Hint on PS3, problem 4

In converting from A(T,V,N) to E(S,V,N), it may simplify your life to use the following relationship:

-E/T^2 = d(A/T)/dT (constant V and N)

You can use this equation to first get E(T,V,N) and then you can make the appropriate substitution to get E(S,V,N).

Be careful of using Mathematica to do all of the manipulations here. Sometimes it doesn't simplify to the best answer.