/Users/yamada/Documents/webPage/public_html/kkk/ 8 プロット

8 8 Mathematica y = f(x) Plot Plot[f, {x, xmin, xmax}] f x x xmin ~ xmax In[]:= Plot@Sin@xD, 8x,, Pi<D. -. 3 4 6 - Out[]= In[]:= Ü Graphics Ü Plot@Tan@xD, 8x,, Pi<D 4 3 4 6 - -4 Out[]= Ü Graphics Ü y=tan(x) - Plot Plot[{f, f,...}, {x, xmin, xmax}] f, f,...

8 In[3]:= Plot@8Sin@xD, Cos@xD, Tan@xD<, 8x,, Pi<D 6 4 - -4-6 3 4 6 Out[3]= Ü Graphics Ü y=tan(x) sin(x), cos(x) Plot x, y Plot Plot option->value Plot[f, {x, xmin, xmax}, option->value, option->value,...] Frame->True PlotRange-> {-., } -. In[4]:= Plot@Sin@xD, 8x,, Pi<, Frame -> True, PlotRange -> 8-., <D.8.6.4. -. -.4 3 4 6 Out[4]= Ü Graphics Ü Automatic None All True False Plot

8 3 AspectRatio ê GoldenRatio ê GoldenRatio.6 Automatic PlotLabel None. PlotRange Automatic 8ymin, ymax< Automatic All Axes Automatic False. AxesLabel None x y 8xlabel, ylabel< AxesOrigin Automatic Ticks Automatic 88x, x,...<, 8y, y,...<< None Frame False True. FrameLabel None FrameTicks Automatic None GridLine None 88x, x,...<, 8y, y,... Automatic PlotStyle Automatic HThicknessL HGrayLevel, RGBColorL 8Thickness@.8D, GrayLevel@.D, Dashing@8.,. PlotPoints Options In[]:= Out[]= Options@PlotD 9AspectRatio Ø ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ, Axes Ø Automatic, AxesLabel Ø None, GoldenRatio AxesOrigin Ø Automatic, AxesStyle Ø Automatic, Background Ø Automatic, ColorOutput Ø Automatic, Compiled Ø True, DefaultColor Ø Automatic, DefaultFont ß $DefaultFont, DisplayFunction ß $DisplayFunction, Epilog Ø 8<, FormatType ß $FormatType, Frame Ø False, FrameLabel Ø None, FrameStyle Ø Automatic, FrameTicks Ø Automatic, GridLines Ø None, ImageSize Ø Automatic, MaxBend Ø., PlotDivision Ø 3., PlotLabel Ø None, PlotPoints Ø, PlotRange Ø Automatic, PlotRegion Ø Automatic, PlotStyle Ø Automatic, Prolog Ø 8<, RotateLabel Ø True, TextStyle ß $TextStyle, Ticks Ø Automatic= "sin curve" "x", "sin(x)" a (Thickness) (GrayLevel) (Dashing)

8 4 In[6]:= sincurve = Plot@Sin@xD, 8x,, Pi<, AspectRatio -> Automatic, PlotLabel -> "sin curve", PlotRange -> 8-.8, <, Axes -> True, AxesLabel -> 8"x", "sinhxl"<, AxesOrigin -> 8Pi ê 3, <, Ticks -> 88, Pi ê, Pi, 3 Pi ê, Pi<, 8-.,,.,, <<, Frame -> True, FrameTicks -> None, GridLines -> 88,,, 3, 4,, 6<, None<, PlotStyle -> 8Thickness@.D, GrayLevel@.D, Dashing@8.,.3<D<D sinhxl sin curve. p -. p 3 p p x Out[6]= Ü Graphics Ü Plot Show PlotStyle PlotPoints Show[g, option->value, option->value,...] g In[7]:= Show@sinCurve, PlotRange -> 88, 3 Pi ê <, All<, Frame -> False, GridLines -> 88,, 4, 6<, None<D sinhxl sin curve. p -. p x 3 p Out[7]= Ü Graphics Ü PlotRangeØ{{xmin,xmax},{ymin,ymax}} PlotStyle->{{- Thickness[.],...}, {Thickness[.],...},...}

