b) Prove: Ifuis harmonic conjugate of V in a domain I and vis harmonic conjugate of u in a domain I, then u and ✓ are constant functions.
b) Prove: Ifuis harmonic conjugate of V in a domain I and vis harmonic conjugate of u in a domain I, then u and ✓ are constant functions.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b030cd5-5424-4c4c-9fb9-bb5124dfa56d%2Faeb08b52-1515-4648-bdfe-4a1328aacb70%2Fj0aa1na_processed.jpeg&w=3840&q=75)
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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