Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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3b written out on paper please, not typed out.
3) a) Prove that the following functions are harmonic and
find for each function its harmonic conjugate.
i) 2e*cosy
ii) x ² + 2x -y²
b) Prove: Ifwis harmonic conjugate of V in a domain I
and V is harmonic conjugate of u in a domain I then
u and ✓ are constant functions.
4) a) Find an analytic function (or functions) if
Ref(Z) = x²= y ² + 2x and fli) = 2i -1
b) Find all the analytic functions for which
Im f(z)
Rez
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Transcribed Image Text:3) a) Prove that the following functions are harmonic and find for each function its harmonic conjugate. i) 2e*cosy ii) x ² + 2x -y² b) Prove: Ifwis harmonic conjugate of V in a domain I and V is harmonic conjugate of u in a domain I then u and ✓ are constant functions. 4) a) Find an analytic function (or functions) if Ref(Z) = x²= y ² + 2x and fli) = 2i -1 b) Find all the analytic functions for which Im f(z) Rez
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