| I phrase it as “The class I cheated my way to an A but didn’t commit any academic dishonesty violation.” > The real fact that is somewhat hidden is that most differential equations can't be solved analytically. You solve analytically only the few cases that are solvable analytically I discovered this very early in my semester of Differential Equations. We were allowed a single 8.5x11 notesheet for the exams. As there were only a handful of the “most general” cases which are solvable on paper with a basic calculator, I simply copied the step by step solution for each of the very most general case completely worked out in whatever techniques we were going to be tested on for that exam. The professor was an engineer before becoming a math professor so he only liked to include real-world situation ODE’s on exams which further reduced the potential problem space. While it greatly confused the professor/grader who scored my exam that I kept adding zero-coefficient terms before solving the differential equation perfectly…I got 100% on all the exams. The catch was that I didn’t learn anything. The next semester it turned out that I needed to know those techniques for Reaction Kinetics and Heat&Mass Transfer and Biochemical Engineering (these courses involved deriving and solving many equations from first principles). I had to crawl back to my Differential Equations professors office hours for 3 weeks and beg him to actually teach me differential equations. He was very confused after asking me what grade I got (an A) and I had to explain to him how I got an A without learning anything. To his credit, he did a fantastic job assigning me custom work for 3 weeks and reviewing it with me and I was able to learn what I needed for the more advanced courses. But without his help and some additional tutelage from my peers, I would have been completely screwed for the rest of my Chemical Engineering major. |