8 In[8]:= coscurve = Plot@8Cos@xD, Cos@ xd<, 8x,, Pi<, PlotStyle Ø 88Thickness@.D, GrayLevel@.D, Dashing@8.4,.<D<, 8Thickness@.D, GrayLevel@.8D<<D. 3 4 6 -. - Out[8]= Ü Graphics Ü Show Show[{g, g,... gk}, option->value,...] g, g,..., gk option,... g In[9]:= Show@8sinCurve, coscurve<, PlotRange -> All, Frame -> False, GridLines -> None, PlotLabel -> None, AxesLabel -> 8"x", None<D. p -. p 3 p p x Out[9]= Ü Graphics Ü g, g,... gk gk y = sinhxl - x ê 4 y = coshxl {d, d,..., dk} List- Plot ListPlot[{d, d,..., dk}, option->value,...] x, y (i, di) In[]:= data = Table@Random@D, 8<D Out[]= 8.3499,.788764,.9897,.398,.696,.88483,.487,.4487,.9483,.94699<

8 6 In[]:= ListPlot@dataD.8.6.4 4 6 8 Out[]= Ü Graphics Ü PlotJoined->True In[]:= ListPlot@data, PlotJoined -> TrueD.8.6.4 4 6 8 Out[]= Ü Graphics Ü ListPlot[{{x,y},{x,y},...},optionØvalue,...] (xi,yi) In[3]:= data = Table@8Random@D, Random@D<, 8<D Out[3]= 88.386,.8897<, 8.779,.773<, 8.6787,.94974<, 8.6944,.988<, 8.88,.836<, 8.78,.4736<, 8.379,.9493<, 8.7634,.6897<, 8.498,.87<, 8.437,.797783<< In[4]:= ListPlot@dataD.8.6.4..3.4..6.7 Out[4]= Ü Graphics Ü PlotJoined->True

8 7 In[]:= ListPlot@data, PlotJoined -> TrueD.8.6.4..3.4..6.7 Out[]= Ü Graphics Ü ListPlot Plot AspectRatio,Axes,AxesLabel,Axes- Origin,Frame,FrameLabel,FrameTicks,GridLines,PlotLabel,PlotRange,Ticks t (x(t), y(t)) x, y ParametricPlot ParametricPlot ParametricPlot[{x, y}, {t, tmin, tmax}] x, y t (x, y) t = tmin~tmax ParametricPlot[{{x, y}, {x, y},...}, {t, tmin, tmax}] (cos(t), sin(t)) t=~p Automatic In[6]:= ParametricPlot@8Cos@tD, Sin@tD<, 8t,, Pi<, AspectRatio -> AutomaticD. - -.. -. - Out[6]= Ü Graphics Ü

8 8 (cos(3t), sin(4t)) t=~p z = f(x,y) Plot3D DensityPlot ContourPlot Plot3D Plot3D[f, {x, xmin, xmax}, {y, ymin, ymax}] f x y z = f(x, y) In[7]:= sinxy = Plot3D@Sin@x yd, 8x, -3, 3<, 8y, -3, 3<D. -. - - - Out[7]= Ü SurfaceGraphics Ü Plot3D Plot3D Mesh True Shading True. PlotRange Automatic All 8zmin, zmax< 88xmin, xmax<, 8ymin, ymax<, 8zmin, zmax<< Axes Automatic False. AxesLabel None 8xlabel, ylabel, zlabel< z Boxed True ColorFunction Automatic FaceGrid None FrameLabel None

