Assuming that all the necessary derivatives exist and are continuous, show that if (x, y) satisfies the

Assuming that all the necessary derivatives exist and are continuous, show that if ƒ(x, y) satisfies the Laplace equation

then

for all closed curves C to which Green’s Theorem applies. (The converse is also true: If the line integral is always zero, then ƒ satisfies the Laplace equation.)

Transcribed Image Text:

a²fa²f ax² + ay² = 0,