Attachment 25242

Answer

u(x,y) is the real part of an analytic function if it has zero Laplacian. Note that

u_x = 2x

u_xx = 2

u_y = -2y - 1

u_yy = -2

Therefore, the Laplacian of u is

u_xx + u_yy = 2 - 2 = 0.

Is the answer correct.....

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- Oct 16th 2012, 05:09 AMmathsforumhelpShow that u is the real part of analytic function
Attachment 25242

Answer

u(x,y) is the real part of an analytic function if it has zero Laplacian. Note that

u_x = 2x

u_xx = 2

u_y = -2y - 1

u_yy = -2

Therefore, the Laplacian of u is

u_xx + u_yy = 2 - 2 = 0.

Is the answer correct..... - Oct 16th 2012, 05:39 AMTheEmptySetRe: Show that u is the real part of analytic function