh[m - 1] = 2*\((\ Du[m - 2] + Du[m - 1])\)\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ Cholesky -
+ Zerlegung\ der\ "\<fast\>"\ Tridiagonalmatrix\ \ \ \ \ \ \ \ \
+\ *) \),
+ "Subsubtitle",
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Ch[0] = Sqrt[Dh[0]]\), ";",
+ " ", \(Cp[0] = Du[m - 1]/Ch[0]\), ";", "\n",
+ " ", \(Do[{Cn[k - 1] = Du[k - 1]/Ch[k - 1],
+ Ch[k] = Sqrt[Dh[k] - Cn[k - 1]^2], \ \ \ Cp[
+ k] = \((\ Dp[k] - Cp[k - 1]*Cn[k - 1]\ )\)/Ch[k]}, {k, 1,
+ m - 2}]\), ";", "\[IndentingNewLine]", " ", \(Csum = 0\),
+ ";", " ", \(Do[\ Csum = Csum + Cp[i]^2, {i, 1, m - 2}]\), ";",
+ "\[IndentingNewLine]", " ", \(Cn[m - 2] = Cp[m - 2]\), ";",
+ " ", \(Ch[m - 1] = Sqrt[\ Dh[m - 1] - Csum]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ Vorw\[ADoubleDot]rtsrechnung\ \
+"\<von oben her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ und\ Erstellen\ der\ rechten\ \
+Seite\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ "\[IndentingNewLine]", \(Dv[0] = ypform[1] - ypform[0]\), ";",
+ " ", \(Dv[m - 1] = ypform[m] - ypform[m - 1]\), ";", "\n",
+ " ", \(Dr[0] = 3 \((Dv[0]/Du[0] - Dv[m - 1]/Du[m - 1])\)\), ";",
+ "\n", " ", \(Z[0] = Dr[0]/Ch[0]\), ";", "\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, 1, m - 1}]\), ";",
+ "\[IndentingNewLine]", " ", \(Zsum = 0\), ";",
+ " ", \(Do[\ Zsum = Zsum + Cp[i]*Z[i], {i, 0, m - 2}]\), ";",
+ "\[IndentingNewLine]",
+ " ", \(Z[m - 1] = \((\ Dr[m - 1] - Zsum\ )\)/Ch[m - 1]\), ";",
+ "\[IndentingNewLine]", " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R\[UDoubleDot]ckw\
+\[ADoubleDot]rtsrechnung\ "\<von unten her\>"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
+\ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox["\n",
+ FontColor->RGBColor[1, 0, 1]], " ",
+
+ StyleBox[\( (*\ \ \ \ \ \ \ \ \ \ \ \ \tBerechnung\ der\ \
+Koeffizienten\ B\_k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ *) \),
+ FontColor->RGBColor[1, 0, 1]], "\[IndentingNewLine]",
+ " ", \(Cp[m - 2] = 0\), ";", "\[IndentingNewLine]",
+ " ", \(B[m - 1] = Z[m - 1]/Ch[m - 1]\), ";", "\n",
+ " ", \(Do[
+ B[k] = \((\ Z[k] - B[k + 1]*Cn[k] - Cp[k]*B[m - 1])\)/Ch[k], {k,
+ m - 2, 0, \(-1\)}]\), ";", "\[IndentingNewLine]",
+ " ", \(B[m] = B[0]\), ";", "\[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[
+ RowBox[{
+ RowBox[{\(ABCDxmat = FunkPerSpl[tp, xp]\ \ ;\), "\n",
+ RowBox[{\(Aperx = ABCDxmat[\([1]\)]\ ;\), " ",
+
+ StyleBox[\( (*\
+ Koeffizienen\ Ak\ \ \(f \[UDoubleDot]r\)\ die\ x -
+ Werte\ *) \),
+ FontColor->RGBColor[1, 0, 1],
+ Background->None]}], "\n", \(Bperx = 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]]}],
+ "\n", \(Cperx = ABCDxmat[\([3]\)];\), " ",
+ RowBox[{
+ StyleBox["(*",
+ FontColor->RGBColor[1, 0, 1]],
+ StyleBox[" ",
+ FontColor->RGBColor[1, 0, 1]],
+ RowBox[{
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+ 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]]}],
+ "\n", \(Dperx = 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],
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