
Please do the following exercises from the text "Foundations of Analysis" by Joseph L. Taylor.
 9.3[1,3*,5,9*]
 9.4[1,4,8*,11,12*,13*] (Problem 7 is not due until next week.)

Please do the following additional exercises.
 A*. (See 9.3[8]) Suppose that (x,y,z) are the Cartesian coordinates of a point in R^{3} and the spherical coordinates of the same point is given by
x = r cos θ sin φ, y = r sin θ sin φ, z = r cos φ.
Let u = f(x,y,z) be a C^{2} function on R^{3}. Find a formula for the partial derivatives of u with respect to x,y,z in terms of partial derivatives with respect to r,θ,φ. Find a formula for the Laplacian of u in terms of partial derivatives with respect to r,θ,φ, where the Laplacian is given by
Δu = ∂^{2}u/∂x^{2} + ∂^{2}u/∂y^{2} + ∂^{2}u/∂z^{2}.
