Partial Differential Equations

Apr 2021

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.

May 2017

The material is a bit unmotivated: it seems like just a bag of tricks to solve PDEs. Some of the more advanced material felt like more effort than it was worth. However, for the most part, the class is not too hard, and I feel like I have a good mastery of the material after taking this class. I can now solve lots of PDEs. Prof Brendle is a good lecturer. He explains the material rigorously and answers questions well.

May 2015

Savin is a boss. Somehow he makes everything seem obvious. He never looked at the book or notes during his lectures, and always talks in a very matter-o-fact manner. It's important to not let this get to your head too much- review the notes and make sure it really is as obvious to you as it is to him. Savin holds the class to a high standard (or, if you ask him, a reasonable standard). He's sad when the average is always less than he thinks it should be. Here is an excerpt from the email he sent us after the class was over: "The average on the final exam was 52. The exam was difficult and also the material we tried to learn." I actually think this class is important for math majors to take, even if it's not as sexy as other subjects. I did most of the homeworks pretty honestly, and I feel as though I learned a lot about how to think about PDEs and how to prove basic stuff about them (uniqueness, maximum/minimum principles, etc.) The class has more in common with analysis than it did with ODEs. (BTW, having taken ODEs before I took this class, the material / approach of the class is completely different; it's not necessary but if you're not a strong student it'll help you out.) Keep in mind that most of your grade will be based on two tests where time pressure will be an important factor. DEFINITELY review the homeworks WELL, but don't stress out about knowing little facts. The tests will see if you understand the general philosophy of the proofs, which I'll outline here: 1. If you have to show the only solution to a PDE is 0, first try to prove that its minimum is >= 0 and its maximum is <= 0 by keeping in mind that if u is maximized then u' = 0, u'' <= 0, plugging those conditions into the PDE. If that doesn't work, analyze the solutions of its characteristic curves or use some maximum principle. 2. If you have to show uniqueness of a linear PDE with certain boundary conditions, show that if u and v satisfy those conditions then u - v = w (with 0 boundary conditions) must be identically 0 (see above). 3. If you have to show that some quantity is decreasing, show that its derivative with its respect to time is always negative. To do this use ALL INFORMATION GIVEN TO YOU IN THE QUESTION, remember mixed partials are equal, and for the love of god integrate by parts (or use the divergence thm) until your expression is a bunch of stuff that looks like the integral over -u^2 or -u'^2 or something. Savin won't tell you these general strategies, but if you're reflective you'll pick these strategies up from the homework and use them all the time on the tests. Also, never leave a test answer blank! Just write something, write down the wave equation or the maximum principle or something. He'll try and give you as much partial credit as his conscious will allow because he's so depressed at how badly his students do. There's no way to fake yourself to an A in this class, but if you take it seriously Savin will be less disappointed in you than he is in everyone else.

May 2014

This class was definitely not one of the better math classes I have taken. I think most people were rather apathetic about the experience and didn’t feel too strongly about the course in either sense. I found the course straightforward and easy to do well in, but less enjoyable and rewarding than other more challenging math classes that required more ingenuity. The class follows the textbook by Walter Strauss extremely closely, covering chapters 1 through 7. The lectures are so similar to the pages of the textbook to the point that the textbook was often a perfectly good substitute for attending lectures. The lectures themselves are okay, but she does get confused and make mistakes on the board more often than would be optimal. She is very often late to class, and end up rushing at the end and inevitably running overtime. She warned the class on the first day that this class is taught at a higher level than ODEs, with the justification that other departments offer more applied courses in PDEs. This is not wrong, but I also found that this class was taught at a lower level of sophistication than most of the other math classes I have taken. The class is mostly computational, as reflected by the proportion of the problems on homework and exams that were computations. A small number of short proofs are presented in lecture (and the textbook), and most of the proofs on homework and exams were simple variations of the proofs from lecture. For the exams, remembering the proofs from lecture should be enough to complete those problems. The weekly homework assignments were pretty long, with most having around 10 problems from the book. Most of the problems are straightforward, though a few are more challenging, and many are quite heavy computationally. Some of the problems just seemed like filler. I think a lot of students used online solutions to complete the homework assignments. I ultimately think the homework assignments were a negative in this class because grading was extremely slow, with some assignments taking as long as a month to be returned, and solutions were not posted until immediately before the exams. I found the exams very straightforward and reasonable. Most of the questions on the exam testing the material in the most straight-forward way possible. Some of the questions were simple tests of whether you remembered a definition/formula/proof, and these things were easy to pick out when studying because she never asked anything remotely obscure.

Sep 2011

If ODE is calculus on steroids with crazy computations, PDE takes a left turn and is very math heavy. Computations can be even more difficult, but the proofs and concepts are the hardest part here. The book by strauss is helpful along with his suggested book by bleecker for additional explanations. They are easy to follow, especially compared to the grad level books that I tried to read through. Prof Monteanu is a very nice and funny guy. He followed Prof Daskalopoulos's syllabus closely which is very close to the book. He explains everything well and (I thought) better than the two text books. A combo of all three sources worked for me. During office hours, he is very patient and answered all questions. The official course description didn't list calc 4 as a prereq, but he did. It was used in the last 1/3 of the class but more abstract, similar to the same way ODE used calc. I got by not having taken calc 4.

Jun 2010

Prof. Daskalopoulos is wonderful! I had a great time in her class, and I have definitely learned a lot. I do want to stress, though, that this class is difficult and time-consuming (due to the subject matter). An applied math major, I spent an average of 15 frustrating hours a week doing homework. I also found the first couple week's homework to be the hardest, so hang in there. However, Prof. D definitely realizes the complexity of the material and does her best to accommodate. She proceeds at a very manageable pace through the material, keeping to the book so that you can review the material easily. While technically this also made her lectures skip-able, I found myself attending each one because she is a decent lecturer. Her accent is slight, and I got used to it after a few classes. She was also very open to questions, both in office hours and in class. The book we used was by Walter Strauss, and while it was somewhat condensed, it was still easy to read and review. Compared to the homeworks which I found very difficult, the exams were much more straightforward. There were no curveballs. There was one proof on the midterm and a couple on the final, but these were the short ones in the book/homework, so you would do well to review them (there were really only 5 or so proved theorems overall, so it's not much to memorize). The rest of the problems were computational. On a final note, the grading was more than fair. The TAs always gave a good chunk of credit for having the right idea of how to solve a problem, even if the final answer was not correct. Also, I thought that the final curve to be generous although to be fair I am not sure what the general distribution of the class was. Overall, I would highly recommend this class with Prof. D!

Dec 2005

Prof. Bhat did not actually teach me anything, I came to class to find out what subjects were being covered. His lectures focused on delivering a lengthy overview of the most fundamental concepts (including jotting down examples of solutions to problems he never talked about), not the details of solving problems. If I wanted to learn random trivia about PDEs, this would be the class I'd take - but I'd prefer to actually learn how to solve them.

Jan 2004

What an idiot. We were supposed to learn Partial Differential Equations, which is a relatively straightforward question if you are good with math, but he decided to teach us whatever he wants. He enjoys humiliating students and assigning work way too difficult for even the brightest of students. All the bad reviews of him below are definitely true. Anyway, if you want to learn math and get a good foundation in the subject specified, don't take him. If you already know PDE or whatever and are taking it for only-god-knows-why, then I guess he's your ideal choice. Have fun!