Multivariate Calculus

Official Description

Multivariate Calculus (17-321)
Topics include functions of several variables, partial differentiation, and multiple integration.

Overview

First half: vector geometry and matrix algebra
Second half: functions of several variables, partial differentiation, and multiple integration

What actually happens

Calc III is taught by Dr. Kurt Fink. This is a class that you really have to attend, or do all of the homework for. It goes too fast to miss classes, though not so fast that you couldn't do well by showing up and taking notes and doing problems in class. The first half of the class really is just preparing you with the tools you need to take the second half, so unless you're already versed in vectors, matrices, and multidimensional analogs to familiar geometric objects, you really need to show up to the first half. In the second half you learn scalar valued (Rⁿ -> R) and vector valued (R^m -> Rⁿ) functions, gradiants (total derivatives) of said functions, and multiple integrals of said functions. Gradients are useful in multiple dimensions in about the same way that derivatives are useful in two: rate of change. Gradients just happen to also give direction, as a slope of four means nothing in >2 dimensions. Multiple integrals are (predictably enough) an analog to single integrals, with just about as many uses. Arclength, surface area, volume, as well as integrating over a solid, giving you values that could be interpreted as temperature, or mass, among other things.

Throughout the class, you do 5 labs, in which you do a bit of math, and then fight with the computer using Matlab, a computer algebra system surely designed by Satan. The math is actually pretty easy, as the goal of the labs is mostly to "get you out of the plane" (meaning stop thinking in two-dimensions), but I hear he may be making it more difficult in future classes. Unfortunately matlab, and drawing altogether, goes out of scope pretty quickly as you increase dimensions. So it's actually more important to understand the math analytically than geometrically.