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Mathematica (2)

Mathematica (2). 3 次元曲線・曲面のパラメータ表示. ParametricPlot3D[{Sin[t],Cos[t],t/3},{t,0,4Pi}];. ParametricPlot3D[{v Sin[u],v Cos[u],u/3}, {u,0,4Pi},{v,-1,1}];. ParametricPlot3D[{Cos[u]Cos[v], Cos[u] Sin[v] , Sin[u]}, {u,-Pi/2,Pi}, {v,0,2Pi}];.

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Mathematica (2)

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  1. Mathematica (2)

  2. 3次元曲線・曲面のパラメータ表示 ParametricPlot3D[{Sin[t],Cos[t],t/3},{t,0,4Pi}]; ParametricPlot3D[{v Sin[u],v Cos[u],u/3}, {u,0,4Pi},{v,-1,1}]; ParametricPlot3D[{Cos[u]Cos[v], Cos[u]Sin[v], Sin[u]}, {u,-Pi/2,Pi},{v,0,2Pi}]; ParametricPlot3D[{Sin[v](3+Cos[u]), Cos[v](3+Cos[u]),Sin[u]},{u,0,2Pi},{v,0,2Pi}];

  3. 式の展開・因数分解・簡単化 展開 In:[1]= Expand[(b+a x)^2] Out[1]= b2 + 2abx + a2x2 In:[2]= Factor[%] Out[2]= (b + ax)2 In:[3]= Factor[x^6 - 1] Out[3]= (-1+x)(1+x)(1-x+x2)(1+x+x2) In:[4]= y = 1/(1+x) + 1/(1-x) Out[4]= In:[5]= Simplify[y] Out[5]= -2/(-1+x2) 因数分解 簡単化

  4. 方程式を解く: Solve[], NSolve[] In:[1]= Solve[x^2 - 2x - 4 ==0, x] Out[1]= In:[2]= N[%] Out[2]= In:[3]= NSolve[x^2 - 2x - 4 ==0, x] Out[3]= 4次方程式までは必ず解ける。 5次以上は（普通は）Solve[]では解けないが、 NSolve[] で数値的に解くことは可能。

  5. 連立方程式 In:[1]= Solve[{2x+3y==0,x-2y+3==0},{x,y}] Out[1]= In:[2]= Solve[{2x+3y==0,x^2+y^2==1},{x,y}] Out[2]= In:[3]= Solve[{a x+b y==0,x^2+y^2==r^2},{x,y}] Out[3]=

  6. 数値解を探す：FindRoot[] In:[1]= Plot[{Exp[-x],Sin[x]},{x,0,8}]; In:[2]= FindRoot[Exp[-x]==Sin[x],{x,0}] Out[2]= {{x → 0.588533}} In:[3]= FindRoot[Exp[-x]==Sin[x],{x,3}] Out[4]= {{x → 3.09636}} 最小値を探す： FindMinimum[] In:[1]= Plot[Sin[x]/x,{x,0,Pi}]; In:[2]= FindMinimum[Sin[x]/x,{x,5}] Out[2]= {-0.217234,{x → 4.49341}}

  7. 微分: D[f,x] In:[1]= D[x^2 - x - 6, x] Out[1]= -1 + 2x In:[2]= D[x^n,x] Out[2]= nx-1+n In:[3]= D[Cos[a x], x] Out[3]= -a Sin[a x] In:[4]= D[Cos[a x], {x,2}] Out[4]= -a2 Cos[a x] In:[5]= D[Cos[x^2 y], x,y] Out[5]= -2x3y Cos[x2y]-2x Sin[x2y]

  8. 積分: Integrate[] In:[1]= Integrate[x^n, x] Out[1]= In:[2]= Integrate[Sqrt[x^2+a],x] Out[2]= In:[3]= Integrage[Sin[a x], {x,0,Pi}] In:[4]= Ingegrate[Sin[Sin[x]],x] In:[5]= NIntegrate[Sin[Sin[x]],{x,0,Pi}]

  9. 級数：Sum[] 極限：Lim[] In:[1]= Sum[x^n/n!,{n,0,5}] Out[1]= 1+x+…（略) In:[2]= NSum[1/n,{n,1,100}] Out[2]= 5.18738 In:[3]= Sum[x^n,{n,0,Infinity}] Out[3]= 1/(1-x) In:[1]= Limit[Sin[x]/x,x->0] Out[1]= 1 In:[2]= Limit[(3x^2-1)/(x^2+5),x->Infinity] Out[2]= 3

  10. Taylor展開： Series[] Series[f[x],{x,x0,n}] In:[1]= Series[Sin[x],{x,0,5}] Out[1]= In:[2]= Series[Exp[-ax]/Cos[x],{x,0,4}] Out[2]=

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