Multivariable Calculus
This is an old review from the Spring 1998 Course Guide. This review may not be accurate.

# Multivariable Calculus

### Staff

 Lectures: 3.7 Precepts/Classes: 3.8 Readings: 3.2 Papers/Exams: 3.6 Overall: 3.6 Enrollment: 99

MAT201 is the first course in the MAT201-202 series required for engineering and science majors. It is less theoretical and rigorous than the 203-204 series, but that doesn't mean you can slack off at all.

The main topic of the course is vectors and vector calculus. Although many of us were exposed to vectors in high school, MAT201 treats them in a much more thorough manner, and applies calculus concepts that most you will have never seen. The course begins with the introduction of vectors and vector operations. More complex vector concepts like determinants, the cross product, and the dot product follow. The biggest conceptual leap occurs with vector functions and their derivatives. From here on, most students will be seeing all new material. The gradient operator, Lagrange multipliers, surface integrals, and co-ordinate transformation are all introduced. This leads in to the real calculus part: vector fields and divergence and curl, finishing with Green's, Gauss's, and Stoke's Theorems'.

The text is quite good and the pace is not too rapid, but as with all underclass math courses, success or failure hinges significantly on your TA. Shop around until you find one you can work with. There are sporadic quizzes (about four in the semester) written and assigned at the TA's discretion. These are usually 15 minutes or so and not difficult, but require fast recollection of the material. You will hate the weekly problem sets. They aren't long, taking 3-4 hours on average, but tremendously boring, especially when you have to hand draw 3-D graphs. The exam and midterm were tough; no single question was extremely difficult, but none were easy and the tests were long. Curving of grades takes care of some of that, but don't expect an A+ with any ease.

This course will introduce you to the basics of vectors, their properties and applications, and vector calculus. It's not especially pretty or enjoyable, but definely do-able and you will learn what you need to know if you do (and understand!) all the problem sets.

There is a great difference between the professors of this course. Prof.R.Vakil is great; namely he is comprehensible, interacts with his students and stops whenever there is a question that refers to something he has said. Professor Hsiang, although obviously a great mathematician, was very difficult to comprehend, not particularly friendly to those who proposed other methods of answering and less interactive with his students. His language also made it much harder for us to understand his meanings
Sat Dec 13 22:14:21 EST 1997
After two weeks in MAT203, I came to my senses and decided to drop down to a course more on my level. The first semester of this course was just fine. The material was intelligible and even somewhat interesting. After the midterm, something changed. The material was no longer decipherable and the course wasn't quite as interesting as a result. Professor Peters was an excellent instructor who would always explain things to the best of his ability. I give this course a thumbs up
Sat Dec 13 22:34:08 EST 1997
• This course took some getting used to. Professr Hsiang seemed harsh at first, but the class came to realize his intentions. There are two sides to having the course director as your teacher. First, he knows exactly what will be happenning in the course. He also tends to hold you to a higher standard. The drawback is that if there is a problem, there is no arbitrator. This appeared to be a problem for me, as my schedule did not allow me to attend his extra Monday night session, and I told him not to worry, that I could handle it. I think this probably had an adverse affect on my grade in the beginning, but later he did accept the fact that I could do well on my own. I'm not big on seeking help when I'm confused. I like to fight my own battles. In the end, I think I actually learn better that way. It took too long to prove this.
• He was fair as a grader. He used take home quizzes to save class time, and I'm sure there were students that abused the privelage. No one should be handing in timed take-homes that were that neatly done. Come on, everyone erases at some point. The final exam was not difficult, but the midterm was confusing.
Sat Dec 13 22:48:26 EST 1997
This course was fine when I understood everything, but not so great when I was having difficulty. The classes were not always well organised, and were virtually no help in solving the problem sets. My biggest complaint, however, concerns the text. The information it provided was minimal, and the author seemed more interested in abstactions than actual analysis or examples.
Thu Apr 9 19:44:56 EDT 1998
The key to 201 was getting Ravi Vakil. Ravi was one of the best professors I've ever encountered...a friendly, intelligable genius who absolutely LOVED teaching the material. Ravi's section is the only way to go through 201.
Thu Apr 16 00:11:09 EDT 1998
This class becomes very very difficult in the second half. Thus, just don't get too relaxed after the midterm; the final will kill you. This is not an extremely difficult class, but it's very tedious. The problem sets take hours. Sergio Fenley is a good instructor, and very helpful, too.
Sun Jan 24 16:48:24 EST 1999
Torok is excellent, clear, and helpful. Take his section if you can.
Sun Apr 18 21:24:18 EDT 1999
MAT 201 is a pretty fun class- it's just a standard vanilla math class- nothing special about it, although coming out of high school math, I was shocked and happy at the curve on the midterm.

