Question

The standard Euclidean metric on R3 is simply ds? = d.x2 + dy? + dz2. (a) Explain why I c = 0) in this basis. (b) Now consider the same metric expressed in spherical coordinates, ds2 = dr2 + pºde2 + sin Odo2). Determine the Christoffel symbols in this coordinate system using the same method as in the earlier question. (c) Write down Laplace's equation v2f = gabv. Vof = 0) where f = f(r,0,0). What happens if f = f(r) (i.e. it is a radial function?) Those of you taking a PDE course should have seen the resulting ODE in discussions of spherically symmetric solutions of Laplace's equation.

Part C

Answer 1

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