(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' 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). 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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[ 1295755, 30221]*) (*NotebookOutlinePosition[ 1296450, 30245]*) (* CellTagsIndexPosition[ 1296406, 30241]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ RowBox[{ StyleBox["\:30d0\:30cd\:306e\:632f\:52d5\:306e\:65b9\:7a0b\:5f0f", "Text", FontSize->16, FontColor->RGBColor[1, 0, 1]], StyleBox[" ", "Text", FontSize->16, FontColor->RGBColor[1, 0, 1]], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`x'' \((t)\) + x(t) = 0\)]]]], StyleBox[" ", "Text", FontSize->16, FontColor->RGBColor[1, 0, 1]], StyleBox["\:3092\:89e3\:304f", "Text", FontSize->16, FontColor->RGBColor[1, 0, 1]]}]], "Input"], Cell[BoxData[{ StyleBox["\:521d\:671f\:6761\:4ef6", "Text"], "\[IndentingNewLine]", RowBox[{ StyleBox[" ", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`x(0) = 1, x' \((0)\) = 0\)]]]]}], "\[IndentingNewLine]", "\:306e\:3082\:3068\:3067\:89e3\:304f\:3068"}], "Input"], Cell[BoxData[ RowBox[{" ", Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(\(\ \ \)\(x( t) = \(\(Cos\)\(\ \)\(t\)\(\ \)\)\)\)\)]]]]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["\:6642\:523b", "Text", FontColor->RGBColor[1, 0, 1]], StyleBox[" ", "Text", FontColor->RGBColor[1, 0, 1]], StyleBox[Cell[TextData[Cell[BoxData[ \(TraditionalForm\`t = k\/n\)]]]], FontColor->RGBColor[1, 0, 1]], StyleBox[ "\:306b\:304a\:3051\:308b\:30d0\:30cd\:306e\:4f4d\:7f6e\:306f", FontColor->RGBColor[1, 0, 1]], StyleBox[" ", FontColor->RGBColor[1, 0, 1]], StyleBox[Cell[TextData[Cell[BoxData[ \(TraditionalForm\`x(t) = Cos(k\/n)\)]]]], FontColor->RGBColor[1, 0, 1]], StyleBox[" ", FontColor->RGBColor[1, 0, 1]], StyleBox["\:3060\:304b\:3089", FontColor->RGBColor[1, 0, 1]]}], StyleBox[",", FontColor->RGBColor[1, 0, 1]], StyleBox[ RowBox[{Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(\(k = 0\)\(,\)\(1\)\(,\)\(2\)\(,\)\(3\)\(\ \)\)\)]]]], " ", \(\(\:3068\:9806\:306b\:4ee3\:5165\:3059\:308b\:3068\:305d\ \:306e\:6642\:523b\:306b\:304a\:3051\:308b\:4f4d\:7f6e\:304c\:308f\:304b\:308b\ \)\(.\)\)}], FontColor->RGBColor[1, 0, 1]]}]], "Input"], Cell[BoxData[ \(Clear[T, F, g]; T[n_, k_] := {PointSize[0.02], RGBColor[1, 0, 0], Point[{N[Cos[k/n]], 0}]}; F[n_, k_] := Graphics[T[n, k], \[IndentingNewLine]AspectRatio \[Rule] Automatic, PlotRange \[Rule] {{\(-2\), 2}, {\(-0.5\), 0.5}}, Axes \[Rule] True, Ticks -> {{\(-1\), 1}, None}, DisplayFunction \[Rule] Identity]; g[n_] := Do[ Show[F[n, k], DisplayFunction \[Rule] $DisplayFunction], {k, 0, 4 \[Pi]*n, 1}]\)], "Input"], Cell[BoxData[ RowBox[{" ", RowBox[{Cell[TextData[Cell[BoxData[ \(TraditionalForm\`x'' \((t)\) + x(t) = 0\)]]]], "\[IndentingNewLine]", StyleBox[\(\:3092\:89e3\:304f\:3068\:306f, \(\(\:4ee5\:4e0b\:306e\ \:3088\:3046\:306a\:52d5\:304d\:3092\:6c7a\:3081\:308b\:3053\:3068\:3067\:3042\ \:308b\)\(.\)\)\), FontSize->16, FontColor->RGBColor[1, 0, 1]]}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(g[20]\)], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! 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%%Creator: Mathematica %%AspectRatio: .25 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.25 0.125 0.25 [ [.25 .1125 -6 -9 ] [.25 .1125 6 0 ] [.75 .1125 -3 -9 ] [.75 .1125 3 0 ] [ 0 0 0 0 ] [ 1 .25 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .25 .125 m .25 .13125 L s [(-1)] .25 .1125 0 1 Mshowa .75 .125 m .75 .13125 L s [(1)] .75 .1125 0 1 Mshowa 0 .125 m 1 .125 L s .5 0 m .5 .25 L s 0 0 m 1 0 L 1 .25 L 0 .25 L closepath clip newpath 1 0 0 r .02 w .59837 .125 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{298, 74.5}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False, Background->GrayLevel[0.501961]], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .25 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.25 0.125 0.25 [ [.25 .1125 -6 -9 ] [.25 .1125 6 0 ] [.75 .1125 -3 -9 ] [.75 .1125 3 0 ] [ 0 0 0 0 ] [ 1 .25 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .25 .125 m .25 .13125 L s [(-1)] .25 .1125 0 1 Mshowa .75 .125 m .75 .13125 L s [(1)] .75 .1125 0 1 Mshowa 0 .125 m 1 .125 L s .5 0 m .5 .25 L s 0 0 m 1 0 L 1 .25 L 0 .25 L closepath clip newpath 1 0 0 r .02 w .60974 .125 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{298, 74.5}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False, Background->GrayLevel[0.501961]], Cell[GraphicsData["PostScript", "\<\ %! 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