Using K-Map to simplify functions I hope this is the right place to ask this.
I have the following problems:
1. Using a K-Map technique perform the following:
   Simplify the following function:
    f = (A,B,C,D) = ∑ m  (0,1,2,3,6,7,8,9,13,15)
    Show all the "prime implicants" and "essential prime implicants"
and 
    Find a minimum SOP expression for:
      f(w,x,y,z) = ∑ m (1,3,5,9,11,14)+d(4,6,7,12)
        Show all the "prime implicants" and "essential prime implicants"
This is what I came up with:

But as you can see, I don't have any essential prime implicants whatsoever. So I'm worried that I'm doing something horribly wrong. Could someone please help me out?
Updated progress:


Fixed up the blue circles a bit to make it more clear.

I'm familiar with K-maps, though not as familiar with the terminology, so I've had to resort to Wikipedia.  First of all, you're allowed to overlap your groupings.  Since you haven't 2 of your implicants from part a are not prime.
You have a square in the upper right corner for a prime implicant of A'C.  Similarly, you have another square in the upper/lower left for another prime implicant of B'C'.  The other 2 prime implicants you have for that part appear to be correct.  Of these 4 prime implicants, it appears 3 are essential.
According to Wikipedia, an implicant is prime if it cannot be covered by an implicant with fewer literals.  A'BC is not a prime implicant since it can be covered by A'C.  Also, from Wikipedia, a prime implicant is essential if covers an output not covered by any combination of other prime implicants.  No other prime implicants cover either output of ABD, so it is essential.  AB'C'D' is covered only by B'C', so it too is essential.  But every output covered by A'B' is covered by other prime implicants; therefore it is not essential.
