He's among the great professors in the math department. Although his exams are quite long, they're coming directly from the problem sets and I don't think it's super hard to do well in his class if you are willing to work. He drops 5 homework and was very understanding during covid. We indeed get 4-days extension for the final! I think he teaches well, knows what he's doing, and is always kind and approachable which is rare.
Caveat: I took this class in Fall 2019. Yes, this class is everything they say it is. Yes, Florian is one of the most rigorous professors I have had thus far. And yes, I spent hours and hours of my life doing each homework, many of which contained material beyond the scope of what other ODE classes cover. However, the insane difficulty and rigor of this course caused me to put an incredible amount of effort into it out of sheer necessity, which meant I got more out of it than any other math course I have taken here. Florian is a very nice guy and helpful during his OH, which you will almost certainly need to go to (the TAs don't always know how to solve the HW). This course will make you suffer, but it will also leave you wanting to study more math, particularly the pure math side of things; this class is much heavier on the theory than other ODE classes I have seen, so you'll want to take real and complex analysis after being teased with tastes of them here. There is obviously a very large curve in this class due to its sheer difficulty, although it is not particularly generous at the top end (most of the class ended up with a B-range grade), but getting a B- required an average in the 50s, if I remember correctly (an A- was a 75% or above). Again, this is by no stretch of the imagination an easy class, but it is a very worthwhile one. Florian is very nice and understands the material very well, and I generally think he gives off positive vibes. This class made me personally want to pursue higher-level mathematics courses, most of which have turned out to be easier than it despite being at the 4000 level.
Structure: I took this class in the fall semester of 2020 so Professor Johne pre-recorded his lectures. They were typically released in sets of 30-40 minute videos. Initially, they were released midnight Sunday or midnight Tuesday. Towards the end of the semester, the pre-recorded lectures would be released closer to 3-4 AM on Monday and Wednesday. During the scheduled lecture time, he would hold a review-style Zoom meeting where students could drop in and ask questions at the beginning of the meeting. He would then answer the questions he received at the beginning of the class and any other questions that came up during the lecture. Most questions were about the content from the lecture that was posted the night before or from that week's homework so if you were in a timezone where you couldn't watch the lecture before the scheduled lecture, you would be entirely out of the loop. These informal lectures were not recorded but occasionally the notes were posted on Courseworks. The good: Professor Johne is incredibly intelligent. He knows what he's talking about when asked questions. He always responded to my emails when he got to them. Homeworks were usually due 2 weeks after they were released thanks to a soft, "preferred" deadline and a hard, final deadline. The grading was very methodical and solutions were posted for just about everything but the final. If you like the harmonic oscillator, this is your class. The bad: Professor Johne's main vehicle for teaching was worked examples. I am sure for some this works best, but his examples usually confused me. The methods of solving ODEs - the bread and butter of the course - were neither mathematically rigorous nor came from applied questions and usually summed up to "somehow this works so we'll go with it and use it a bunch". The harmonic oscillator was used to derive a lot of solutions and was also used as an example for other solutions where they were derived some other way. The homeworks were very difficult but usually doable. Usually they took me about 15 to 20 hours to finish. The hardest part about the homeworks was taking what was taught in class - the worked example - and applying that to problems that looked nothing like the example from class. The procedure from the worked example didn't always work on the homework either so you had to get creative or learn about the solution method from somewhere else. All exams were open-note, take-home exams without a time limit. Regardless, the midterms were brutal. I took most of the time I was awake during the 48 hour midterm windows taking the exams. The final exam was no different. We were given about a week to finish the exam. I took about 3 or 4 of those days to finish the exam. As another person noted, his challenge questions were extremely difficult and were impossible to do. The exams consisted of a few "straightforward" ODEs followed by conceptual problems that were not answered during the pre-recorded lectures. The grading was very methodical which, while helpful for studying, usually meant that very specific answers were needed to get full points. Not fun. Summary: Overall, the content of the class itself is interesting and worth learning. But, if you can find a similar class with a different professor, try them instead. If you want a challenge, enjoy pain, or have a light course load, this class won't be so bad.
Johne is a piece of work. The sole source of my stress for the majority of the semester. I'll start with the good. This class is conceptually challenging and will force you to learn a lot of ODEs at a very high level. You will cover a lot of proofs. You will become intimately familiar with modeling the harmonic oscillator using an ODE. You will definitely never be bored. Now the bad. Johne is incredibly incompetent. His problem sets are atrocious and sometimes took me upwards of 20 hours. He writes all of his own problems, and they tend to be of the form "prove xyz = abc", which is hellish. Additionally, in 2020, his exams were take home, which sounds kind and forgiving, but in reality, Johne formatted it so instead of a 2-hour exam it was a 48-hour exam. Exams had millions of parts, were convoluted, and were incredibly difficult. And on top of it all, harshly graded! Finally, Johne's lectures suck. He just does a bad job telling you what is important, what you should write down, and what is irrelevant. His lectures are basically a series of worked examples, with a little theory thrown in. So you always have to go back and decipher his work. In essence, Johne takes an already-difficult class and makes it so indecipherable that it doesn't feel real anymore. If this class wasn't required for my major, I would have dropped it.
To this day, this class is probably the worst academic experience that I've ever had in my life. Prof. Johne is very nice and willing to help out as much as he can, but his class is way too difficult and the workload is too high. The lectures include extremely long examples and he makes concepts seem way more complicated than they are. If you are taking this course, prepare to self-teach the entire thing. The problem sets are unnecessarily difficult and take way too many hours to complete. The same goes for the exams: they were take-home exams but included 8-12 questions with 3-10 sub-sections each. On the exams, he has a couple of questions that he marks with a bat symbol that are supposed to be more challenging: these problems are practically unsolvable and/or will require you to make sacrifices to Batman and Robin to solve. Based on what I've heard from other students, other professors run much easier ODE courses and Florian's version is particularly difficult and rigorous. Again, he's a really nice guy, but DEFINITELY avoid this section of ODE unless you want to sacrifice your soul for an entire semester.