8 9 HiddenSurface True Lighting True PlotPoints In[8]:= Out[8]= Options@Plot3DD 8AmbientLight Ø GrayLevel@D, AspectRatio Ø Automatic, Axes Ø True, AxesEdge Ø Automatic, AxesLabel Ø None, AxesStyle Ø Automatic, Background Ø Automatic, Boxed Ø True, BoxRatios Ø 8,,.4<, BoxStyle Ø Automatic, ClipFill Ø Automatic, ColorFunction Ø Automatic, ColorFunctionScaling Ø True, ColorOutput Ø Automatic, Compiled Ø True, DefaultColor Ø Automatic, DefaultFont ß $DefaultFont, DisplayFunction ß $DisplayFunction, Epilog Ø 8<, FaceGrids Ø None, FormatType ß $FormatType, HiddenSurface Ø True, ImageSize Ø Automatic, Lighting Ø True, LightSources Ø 888.,.,.<, RGBColor@,, D<, 88.,.,.<, RGBColor@,, D<, 88.,.,.<, RGBColor@,, D<<, Mesh Ø True, MeshStyle Ø Automatic, Plot3Matrix Ø Automatic, PlotLabel Ø None, PlotPoints Ø, PlotRange Ø Automatic, PlotRegion Ø Automatic, Prolog Ø 8<, Shading Ø True, SphericalRegion Ø False, TextStyle ß $TextStyle, Ticks Ø Automatic, ViewCenter Ø Automatic, ViewPoint Ø 8.3, -.4,.<, ViewVertical Ø 8.,.,.<< Show PlotPoints x=~3, y=~3, z=-~/ In[9]:= Show@sinxy, PlotRange -> 88, 3<, 8, 3<, 8-, ê <<D. -. - 3 3 Out[9]= Ü SurfaceGraphics Ü x, y, z

8 In[]:= Show@sinxy, Boxed -> False, AxesLabel -> 8"x", "y", "z"<d z. -. - - y x - Out[]= Ü SurfaceGraphics Ü In[]:= Show@sinxy, FaceGrids -> All, Mesh -> FalseD. -. - - - Out[]= Ü SurfaceGraphics Ü In[]:= Show@sinxy, Axes -> False, Boxed -> False, HiddenSurface -> FalseD Out[]= Ü SurfaceGraphics Ü

8 In[3]:= Plot3D@Sin@x yd, 8x, -3, 3<, 8y, -3, 3<, PlotPoints ->, Mesh -> False, Axes -> FalseD Out[3]= Ü SurfaceGraphics Ü DensityPlot Plot3D DensityPlot DensityPlot[f, {x, xmin, xmax}, {y, ymin, ymax}], f x, y x = xmin~xmax, y = ymin~ymax In[4]:= DensityPlot@Sin@x yd, 8x, -3, 3<, 8y, -3, 3<D 3 - - -3-3 - - 3 Out[4]= Ü DensityGraphics Ü DensityPlot

8 In[]:= Out[]= Options@DensityPlotD 8AspectRatio Ø, Axes Ø False, AxesLabel Ø None, AxesOrigin Ø Automatic, AxesStyle Ø Automatic, Background Ø Automatic, ColorFunction Ø Automatic, ColorFunctionScaling Ø True, ColorOutput Ø Automatic, Compiled Ø True, DefaultColor Ø Automatic, DefaultFont ß $DefaultFont, DisplayFunction ß $DisplayFunction, Epilog Ø 8<, FormatType ß $FormatType, Frame Ø True, FrameLabel Ø None, FrameStyle Ø Automatic, FrameTicks Ø Automatic, ImageSize Ø Automatic, Mesh Ø True, MeshStyle Ø Automatic, PlotLabel Ø None, PlotPoints Ø, PlotRange Ø Automatic, PlotRegion Ø Automatic, Prolog Ø 8<, RotateLabel Ø True, TextStyle ß $TextStyle, Ticks Ø Automatic< [ <--> ] ColorFunction ColorFunction ~ GrayLevel x, y x, y 3 In[6]:= DensityPlot@Sin@x yd, 8x, -3, 3<, 8y, -3, 3<, PlotPoints -> 3, Mesh -> False, ColorFunction -> HGrayLevel@ - #D &LD 3 - - -3-3 - - 3 Out[6]= Ü DensityGraphics Ü GrayLevel[] GrayLevel[] ContourPlot CountourPlot ContourPlot[f, {x, xmin, xmax}, {y, ymin, ymax}] f x, y x = xmin~xmax, y = ymin~ymax

