Multivariable Calculus

Description of Course Goals and Curriculum

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. The stated objectives of this course are to give a thorough introduction to multivariable calculus and mathematical methods needed to understand real world questions involving quantities changing over time in three-dimensional space. Because this course emphasizes concrete computations over more theoretical considerations (which is more appropriate for MAT 203), there is a much greater emphasis on actually solving math problems rather than proving them; however, even though the topics covered are useful for solving “real world questions,” almost none of the problems are in an applied context. The pace of this course is extremely fast, and many students who do not have prior knowledge of multivariable calculus find it to be very intense. The course description indicates that a prior knowledge of calculus (MAT 103 and MAT 104) is required; however there are several hidden expectations. This course is comprised of many sophomore students who are continuing the math sequence from previous semesters, so professors do not treat this as an introductory course. For many freshmen students who are taking this as their first math class at Princeton, jumping right into a comprehensive class that is not catered toward freshmen can be very difficult.

Learning From Classroom Instruction

It is important to note that the structure of this class is somewhat atypical from most classes taught at Princeton. Instead of a having a large lecture accompanied by smaller precepts, there are multiple sections of MAT201 classes that are taught by different professors. In order to standardize the material taught, professors will often teach the same questions, based off of very similar problems seen in the textbook. This is the only component of the course, so if you do not understand the material being taught, you need to either switch to a different professor in another section, or else attend office hours or the McGraw Center. In order to get the most out of the class, it is recommended to read the material in the textbook before the lecture, so that you are familiar with the terminology and basic concepts prior to coming to class. The material covered in this course is strictly from the textbook.

Learning For and From Assignments

The purpose of problem sets in this course is to ensure that you are keeping up with the material covered in class. They are in no way indicative of the level of rigor of quizzes and exams, and primarily serve to boost your grade and get familiar with applying new concepts. The quizzes and exams are very challenging, and require the ability to approach complex and unfamiliar questions using the techniques learned in class. The most useful thing one can do to prepare for these assessments is to do as many previous exams as possible; once you do several of them, it is very easy to see what types of questions they ask and what topics they feel are the most important.

External Resources

Because this class is so fast-paced and there is only one class component to this course, many students use external resources to learn and review the material. The McGraw Center has both individual tutoring options and group problem-solving study halls that are tailored towards MAT 201. Almost all students work together on problem sets, and will go to office hours to seek help. Additionally, there is an amazing series of lectures, taught by a visiting Princeton professor Adrian Banner, available on YouTube. These lectures cover essentially the same material covered in the actual class, and is extraordinarily well taught, with excellent example problems. The link for all of his lectures can be found here: www.youtube.com/playlist?list=PLGqzsq0erqU7h6_bpE-CgJp4iX5aRju28

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

A very significant percentage of students enrolled in MAT 201 have actually already taken a course in multivariable calculus in high school, and are taking this class for the second time to fulfill distribution requirements. This means that because you are graded on a strict curve relative to your peers, there is a significant disadvantage from the very start for students who do not have experience with multivariable calculus. Due to the nature of the class being split into multiple sections, there are inherent differences in the styles of teaching in each class. It is strongly recommended that you “shop” around between different MAT 201 sections to find the professor that suits you the best. Keep in mind that although this course in extremely rigorous and is graded on a curve, the distribution of grades is often so low that the curves will actually help most students. Getting a 40%-50% on an exam is not necessarily cause for alarm if the passing grade is a 20%. Lastly, even though people should not focus solely on the grade earned, because this is a very large quantitative course, it is very easy for professors to only take into account your performance on assessments when determining your grade. It is completely common to get an exam back fraught with grading mistakes because the graders did not take enough time to actually understand the student’s work (i.e. if the answer is wrong, you will likely receive very little or no partial credit). Always review your exams with your professor and take the time to walk him or her through your work so that you get the grade that you actually earned.