# MAT 201: Multivariable Calculus

Posted on by Tejas Gupta

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.

## Opinions

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.

## Course Materials

**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.

## Advice

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.

## Additional Materials

- Khan Academy – videos, problems, and solutions by Grant Sanderson (of 3blue1brown)
- Lamar University Notes