# (it is advanced theory of complex funtion question.) solve the question 2 in the picture Transcribed Image Text: 2. a) Let u(x, y) be a

(it is advanced theory of complex funtion question.) solve the question 2 in the picture Transcribed Image Text: 2. a) Let u(x, y) be a continous function on a closed and bounded, simply connected region R.
Also let u(x, y) be non-constant harmonic function in R. Show that u(x, y) has a maximum value in
R which is assumed on the boundary of R and never in the interior.
b) Find the maximum and minimum values of the function u(x, y) = e’ cos x throughout the
region {(x, y):0sxs 2n, 0 s ys n}.

(550 words)

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