(b)Suppose that functions u and v are harmonic in D. Are the following functions harmonic? (1) u²v²; (2) uv; (3) 9u + 13v; (4) Vry + Au (Assume that harmonic functions are smooth functions with all derivatives.)
(b)Suppose that functions u and v are harmonic in D. Are the following functions harmonic? (1) u²v²; (2) uv; (3) 9u + 13v; (4) Vry + Au (Assume that harmonic functions are smooth functions with all derivatives.)
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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need part b) expression number 4.Thank you
![4. (a) Let u be a harmonic function in D. Show that if v is a harmonic conjugate of u in a
domain D, then both u²v² and u³ - 3uv² are harmonic in D.
(b)Suppose that functions u and v are harmonic in D. Are the following functions harmonic?
(1) u² − v²; (2) uv; (3) 9u + 13v; (4) Vxy + Au
(Assume that harmonic functions are smooth functions with all derivatives.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e9ca648-396a-488a-88dd-91544590f068%2F50022e69-912e-4478-a1c5-158888707b75%2F4gp1adg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. (a) Let u be a harmonic function in D. Show that if v is a harmonic conjugate of u in a
domain D, then both u²v² and u³ - 3uv² are harmonic in D.
(b)Suppose that functions u and v are harmonic in D. Are the following functions harmonic?
(1) u² − v²; (2) uv; (3) 9u + 13v; (4) Vxy + Au
(Assume that harmonic functions are smooth functions with all derivatives.)
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