“Tell me and I’ll forget. Show me and I may remember. Involve me and I’ll understand.” ~Lao Tze
A traditional engineering homework assignment wants you to tell us the answer. Need proof? Look at a calculator and see how hard it is to plot a function or curve. Calculators are typewriters and should have vanished long ago. Asking someone to tell us an answer is much easier than plotting a trend or curve. Plotting requires spatial awareness of the physical interplay of operators within your mathematical function. Explaining plots shows us that we understand why trends appear.
Showing by theory is essential in complex systems design because the number of connections and fluctuations in a system are onerous to recalcuate by hand. We have to have plots over ranges of acceptable values to know where to draw the boundaries of acceptable design specifications. Mathematical processors such as Engineering Equation Solver (EES), Matlab, Mathematica, and Maple are essential to the modern designer for this reason. You can readily open an old code and enter new specifications from a potential manufacturer.
Instead of telling us “it should work,” which anybody can say, you’ll show us why it will work with quantifiable statistics over relevant ranges of operating conditions. Now you’ve earned your paycheck.