This assignment is intended to sharpen up your elementary math skills.

1. The differential element of area in cartesian coordinates is dxdy. What is it in plane polar coordinates r and f? Hint first, give the transformation between r and f and x and y and use the Jacobian of the transformation.
2. Give e^ix in terms of cosx and sinx
3. Give the series expansion of e^x about x = 0. Do it again about x =1.
4. Give the general solution to the differential equation

The general solution has two unknown constants. They are determined by specifying boundary conditions. How is this done?