course
Multivariable Calculus for Engineers and Applied Scientists

I am cautioning you to take someone else for Multi. He doesn't explain anything and his whole teaching style is "this theorem works because, it works" and you have to just take his word on it. And he hardly does practice problems to show you how to apply the concept. I would not be able to get through that class if it weren't for the TAs. The homeworks don't even test you on what you actually learned in class, they're more like, "hey so you know how we defined a dot product as multiplying and adding all the components together? What if the dot product actually SUBTRACTED the vectors, got the frobenius norm of the new vector, and rounded it to the nearest prime number??? Use this new definition of 'dot products' and calculate the projection onto a dodecahedral plane even though nothing remotely similar to this was taught in class!" The first exam goes bad for everyone, the second is better but the final still sends a tingle down my spine to this day. The quizzes are extremely straight forward though and even you don't pay attention much you'll do well on these.

Challenging but I learned a lot. It was online so the 3D visualizations and demos really helped. The first test and most of the psets stretched what we had learned a lot which required a lot of thought, but the second midterm and final were very reasonable if you were able to do the practice problems consistently. Youngren is positive and good at explaining things so it's all about the effort and attention you put in.

Although he is a lovely person and entertaining I must say his class on zoom was in the top 5 most challenging classes of my life. His class structure was not helpful at all and hard to keep up with. I attended Youngren's classes too to see if it was about the course or my prof. Unfortunately, youngren was great with extra visuals, graphs, and a thorough presentation of the content. The material in multi is definitely hard and you have to build on each new concept and with amir, everything felt out of context. I loved Amir as a person and enjoyed his company but regret taking this course from him.

Amazing teaching! It's often hard to describe what makes a good math teacher, but Youngren checks all the boxes. Clear, passionate, down-to-earth, and is always looking out for his students. There was never an unfair assignment, an unclear lecture, or really any moment where I was frustrated with him or the class. Yeah, the material is tough, but he makes it very understandable. He uses a lot of 3D models in class, and a lot of real-world analogies, which really helped me understand what the hell Muli actually was. He puts a lot of emphasis on learning vs just memorizing, and he really wants you to understand why you're doing something, not just how to do it. I hope I get to take more classes with Youngren because he is absolutely phenomenal!

To begin with, the class is not curved despite the fact that the averages are not good (around 70% for the first meaning most people get Cs and around (80% for the second meaning most get B-). Drew is a boring lecturer who does not really know how to teach the material. You are better off learning from the textbook and other sources because his lectures do not have much information and when they do it is simply a formula and example, no explanation on the slides themselves and his explanations if you decide to attend lecture are pretty bad.

Drew in an angelic human being who loves teaching math. His lectures are engaging, presentation of material is at a comfortably brisk pace if you're prepared for the class, and his humor is underrated. His voice is very audible and his blackboard writing, very legible. He's also great about answering questions, and not at all intimidating. His class was by far my favorite freshman year class.

Professor Montanelli was amazing. He was a really great lecturer who managed to keep a large 8:40 lecture class engaged in his material. He is very approachable and willing to answer questions throughout the lecture and afterwards. One of the best professors I had my freshman year.

One thing I will credit Drew for is that he doesn't waste time. Pretty much within the first two lectures you will get into maths that you will not have learned before (if you're from an AP Calculus BC background). The class was fairly difficult, but if you studied well and hard, you would be rewarded. Personally, I thought that the exams were very straight-forward and fair. His midterm and exam comprise of two parts: multiple choice and free response. In my opinion, the free response has always been easy and true to what we learned. On the other hand, the multiple choice is a lot more specific and harder, requiring much more thought and knowledge. The homeworks were much harder than the exams ever were. I think the average time someone has spent on the homework hovers around 5-8 hours. There are also weekly quizzes in recitation that can be difficult, just because of the time crunch (need to complete in ~15 min) and tricky wording. I would advise taking it second semester. Since this class is a requirement for SEAS kids, in the first semester there are always a lot of new freshmen who have taken this class before or taken higher maths. Second semester are the students who moved up from Calculus II to Multivariable and the curve in that semester is a lot better. Drew Youngren is a pretty good prof. His lectures can be hard to follow sometimes, but he's extremely enthusiastic and loves this subject. He's good at answering questions you may have on the subject, and will go over practice final/midterm questions with us.

The class itself is a mixed bag of people coming straight out of Calc I/II and a few people who couldn't get credit for having already taken it. It did sometimes feel like the professor measured the success of the class based on the overall average, which didn't consider how well those learning the material for the first time were doing. That being said, Youngren is a great lecturer and very accessible both with his office hours (a 2 hour block that expectedly gets over-crowed around exams) and with scheduled appointments where he can explain things more in depth. He's very focused on actually teaching the material and posts his dynamic Mathematica lecture slides immediately after lecture. I don't recommend skipping lecture though; despite his general tech savvy, Youngren has not figured out how to include the notes/examples written during class (which are essential). I felt like the course was rushed. There's a lot of material from both Calc III and IV. The focus of the class is obviously on the more applicable aspects of Calculus, but it did seem like there were gaps in what we covered that might've made the material make more sense. If you have the time and space in your schedule and are someone who needs an explanation for math rather than just examples/applications, I recommend the old III/IV track instead. There is no curve but he sets the ranges for letter grades himself. Another note: most of the applications we learned didn't make any sense to me until after I took Physics 1402 (flux and fields) so don't feel bad if some stuff doesn't click until after the final. Summary: Good teaching, nice guy, go to lectures, fast paced class

Really boring lecturer, especially hard to stay awake in the 8:40 lecture. Nothing he teaches in class can't be picked up through the notes he posts. I was in his very first section, and there was no curve for the class, despite many people doing very poorly on the exams. Weekly quizzes were sometimes tough, and the compensation would be to "make the next one super easy" instead of curving. (Which, as anyone who teaches a math class should now, does not balance that out...) Tl;dr Boring + harsh avoid if possible

This class is very different from standard Calculus classes that you will take/have taken. Professor Youngren puts a lot of emphasis on conceptually understanding the material as opposed to just knowing how to do the problems/regurgitating equations. For a class geared towards engineers and applied scientists, it was surprisingly theoretical and not applied at all. Although Professor Youngren is an enthusiastic and intelligent professor who is very approachable, the reason this class is more difficult is because you get so lost in the basis of the theorems and the proofs during lecture that you come out not knowing what you even learned. The second problem with my experience wasn't the professor, but since this is the highest level math class a freshman can place into, the class is filled with mathematical geniuses and students who took the class three years ago, making it very difficult for those who haven't taken the class to keep up. He also doesn't curve your grade as a result, but will shift it up 1-2% to the next highest grade increment if you're close. My 87 was still a B+ after the curve. Take this class if you're really good at math and don't want to do much work, or if you want to learn a lot of conceptual stuff about math and are fine with a lower grade. Definitely don't expect a free A or A-