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.)

Question

There are two parts of question a and b parts

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.)
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Transcribed Image Text

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.)

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