ContourPlot[{x^+y^==,(x-)^+y^==}, {x,-,}, {y,-,}, AspectRatio -> Automatic].5. ContourPlot Plot AspectRatio->Automatic.. x a + y = ( ). b ContourPlot[

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1 5 3. Mathematica., : f(x) sin x Plot f(x, y) = x + y = ContourPlot f(x, y) > x 4 + (x y ) > RegionPlot (x(t), y(t)) (t sin t, cos t) ParametricPlot r = f(θ) r = sin 4θ PolarPlot.,. 5. x + y = (x, y). x, y. y, y = ± x,. ContourPlot.. f(x, y) = g(x, y) a x b, c y d ContourPlot[f==g,{x,a,b},{y,c,d}] ( == ). ContourPlot[x^+y^==, {x,-,}, {y,-,}] ( {} ).

2 ContourPlot[{x^+y^==,(x-)^+y^==}, {x,-,}, {y,-,}, AspectRatio -> Automatic].5. ContourPlot Plot AspectRatio->Automatic.. x a + y = ( ). b ContourPlot[x^/9 + y^/4 ==, {x, -3, 3}, {y,-,}, AspectRatio -> Automatic],. contour,.. ContourPlot[x^+y^, {x,-,}, {y,-,}], z = f(x, y), z

$x 4 + (x y ) > : RegionPlot[x^4+(x-y^)>, {x,-,}, {y,-,}],, <=, >=.$

3 5.,. RegionPlot. f(x, y) > a x b, c y d RegionPlot[f>, {x,a,b}, {y,c,d}]. x 4 + (x y ) > : RegionPlot[x^4+(x-y^)>, {x,-,}, {y,-,}],, <=, >=., BoundaryStyle->Dashed. 3

4 5.3 ( ) : ( ) c(t) = f(t), g(t), a t b ( ),, t f(t), g(t). Mathematica ParametricPlot[{f(t),g(t)}, {t,a,b}]. c(t) = (t sin t, cos t), ( t π). ParametricPlot[{t-Sin[t],-Cos[t]}, {t,,pi}] AspectRatio->Automatic. p x q, r y s PlotRange->{{p,q},{r,s}}.. {f(t),g(t)} {f(t),g(t)} t ParametricPlot[{{f(t),g(t)}, {f(t),g(t)}}, {t,a,b}]. {}. ParametricPlot[{{t-Sin[t],-Cos[t]}, {t-sin[t],+cos[t]}}, {t,,pi}] : c(t) = (cos(mt), sin(nt + a)), ( t π) m, n, a. (Lissajous),. m = 3, n = 5, a = 3 π : 4

5 ParametricPlot[{Cos[3t],Sin[5t-3Pi/]},{t,,Pi}]. f(t), g(t) x,y, ( m, n )., (x = ) x 3, (y = ) y 5. m = 3, n = 5. a t = (, sin a), 3 π,.. m, n, a?, Mathematica. 5

6 5.4 r = f(θ), a θ b. x θ, f(θ), θ. ( x = r cos θ, y = r sin θ θ c(θ) = (f(θ) cos θ, f(θ) sin θ).) Mathematica. r = f(t) a t b PolarPlot[f[t], {t,a,b}]. ( Mathematica θ t.) ( ) r = θ, ( θ 4π) : PolarPlot[t,{t,,4Pi}] PolarPlot AspectRatio->Automatic. PolarPlot. PolarPlot[{t, -t}, {t,, 4 Pi}] (r, θ) r,. 6

7 r = sin(nθ), ( θ π) (Rose). n. n = 4. PolarPlot[Sin[4t],{t,,Pi}] n. t, n = p q t qπ (sin( p q t) qπ, (r, θ) θ π ). n, (, ). PolarPlot[Sin[/5t],{t,,Pi}] PolarPlot[Sin[Sqrt[]t],{t,,3Pi}] Mathematica. (x + y ) = x y ( x, y ) [.] x 3 + y 3 = 6xy ( 4 x 4, 4 y 4) [ (folium)] 3 x + y y + x ( x, y ) 4 c(t) = (cos 3 t, sin 3 t) ( t π) [ ] 5 c(t) = (sin t, cos t + log(tan t )) ( < t < π) [ (tractrix). y, (, ). Hundkurve( ),.] 6 r = + cos θ ( θ π) [ (Cardioid),.] 7

8 7 (butterfly fancy butterfly) r = e sin θ cos(4θ) ( θ 4π) r = e sin θ cos(4θ) + sin 5 θ ( θ π) 8 ((chrysanthemum ( )) curve ( ) ) θ 7θ r = 5 + sin 4 sin 4 sin 8 ( cos (3θ) 8θ) ( θ π) a = π 3. Mathematica ( )... 8

