Math/Mthe 280 — Advanced Calculus About Lectures OnQ About Lectures OnQ

This course is an introduction to multivariable calculus, suitable for students with a background in Math 120 or APSC 171—172, and with at least one course in linear algebra.

The most obvious difference between multivariable (or vector) calculus and the first year version is that there is simply more of everything: more variables, more types of integrals, and certainly much more notation.

But, along with the sometimes bewildering profusion of new symbols comes something wonderful. The procedure of going from one to several variables is not just mindless generalization, and the process reveals something genuinely new about calculus, something which we don't see in the one variable version.

What's new is that we see that calculus is intimately related to geometry. At first, geometry enters on a very basic level; in order to describe multivariable functions and various integrals we'll naturally need to use the geometric language of curves, surfaces, and vector fields. But later on, geometry returns in a much deeper way. The correct generalization of the fundamental theorem of calculus to the multivariable world intimately links the process of integration to the geometric features of the object being integrated over.

Goals of the course
The primary goal of the course is computation. I want you to be able to set up and compute all types of the integrals and derivatives which appear. The secondary goal is that you understand the ideas in the course and how they fit together.