ラプラシアンの計算と調和関数のグラフ

Mathematica プログラム例

1. lap[f_]:=D[f,{x,2}]+D[f,{y,2}]
2. lap[E^(x+y)]
3. lap[Sqrt[x+y]]
4. lap[x^2-y^2]
5. lap[Log[x,y]]//Simplify
6. lap[y Log[x/y]]
7. lap[Log[2,x^2+y^2]]//Simplify
8. lap[2x/(x^2+y^2)]//Simplify
9. lap[(x+y)/(x^2+y^2)]//Simplify
10. Plot3D[x^2-y^2,{x,-4,4},{y,-4,4}]
11. Plot3D[Log[2,x^2+y^2],{x,-4,4},{y,-4,4}]
12. Plot3D[2x/(x^2+y^2),{x,-2,2},{y,-2,2}]
13. Plot3D[(x+y)/(x^2+y^2),{x,-2,2},{y,-2,2}]

計算結果