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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Questions: 3b 4a
3) a) Prove that the following functions are harmonic and find for each function its harmonic conjugate. i) 2e*cosy ii) x² + 2x - y² b) Prove: Ifwis harmonic conjugate of V in a domain I and vis 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= y² + 2x and fli) = 2i -1 b) Find all the analytic functions for which Im f(z) Rez
Transcribed Image Text:3) a) Prove that the following functions are harmonic and find for each function its harmonic conjugate. i) 2e*cosy ii) x² + 2x - y² b) Prove: Ifwis harmonic conjugate of V in a domain I and vis 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= y² + 2x and fli) = 2i -1 b) Find all the analytic functions for which Im f(z) Rez
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