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a)Suppose, w = d(z,9) + ip(z, v) defines a complex potential function. Terify whether w is analytic or not. Hint: Don't calculate. Use the equations given for velocity companents to erify. b)Show that, 6(z, y) = 3z°y – g° and p(z,9) =-² +3ry are harmonie unctions. c)Also prove that (1,9) and (z,y) are harmonic conjugates of each cher.[Use the functions of (b))

a)Suppose, w = d(z,9) + ip(z, v) defines a complex potential function. Terify whether w is analytic or not. Hint: Don't calculate. Use the equations given for velocity companents to erify. b)Show that, 6(z, y) = 3z°y – g° and p(z,9) =-² +3ry are harmonie unctions. c)Also prove that (1,9) and (z,y) are harmonic conjugates of each cher.[Use the functions of (b))

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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a)Suppose, w = d(z,9) + ip(z, v) defines a complex potential function. Terify whether w is analytic or not. Hint: Don't calculate. Use the equations given for velocity companents to erify. b)Show that, 6(z, y) = 3z°y – g° and p(z,9) =-² +3ry are harmonie unctions. c)Also prove that (1,9) and (z,y) are harmonic conjugates of each cher.[Use the functions of (b))
Transcribed Image Text:a)Suppose, w = d(z,9) + ip(z, v) defines a complex potential function. Terify whether w is analytic or not. Hint: Don't calculate. Use the equations given for velocity companents to erify. b)Show that, 6(z, y) = 3z°y – g° and p(z,9) =-² +3ry are harmonie unctions. c)Also prove that (1,9) and (z,y) are harmonic conjugates of each cher.[Use the functions of (b))
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