MAT201 Multivariable Calculus

Schedule: (Note that we are trying out a different meeting pattern for MAT201 in Fall 2025 to facilitate course registration for students who need to take both MAT201 and PHY103 in the early morning time slots.) The early morning lecture sessions will be offered in three 50-minute sessions held on Mondays, Tuesdays and Wednesdays starting at 8:30AM or at 9:35AM. The other lecture sessions will be offered in two 80-minute sessions on Mondays and Wednesdays, starting at 10:40AM or 1:20PM or 2:55PM. The class also has a precept component for which students register independently. The 50-minute precepts will all be held on Fridays, starting at 8:30AM or 9:35AM or 10:40AM or 12:15PM or 1:20PM.

In the Fall we will offer (optional but recommended) review sessions and homework help two evenings each week, staffed by instructors, preceptors and undergraduate course assistants. (The exact details of this schedule will be determined once 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's theorem and Gauss's theorem, also known as the divergence theorem). Note: no computational technology or internet resources are allowed on homework or exams in this class. 

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 take this course instead of 175.  Many students in the course will have had some multivariable calculus in high school, although this is not a prerequisite.

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 without referring back to notes or textbooks or other resources.  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.