# MAT201 Multivariable Calculus

Announcement:

This summer, Princeton  will be offering a small suite of  STEM courses this summer (MAT 103, 104, 201, 202 and PHY 110) for students who need these specific courses for degree or concentration progress. Students accepted to the program will not be charged tuition for the courses; students on financial aid will also receive an allotted living expense budget.Please visit: https://forms.gle/52iszwnhbMGLXmCe7 for more information and to apply. The deadline for application is April 7, 2021.

Schedule: MW at 8:30 AM, at 11 AM, at 1:30 PM, and at 3:00 PM (Fall only), Friday precepts; Fall and Spring. Optional review sessions are very helpful, but they are scheduled only after classes begin.

Brief Course Description: Third semester of the standard 3-semester calculus sequence. Gives a thorough introduction to multivariable calculus and mathematical methods needed to understand real world problems involving quantities changing over time in two and three dimensions. Topics include vectors, lines, planes, curves, and surfaces in 3-space; limits, continuity, and differentiation of multivariable functions; gradient, chain rule, linear approximation, optimization of multivariable functions; double and triple integrals in different coordinate systems; vector fields and vector calculus in 2- and 3-space, line integrals, flux integrals, and integration theorems generalizing the Fundamental Theorem of Calculus (Green's theorem, Stokes' theorem and Gauss's theorem, also known as the divergence theorem).

Why take this course? It provides important mathematical foundations for advanced studies in life sciences, physical sciences, social sciences, computer science and engineering, building vocabulary and tools to describe and understand phenomena in the natural world, and improving analytic and problem-solving skills valuable in many disciplines.

Who takes this course? Most students in this course are first- or second-year students who consider majoring in one of the sciences or engineering.   More mathematically inclined economics majors will take this course along with 202 (instead of 175).  Although it is not a prerequisite, many students in the course will have had a more basic multivariable calculus course in high school.

Prerequisites:  104 or equivalent. A solid knowledge of single-variable calculus and precalculus is essential: how to analyze and graph functions, how to compute and interpret derivatives, how to interpret, set up, and calculate definite integrals with speed and accuracy. The very fast pace means that solid grasp of the prerequisite material is especially important.

### FAQ:

• You already took multivariable in high school or at a local college, so you want to place out of MAT201.  Most students in 201 have some multivariable calculus and/or linear algebra before, but very rarely with the same depth and thoroughness.  Most students will find that the sample problems are much more sophisticated than problems they have encountered in high school. You may want to consider 203, which requires an intense commitment and interest in deeper understanding of the subject and its applications.
• How much work is this course?  This course generalizes both 103 and 104 to higher dimensions. To accomplish this in a single semester, 201 keeps an extremely fast pace and requires that students be fluent in all the main ideas and techniques from single variable calculus. All math courses require a steady time commitment, but this one is particularly demanding. We expect that the weekly problem sets will take at least 3 hours to complete, although this can vary quite a lot for individual students, and this is only the beginning! The exams often include more challenging problems which require complex analytic skills. Learning to think independently and creatively in a mathematical setting takes time and lots of practice.  To do well on math exams, you need to work through a lot of extra problems from past exams and quizzes. All in all, you should be ready to spend at least 10 hours per week working outside of class.
• You want to take both MAT201 and MAT202 in the same semester to get your engineering prerequisites over with. Is this possible? It is not impossible but this is not a good idea for most students. The work load and pace of 201 is particularly overwhelming for many students, and adjusting to the abstraction in 202 is also a big step. Doing both these demanding courses in a single semester should not be undertaken lightly. We would not recommend it for anyone, but it is especially inadvisable for anyone who got less than an A in 104
• You think MAT201 is too hard after looking at the sample problems or attending the first couple classes.  MAT201 is a cumulative course -- the topics build upon themselves throughout the semester.  If you are having difficulty at the beginning of the semester and you want to major in engineering, you should consider switching to 104 to get a thorough foundation for 201.  You should switch as soon as possible, as there is no overlap between 201 and 104 early in the semester, and it will be very difficult to catch up and do well in 104.   You may also consider a switch into 175 if you are absolutely sure that you don’t need to take any further math courses and your program will allow this substitution. (175 is not enough for BSE degrees.)
• You think MAT201 is not challenging enough.  Wait till you have had a quiz, which usually occurs in the 3rd week.  Homework problems are often quite routine compared to exam questions.  Try some old quiz problems, but don’t just read the questions and solutions. Instead, see if you can produce correct solutions to most of the problems in the allotted time.  If you can do well on old exams, then you may consider taking 203 or 215 instead.  201 and 203 cover essentially the same topics, so it is quite easy to switch between the two courses in the first few weeks.  There is no overlap between 201 and 215, so this course switch should take place as early as possible.
• What kind of calculator do I need for this class? We don't use calculators in Princeton calculus classes. If you would normally rely on your calculator for graphing functions, solving equations and computing values of trigonometric functions, you should be very conservative in choosing your first math course.
• Are you serious about no calculators? Why? Calculators can be useful, but these courses want to teach students how to think independently in a quantitative setting and calculators can function as substitute for thinking at the beginning. Students need to learn the basic vocabulary and grammar of mathematics so that they can recognize patterns and common features by working through simple well-chosen examples. For instance, a program like 'Google translate' can be helpful to a person with basic knowledge of a language to decipher a complicated sentence or even to write a correct one, but without a good foundation to refine and direct its application, the results of blindly applying this useful technological tool can be wildly off the mark.
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