Multivariable Calculus

Description of Course Goals and Curriculum

This course is described as including:  "Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields and Stokes's theorem."  It consists of weekly problem sets and readings from the textbook, with quizzes being determined by instructor.  Although the only prerequisite is MAT104 (or equivalent), many students taking this course have already been exposed to many multivariable concepts in previous math classes.  This means that for students who are learning these concepts for the first time, this course may seem intense and fast-paced from the start.

Learning From Classroom Instruction

This course is different than many other STEM courses at Princeton since it only consists of smaller, classroom-sized precepts, which meet three times a week, rather than lectures.  These precepts are taught by many different professors, which means that finding a professor you like is easier than many other classes that only have one professor.  Because of this, many students go to different precepts at the beginning of the semester in an attempt to find the professor that is best fit for them.  As far as actual classroom instruction, each class, the professor will work through and teach the weekly content from the book, supplementing this teaching are various example problems that tend to go beyond what is shown in the book.  One thing to note is that the content covered in this course is strictly from the textbook, so doing the readings before class is beneficial since it allows you to already be familiar with the weekly content.

Learning For and From Assignments

The problem sets in this course are primarily used to make sure that students are keeping up with the material.  They are completely different, and far easier, than the problems that are included in the quizzes and exams.  Thus, the problem sets can help students make sure that they understand the basic concepts, while example problems from class and the past exams are the real application of the learned content.  To make sure you thoroughly learn the content, gain the ability to think intuitively about problems, and prepare for the quizzes/exams, make sure you look at these example problems from class and past exams.

External Resources

Because this is still considered an introductory math course, there are many resources available for struggling students.  One of the best resources available is the McGraw Center, which has individual and group tutoring options.  These individual and group tutoring options are available for a few hours every day from Sunday to Wednesday, and are a great way to make sure you are keeping up with your work and understanding the content.  The individual tutoring option is mostly used for supplementing and reteaching the content covered in previous weeks, while the group tutoring option is mostly used for help on problem sets and working on other problems.  Another great resource available is office hours.  Since there are so many professors teaching this class, there are also many different office hours available throughout the week.  So even if you can't make your professor's office hours, you can always go to someone else's.

What Students Should Know About This Course For Purposes Of Course Selection

As mentioned above, many students taking this course have already been exposed to many multivariable concepts in previous math classes.  This means that there is a steep learning curve at the beginning of the semester as you cover the basics of three-dimensional space, topics that these students already have a good understanding of.  Because of this, you might find yourself discouraged, especially after the first quiz, as the curve is higher than usual.  But it gets better.  As the semester progresses, you become more familiar with the basic concepts of the class and get into topics that are new for everyone in the class.  Once this happens, the curve will become better and more lenient. And as far as course selection, this course is purely computational while other classes, such as MAT203, cover the same content but in a more theoretical sense.  For most people, this computational and application-based side of multivariable calculus is more than enough for what they need, but for those that want a more theoretical and abstract understanding of math, other courses might be a better fit.