9 A Mathematica,.. A.,,. Manipulate. x a + y = a, b 3, : b Manipulate[ContourPlot[x^/a^+y^/b^==, {x,-3,3}, {y,-3,3}, AspectRatio->Automatic], {a,, 3},{b,,3}] a.,, Manipulate. m, n, a : Manipulate[ParametricPlot[{Cos[m t], Sin[n t+a]}, {t,,pi}, PlotRange->{{-,},{-,}}], {a, -Pi, Pi}, {n,,, }, {n,,, }] {n,,,} n,.,a, m, n, PlotRange. A. :,,., f(x) = x,.,,.,., 3., f(x). f[x_] := Abs[x - Floor[x + /]] Plot[f[x], {x,, }, AspectRatio -> Automatic]

10 ,, k f(k x) k. saw[x, k]. saw[x_, k_] := f[^k x]/^k Manipulate[Plot[saw[x,k], {x,,}, PlotRange->{,}, AspectRatio->Automatic], {k,,,}] , k, Manipulate[...,{k,,,}] (k ).,, k., k takagi[x_, k_] := Sum[saw[x, i], {i,, k}] k., Sum[..., {i,, k}]. i= Manipulate[Plot[takagi[x,k],{x,,},PlotRange->{,},AspectRatio->Automatic],{k,,,}] k, T (x) = i= f( i x) i. 93,. Mathematica k,.... A.3 Mathematica. : f(x, y) sin(x + y )e x Plot3D f(x, y, z) = 6x x 4 y z = ContourPlot3D f(x, y, z) > x 4 + (x y ) z > RegionPlot3D (x(t), y(t), z(t)) (sin 3t, cos 4t, sin 5t) ParametricPlot3D

11 以下, 例を挙げることで説明としたい. まず Plot3D は変数関数の曲面グラフのプロットを行う. Plot3D[Sin[x^ + y^] Exp[-x^], {x, -, }, {y, -, }] 変数関数の等位面 f (x, y, z) = c は ContourPlot3D によって表わすことができる. ここで z 座標の範囲も指定していることに注意しよう. ContourPlot3D[6 x^ - x^4-y^ z^ ==, {x,-5,5}, {y,-5,5}, {z,-5,5}] 平面の場合と同様, 等式を不等式にするなら RegionPlot3D を使えばよい. RegionPlot3D[x^4 + (x - y^) - z >, {x,-,}, {y,-,}, {z,-,}]

12 ParametricPlot3D. ParametricPlot3D[{Sin[3 t],cos[4 t],sin[5 t]}, {t,,pi}],. PlotStyle. ParametricPlot3D[{Sin[3 t],cos[4 t],sin[5 t]}, {t,,pi}, PlotStyle->Tube[5]]

13 Manipulate. Manipulate[ ParametricPlot3D[{Sin[n t], Cos[4 m t], Sin[5 t]}, {t,, Pi}, PlotStyle -> Tube[5]], {n,,, }, {m,,, }] A.4, : ParametricPlot[{Cos[3 t] + / Cos[3 t], Sin[5 t - 3 Pi/] + / Sin[5 t]}, {t,, Pi}, AspectRatio -> Automatic] 3

14 PolarPlot[E^Cos[t] - Cos[6 t], {t,, Pi}] 3 PolarPlot[{Sin[Sqrt[E] t], Cos[Sqrt[E] t], Tan[Sqrt[E] t]}, {t,, 5 Pi}] 4

15 ContourPlot[y==Sum[(/)^n Cos[9^n Pi x], {n,, 3}], {x, -, }, {y, -, }] ParametricPlot[{Cos[5 t] + Sin[3 t], Sin[3 t] + Cos[5 Pi]}, {t,, Pi}].5. PolarPlot[Exp[Sin[3 t]] - Abs[ Cos[7 t]], {t,, 4 Pi}].5.5 5

16 追加問題 A.5 問題次の方程式で表わされる曲面を描け. 次頁の図を参考にして, 描画範囲は適当に指定すること.. x6 + y 6 + z 6 =. x + y + z + (x + y )(x + z )(y + z ) = ( ) x + y + z x z 3 y z 3 = x + y + z 3 = z

ContourPlot[{x^+y^==,(x-)^+y^==}, {x,-,}, {y,-,}, AspectRatio -> Automatic].. ContourPlot Plot AspectRatio->Automatic.. x a + y = ( ). b ContourPlot[x

$ContourPlot[{x^+y^==,(x-)^+y^==}, {x,-,}, {y,-,}, AspectRatio -> Automatic].. ContourPlot Plot AspectRatio->Automatic.. x a + y = ( ). b ContourPlot[x$ 3. Mathematica., : f(x) sin x Plot f(x, y) = x + y = ContourPlot f(x, y) > x 4 + (x y ) > RegionPlot (x(t), y(t)) (t sin t, cos t) ParametricPlot r = f(θ) r = sin 4θ PolarPlot.,.. x + y = (x, y). x, y.