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...

There are two parts of question a and b parts

Extracted 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.)