8 3 In[7]:= ContourPlot@Sin@x yd, 8x, -3, 3<, 8y, -3, 3<D 3 - - -3-3 - - 3 Out[7]= Ü ContourGraphics Ü Plot3D ContourPlot ContourPlot Options[ContourPlot] In[8]:= Out[8]= Options@ContourPlotD 8AspectRatio Ø, Axes Ø False, AxesLabel Ø None, AxesOrigin Ø Automatic, AxesStyle Ø Automatic, Background Ø Automatic, ColorFunction Ø Automatic, ColorFunctionScaling Ø True, ColorOutput Ø Automatic, Compiled Ø True, ContourLines Ø True, Contours Ø, ContourShading Ø True, ContourSmoothing Ø True, ContourStyle Ø Automatic, DefaultColor Ø Automatic, DefaultFont ß $DefaultFont, DisplayFunction ß $DisplayFunction, Epilog Ø 8<, FormatType ß $FormatType, Frame Ø True, FrameLabel Ø None, FrameStyle Ø Automatic, FrameTicks Ø Automatic, ImageSize Ø Automatic, PlotLabel Ø None, PlotPoints Ø, PlotRange Ø Automatic, PlotRegion Ø Automatic, Prolog Ø 8<, RotateLabel Ø True, TextStyle ß $TextStyle, Ticks Ø Automatic< x, y 3 ColorFunction

8 4 In[9]:= ContourPlot@Sin@x yd, 8x, -3, 3<, 8y, -3, 3<, PlotPoints -> 3, ColorFunction -> HGrayLevel@# ê + ê D &LD 3 - - -3-3 - - 3 Out[9]= Ü ContourGraphics Ü {{f, f,..., fn}, {f, f,..., fn},..., {fm, fm,..., fmn}} ListPlot3D, ListDensityPlot, ListContour- Plot ListPlot3D ListPlot3D[{{f,..., fn},..., {fm,..., fmn}}] x=i, y=j z=fij µ ListPlot3D In[3]:= data = Table@i j + Mod@i ^ j, 7D, 8i, <, 8j, <D Out[3]= 88,, 3, 4,, 6, 7, 8, 9,,,, 3, 4, <, 8, 44, 6, 8,,, 34, 6, 8, 4, 6, 34, 46, 68, 4<, 833, 6, 69,, 6, 8,, 44, 87, 7, 83, 46, 69, 6, <, 844, 8,, 6, 4, 34, 68,, 46, 8, 64, 8, 9, 76, 7<, 8,, 7, 4,, 4, 8, 8,, 7, 8, 7,,, 3<, 866,, 78, 34, 9, 46,, 8, 4, 7, 6, 8, 38, 94, <, 87, 4,, 8, 3, 4, 49, 6, 63, 7, 77, 84, 9, 98, <, 88, 6, 34, 4,, 8, 66, 74, 8, 9, 98, 6, 4,, 3<, 89, 8, 37, 6, 8, 64, 83,, 9,, 39, 8, 37, 66, 4<, 84, 4, 9, 8,, 7,,,, 4, 6, 3, 6, 6, <, 8, 4, 43, 84, 7, 76, 7, 8, 9,, 4, 4, 83, 74, 7<, 86, 64, 96, 68, 9, 8, 34, 36, 68, 4, 6, 4, 6, 8, 4<, 873, 36, 99, 6,, 88,, 4, 77, 4, 3, 66, 9, 9, <, 84, 8, 4, 6, 7, 84, 98,, 6, 4, 4, 68, 8, 96, <, 8, 4,, 7, 8,,, 3, 4, 6, 7, 9,,, 3<<

