Harmonic Function: Two-Dimensional

M.M. Yovanovich

2DHARMONIC1.MWS

> restart:

Two-dimensional harmonic function is a solution of the two-dimensional Laplace equation . The parameter .

> u:= C*ln(sqrt(x^2+y^2));

> u_x:= diff(u,x);

> u_xx:= diff(u_x,x);

> u_y:= diff(u,y);

> u_yy:= diff(u_y,y);

> u_xx+u_yy;

> simplify(%);

Use Maple in one step to show that the given harmonic function satisfies the Laplace equation.

> simplify(diff(u,x$2) + diff(u,y$2));

Check alternative forms of the harmonic function.

> u2:= C*ln(x^2+y^2);

> simplify(diff(u2,x$2) + diff(u2,y$2));

> u3:= C*ln(1/sqrt(x^2+y^2));

> simplify(diff(u3,x$2) + diff(u3,y$2));

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