Show that in cylindrical coordinates r, 8, z defined by the relations x = r cos 0,y = r sin 0, z = z, the Laplace equation V²u = 0 takes the form² u 1 du+ar²+r dr1 22 иr² 20²+22u2az²= 0

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Answered: Show that in cylindrical coordinates r,…

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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Show that in cylindrical coordinates r, 0, z defined by the relations x = r cos 0, y = r sin 8, z = z, the Laplace equation V²u=0 takes the form ди 1 ди + ar² 1 2²u r dr r² 20² + + zu dz² =0