Show that u(x, y) is harmonic in some domain and find a harmonic conjugate v(x, y) when

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Show that u(x, y) is harmonic in some domain and find a harmonic conjugate v(x, y) when
(a) u(x, y) = 2x(1 − y);
(b) u(x, y) = 2x − x3 + 3xy2;
(c) u(x, y) = sinh x sin y;
(d) u(x, y) = y/(x2 + y2).

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Complex Variables and Applications

ISBN: 978-0073051949

8th edition

Authors: James Brown, Ruel Churchill

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Question Posted: Jun 01, 2016 01:38 AM

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Show that u(x, y) is harmonic in some domain and find a harmonic conjugate v(x, y) when

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a It is straightforward to show that u xx u yy 0 when ux y 2x1 y To find ...View the full answer

Complex Variables and Applications

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