This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating ...
I would just like to mention that other similar flowcharts have been developed, of varying degrees of generality, which you might consult.
Here is one (by Adam Monahan).
And another (by Jeremy Higgins):
And another (by Enrique Areyan):
Comment-answer, but too long for a comment:
I think you are thinking about this wrong.
Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine ...
I would consider to add two items to the list, both from a systems slant:
Predator prey relations. The behavior can be graphically investigated, but the actual solution function is not analytically soluble. Any solid ODE book will cover this. E.g. Speigel's
(In before the close!)
I'd say the PDE course looks more like a traditional course than the prob/stats course. Look at the hours expected, for example (~6.5 versus ~1.5), each times 8 weeks.
The PDE course looks like a solid half to two thirds of a semester of a normal, engineering support course. You cover a couple of the 3-4 major equations. And get ...
Leave more conceptual questions for take home. They have more time, can think things over. Encourage using technology, ask for a sketch of how they think the solution to something hairy looks like (Asymptotes? Increasing? Maxima?). Explore e.g. the effect of initial values on the plot of the solution.