Schulz's only appearance last year came in Utah's 49-6 win over Washington State when he threw two passes for 52 yards.
However, the walk-on has improved in "a lot of things," this spring, Whittingham said.
According to Whittingham, Schulz has improved in "his decision making, his quickness in getting the ball out of his hands and his velocity and accuracy of where he puts the ball, just his sheer ability to throw."
Cox, who enrolled early to participate in spring ball, might miss the remainder of the spring session with a left foot injury. However, Whittingham was complimentary of him as well.
"He showed enough this spring for us to realize we have something special," he said.
Whittingham wasn't surprised that Star Lotulelei declined on Wednesday an invitation to go to New York for the NFL Draft, given Lotulelei's nature.
"He is a unique individual, a family guy," Whittingham said. "Family is so important to him. To just go to New York, waiting in a room and sitting around is not his deal and if it's not going to affect your draft status, why go is his mentality. I support Star and his decision. He is just different than most guys. He isn't a limelight guy. He just wants to play football and be with his family."
Whittingham said it is still too early to declare much separation at several positions, but noted tight ends Jake Murphy and Westlee Tonga are both having strong practices.
Murphy was second on the team with 33 catches for 349 yards last year while Tonga had four catches for 39 yards in nine games.
"They could be one of the best tandems in the conference this year," Whittingham boasted.
The Utes plan to use their tight ends more this year than ever before, a plan that both Murphy and Tonga are embracing.
"It has been great this spring," Tonga said. "We've been getting a lot of balls, a lot of reps and spreading it around and that is a testimony to the offense. I don't think we have ever been this far ahead at this point in the spring."
The Utes scrimmage Saturday from 10 a.m. to noon at Rice-Eccles Stadium. Whittingham said the scrimmage won't be quite as extensive as the one a week ago.
"We're going to work on the same things, just try and do them better," he said. "We had more install this week so we have something to teach going forward."