Prof. T.J. Li is great- he's funny, understanding, and is the easiest to understand out of all of the lecturers.

Semester Taken: Fall 99
Professor: T.J. Li
User's major: Electrical Engineering

Sun Nov 28 21:35:36 EST 1999

this class is by far the worst that i have taken. the instructors were barely understandable, even though that seems to be standard for intro math courses. the lectures in the second half of the semester were absurd. the entire class was lost on the material, yet our instructor marched on in order to keep up with the syllabus. i felt that the class didnt prepare me for the midterm or final, only my own preparation outside of class. our preceptor was unwilling to give any in depth answers during the class time in order to keep up with fast paced syllabus. incidentally, not many questions were asked because the responses were pretty much unintelligible.

the material is definitely usefull later on from what previous students have told me, so be prepared to do a lot of work on your own if this class is important for your major.

in general, if you feel that you can study on your own and math concepts come pretty naturally to you, you should be ok with the course. however, i wouldnt recommend it if you are just looking for a non required course.

Semester Taken: fall 1999
Professor:
User's major: engineering

Fri Jan 14 00:44:20 EST 2000

the essential problem with the class, was the professors who seemed as though they had just escaped from the grasp of the ins. not only was the language barrier a problem, but the blatant disregard for the students level of comprehension created a one, two punch of one of the worst sides of princeton.

Semester Taken: fall 1999
Professor:
User's major: not math

Fri Jan 14 14:05:26 EST 2000

This class isn't terribly hard, but you can be deceived as to how well you're doing. The problem sets aren't too bad, and the take home quizzes are pretty easy. But the midterm and final are hard. I thought I was in great shape for the midterm, but while I was taking it I quickly realized that it was probably the hardest math test I had ever seen. But don't worry, the curve is very generous (the mean for the midterm was 50---a "B"). The course does get harder in the second half, so be prepared. And the final basically covers the last two weeks of the course and nothing else. But, overall, the class isn't that bad, and I suspect most of you have to take it anyway

Semester Taken: Fall 1999
Professor: Schlag
User's major: Operations Research

Thu Mar 16 19:26:55 EST 2000

If you don't need this class (read: if you're not an engineer or science or math major) DON'T TAKE IT. I'm not a math/science/engineering major but was pretty good at that kind of stuff in high school, and placed into MAT 201 based on my AP score. Big mistake -- this class served as my first Princeton reality check. The course starts off incredibly easy (at least in retrospect) and gets progressively harder and faster each week. The actual quality of the teaching varies hugely depending on who your instructor is -- Schlag is difficult to understand but he was rather receptive to the blank, glassy-eyed looks on our faces and took the time to explain and re-explain. However, if you do need this course, don't be discouraged. Extra help is always available if you go after it, and hard work pays huge dividends so long as you really, really stay up on the work and put out an honest effort on the problem sets. Most importantly, this is a class where you worship the curve: the midterm was the singularly most painful experience of my life, yet I'm happy to say I got an A- (though I still don't understand half the material).

Semester Taken: Fall 1999
Professor: Schlag
User's major: ROM

Mon Apr 17 18:52:39 EDT 2000

If you got an A- and the midterm was "the singularly most painful experience of your life", I got a C- on it...I would rethink that statement if I were you. Comments like these make me despise this school--come on, how could you possibly be that hard on yourself.

Semester Taken:
Professor:

Tue Apr 18 00:00:36 EDT 2000

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