Section 5 Course description
Math 2575 deals with the calculus of vectors, and functions of several variables. We begin with vectors, and vector valued functions, before moving on to several variables, and then finally, combining the two at the end. Just like in one variable, differentiability corresponds to the existence of a linear approximation. We’ll then explore multivariable versions of familiar topics, like critical points, extrema, and optimization.
Since Math 1410 is a prerequisite for this course, we can do a few things that don’t always make it into a standard calculus course. (At many universities, linear algebra is taken after the calculus sequence is complete.) In particular, we’ll be able to make better sense of the notion of linear approximation: the linear approximation to a surface is a plane; the linear approximation to a differentiable function is a matrix transformation!
We’ll then move on to double and triple integrals, and finally, to vector calculus. Most of what we see in the standard curriculum for vector calculus was developed to deal with problems in Physics, and in particular, electrodynamics. Those of you who have done a course or two in Physics will hopefully be able to make some connections.
