3-a) Consider elliptical cylindrical coordinates (u, p, 2) which are related to the Cartesian coordi- nates by = a cosh u cos , y = a sinh u sin p, Z = z, x where a is a constant. Write down Laplace's equation V2V = 0 in elliptical cylindrical coordinates. b) Show that Laplace's equation in elliptical cylindrical coordinates is separable. How many in- dependent separation constants are there? (You don't have to solve the ODES, but you have to derive them.)
3-a) Consider elliptical cylindrical coordinates (u, p, 2) which are related to the Cartesian coordi- nates by = a cosh u cos , y = a sinh u sin p, Z = z, x where a is a constant. Write down Laplace's equation V2V = 0 in elliptical cylindrical coordinates. b) Show that Laplace's equation in elliptical cylindrical coordinates is separable. How many in- dependent separation constants are there? (You don't have to solve the ODES, but you have to derive them.)
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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