Professor Quenneville-Belair is a nice guy and very intelligent, but be wary, he doesn't pull any punches with this class. The course moves quickly and builds on itself throughout, so you have to stay on top of the material. Everything is taught directly from the textbook though, which certainly helps, and the TAs were great. My biggest reservation with Professor Quenneville-Belair is his unwillingness to release solutions. He explained that at our level of mathematical sophistication we shouldn't need solutions released for the homeworks because we should be able to identify when we've done something wrong and correct it... Like what? How are we supposed to learn if nobody tells us what we're doing wrong? Granted, this was his first semester teaching this course here, so I'm sure he got plenty of feedback on this point and will hopefully take a different approach in future semesters. Overall I worked very hard in this course and learned a lot. Not for the faint of heart, but if you're up for it you'll come out the other side knowing a lot about PDEs.
Guillaume Bal could be your nightmare if you were to come to Columbia as a international student: He's got an accent, doesn't speak loud enough, and the class is very, very crowded, which means even if everyone tries to keep quiet, the heat in the room can still easily put you asleep. Yet he does provide very detailed explanation and derivation if you can adapt to the way he conveys his ideas, and with the help of CVN, you might be able to review the materials online after the course, or at least we were able to do so last Fall.
This class basically exposes you to a few PDE's and a handful of methods for solving them. Sobel is a much, much better teacher than most higher math professors. However, that places him slightly below the average in clarity and teaching ability. You will not learn everything you need to know in lecture. To do well, you need to be able to interpret the (laughably unfriendly) textbook's explanations and cryptic homework questions. His office hours are lightly attended, though sometimes a few very lost souls monopolize his time with silly questions. Solutions to the homeworks and previous tests are on courseworks which is quite helpful for exam prep.
Good prof. The material in this class starts easy, but gets pretty difficult by the end (There's a big learning curve if this is your first introduction to Fourier Series / Transforms). Sobel does a good job conveying intuition and providing useful analogies to get a feel for what's going on. The physical motivations are sometimes overly lengthy (especially for someone with no interest in physics), but can be helpful in certain cases. I took and dropped other profs for this course (looking at you, Courdourier) before Sobel; the difference is huge. As a math major in the college, this is the first app math course I took, and I think I walked away with a very good understanding of the material. Recommended.
One of the worst professors I have had at Columbia. I did not think he was that bad until the end of the semester, when he decided that it would be a great idea to e-mail his students about a final review session 1 hour before the actual review session took place, making an assumption that a. students would be awake at 10am to read this e-mail, and b. students check their e-mail CONSTANTLY and will have read the e-mail. To top it all off, he refused to post the practice final online saying that it was our fault for not attending the review session. Overall, a very disorganized professor, and not particularly great at teaching either. Homeworks were assigned erratically so we would not know what week a homework would be due, so it was definitely difficult to plan ahead.
Lorenzo Polvani was a great teacher. He made a subject that students probably usually hate painless. I hated Ordinary Differential Equations (taught by Krichever) and was dreading taking PDE, but it turned out to be one of the better classes I've had. This is probably the only painfree PDE experience at Columbia: everyone hates the pure math one and I think Bal, APMA 3102 is worse than Lorenzo. Polvani's lectures broke down lengthy problems into very straight forward techniques. He's not a native English speaker, but it's good enough that I shouldn't have even mentioned it. This class is identical to APMA 3102: Applied Mathematics II, but has a graduate course number for first year grad students (mostly Biomedical Engineers and some Applied Phyics/Math). The midterm had its share of tricky questions but was not too hard. I thought the class was really straight forward until the last 3 weeks (the worst time for a class to get hard) when we started doing non-homogeneous problems and Green functions. Of course they were the focus of the final and I thought it was impossible. It's one of those courses where the final includes what's on the midterm indirectly, but all of the questions are from the last half of the semester, so I felt totally incompetent even though I was really comfortable with at least 75% of the material.
The previous review of Sean Paul's PDE class was written only one week into the semester, so how could that person be so sure? Anyway, PDE is incredibly hard, a subject for grad school - and a VERY advanced subject for undergrads. It is by no means straightforward.. Sean Paul is not a good instructor, but let's face it, he speaks English which is better than the majority of the math department. Suck it up, and wait to the end of the semester to review. PDE with anyone is a mind-expanding experience, and expect to be overwhelmed
In my opinion, Alex Casti could not teach his way out of a paper bag. He goes through material very quickly, often skipping steps and not explaining key points. This combined with his inane sense of humor make this class a really unbearable experience. Almost nothing was learned during the course of the semester and any motivated student would be able to cover all of the material that Casti covered within a few days of motivated study. I definitely do not recommend this class.