MAT 201: Multivariable Calculus is the standard mathematics course that Princeton engineers and math-track Economics majors complete, usually in their first year. The class is formatted to have large lectures as well as two/three 40 minute small discussion sections led by a preceptor, who is almost always a postdoc in the Mathematics department.
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather than just one.
Many students struggle in this course, depending on their mathematical preparation, their individual preceptor, and to be honest, their problem set group. I took this course during the COVID-19 pandemic, while living in an apartment with three other engineering students in the course, which aided my preparation in the course. However, I truly believe that anyone can succeed in this course, as there are an abundance of resources on this topic. I personally enjoyed the course due to its extension of single-variable concepts that I remembered, the rigid but clear structure of the course and the friends I made through the problem sets we had to solve.
Textbook: Thomas’ Calculus: Multivariable, 14th edition by Joel R. Hass, Christopher E. Heil, Maurice D. Weir, ISBN-13: 978-0134439020.
Topics: vector calculus, partial differentiation and optimization, double and triple integrals in various coordinate systems, line and surface integrals, as well as Green’s, Stokes’ and Divergence theorems.
To succeed in this course and learn the material in an in-depth manner, I believe you ought to learn the material before the precepts, either through the lectures or reading the textbook material. I personally never watched any of the lectures because I believe completing the textbook examples and referencing them while completing the assigned problems provided sufficient understanding.
In replacement for lectures and precepts, I found Alexandra Niedden’s breakdown of each chapter very helpful:
- Chapter 12: Vectors and the Geometry of Space
- Chapter 13: Vector-Valued Functions and Motion in Space
- Chapter 14: Partial Derivatives
- Chapter 15: Multiple Integrals
- Chapter 16: Integrals and Vector Fields
I believe the only way to truly understand the material is to do as many problems as possible. Before each exam, I attempted to complete at least 40-50 problems from previous exams. Though I probably cannot release Princeton’s specific course materials, here are Berkeley’s.
For the problem sets, I recommend you attempt them with friends smarter than you.