8 In[3]:= ListPlot3D@dataD Out[3]= Ü SurfaceGraphics Ü ListPlot3D In[3]:= Out[3]= Options@ListPlot3DD 8AmbientLight Ø GrayLevel@D, AspectRatio Ø Automatic, Axes Ø True, AxesEdge Ø Automatic, AxesLabel Ø None, AxesStyle Ø Automatic, Background Ø Automatic, Boxed Ø True, BoxRatios Ø 8,,.4<, BoxStyle Ø Automatic, ClipFill Ø Automatic, ColorFunction Ø Automatic, ColorFunctionScaling Ø True, ColorOutput Ø Automatic, DefaultColor Ø Automatic, DefaultFont ß $DefaultFont, DisplayFunction ß $DisplayFunction, Epilog Ø 8<, FaceGrids Ø None, FormatType ß $FormatType, HiddenSurface Ø True, ImageSize Ø Automatic, Lighting Ø True, LightSources Ø 888.,.,.<, RGBColor@,, D<, 88.,.,.<, RGBColor@,, D<, 88.,.,.<, RGBColor@,, D<<, Mesh Ø True, MeshRange Ø Automatic, MeshStyle Ø Automatic, Plot3Matrix Ø Automatic, PlotLabel Ø None, PlotRange Ø Automatic, PlotRegion Ø Automatic, Prolog Ø 8<, Shading Ø True, SphericalRegion Ø False, TextStyle ß $TextStyle, Ticks Ø Automatic, ViewCenter Ø Automatic, ViewPoint Ø 8.3, -.4,.<, ViewVertical Ø 8.,.,.<< ListDensityPlot ListDensityPlot[{{f,..., fn},..., {fm,..., fmn}}] fij ListDensityPlot [ <--> ]

8 6 In[33]:= ListDensityPlot@dataD 4 8 6 4 4 6 8 4 Out[33]= Ü DensityGraphics Ü ListContourPlot ListContourPlot[{{f,..., fn},..., {fm,..., fmn}}] fij In[34]:= ListContourPlot@dataD 4 8 6 4 4 6 8 4 Out[34]= Ü ContourGraphics Ü ParametricPlot3D

8 7 ParametricPlot3D[{x, y, z}, {t, tmin, tmax}] x, y, z t (x, y, z) t = tmin~tmax In[3]:= ParametricPlot3D@8Cos@tD, Sin@tD, t ê 4<, 8t,, 4 Pi<D - -... -. - 3 Out[3]= Ü Graphics3D Ü ParametricPlot3D[{x, y, z}, {t, tmin, tmax}, {u, umin, umax}] x, y, z t, u (x, y, z) t = tmin~tmax, u = umin~umax t H- ÅÅÅ p t ÅÅÅ p L u H u pl HcosHtL coshul, coshtl sinhul, sinhtll In[36]:= sphere = ParametricPlot3D@ 8Cos@tD Cos@uD, Cos@tD Sin@uD, Sin@tD<, 8t, -Pi ê, Pi ê <, 8u,, Pi<D -. -.. -. - - -.. Out[36]= Ü Graphics3D Ü

8 8 (torus) R r HcosHtL HR + r coshull, sinhtl HR + r coshull, r sinhull In[37]:= R = ; r = ê ; In[38]:= torus = ParametricPlot3D@8Cos@tD HR + r Cos@uDL, Sin@tD HR + r Cos@uDL, r Sin@uD<, 8t,, Pi<, 8u,, Pi<, Axes -> False, Boxed -> FalseD Out[38]= Ü Graphics3D Ü Show In[39]:= Show@torus, sphere, PlotRange -> 88-3, <, 8-, 3<, 8-, ê <<, ViewPoint -> 8.3, -, <D Out[39]= Ü Graphics3D Ü ] (Cell) (Animate Selected Graphics) In[4]:= Table@Plot3D@Sin@Sqrt@x^ + y ^D - td, 8x, -, <, 8y, -, <, PlotPoints Ø, Mesh Ø FalseD, 8t, Pi ê, Pi, Pi ê <D

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8. -. - - - - -. -. - - - - - Out[4]= 8Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü, Ü SurfaceGraphics Ü< [-] y = sinhxl + x y= ÅÅÅ 6 x - x x [-] y = x 3 - x - 4 x + 3 Plot H, -L ParametricPlot Show

8 6 [-3] -.. -. -. - - -.. [-4] - - - - - - [-]