1. Let u = u(x, y) be harmonic in a domain D. Show that the following variations of uare also harmonic wherever they are defined.(a) Translation: v(x, y) = u(x - a, y – b), where a, b are constants.(b) Rotation: v(r, 0) = u(r,0 + ), where (r, 0) is the polar coordinates and y is aconstant.(c) Dilation: v(x, y) = u(x/8, y/8), where d > 0 is a constant.%3D

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1. Let u = u(x, y) be harmonic in a domain D. Show that the following variations of u are also harmonic wherever they are defined. mwn (a) Translation: v(x, y) = u(x – a, y – b), where a, b are constants. (b) Rotation: v(r, 0) = u(r,0 + y), where (r, 0) is the polar coordinates and y is a %3D constant. (c) Dilation: v(x, y) = u(x/6, y/8), where d > 0 is a constant.

1. Let u = u(x, y) be harmonic in a domain D. Show that the following variations of u are also harmonic wherever they are defined. mwn (a) Translation: v(x, y) = u(x – a, y – b), where a, b are constants. (b) Rotation: v(r, 0) = u(r,0 + y), where (r, 0) is the polar coordinates and y is a %3D constant. (c) Dilation: v(x, y) = u(x/6, y/8), where d > 0 is a constant.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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