Example 11.16. Find the temperature T(x,y) at each point in the upper
half-disk H: Im z > 0, |z| < 1 if the temperature at points on the boundary satisfies
T(x,y) = 100 for (x,y) on the upper semi-circle,
T(x,0) = 50 for -1 < x < 1, on the diameter.

Solution: Use the mapping .

The temperature function is:

A graph for the solution is:

Temperature in a half disk.

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(c) John Mathews, 1998, 2006