This is one of those courses that students from a variety of backgrounds still have to take. Math 200 is a course in multivariable calculus. Your standard first year calculus courses cover topics in differential and integral calculus, analytical methods for understanding rate relations and modeling systems. What you may have noticed, however, is that these courses are largely one-dimensional. You deal with some quantity as it varies with respect to some dependent variable. Math 200 is the extension of first year calculus to multiple dimensions.
By multiple, I mean 2 or 3. Concepts remain well within the realm of visualizability, though they are more brain-bending than anything in Math thus far. You will begin with concepts in vector analysis such as using dot products and cross products, lead into partial derivatives (which are just derivatives with respect to one variable, treating all the other variables as constants) and their applications, and then into multiple integration (integrating over a 2 dimensional or 3 dimensional space instead of just along one axis).
Math 200 sets the groundwork for future courses in Mathematics, such as Math 215 and Math 317, and is therefore a cornerstone for prerequisites in Physics. Physical systems are often modelled in one or two dimensions to start with, but most concepts are extended to three or more dimensions when applied to real-world situations. It is key to develop a solid understanding of the analytic approach to such problems, which can be difficult to interpret by visualization alone.
Math 317 (vector calculus) starts where 200 left off. It can be divided into three main parts: (1) analysis of space curves, (2) scalar and vector fields in two dimensions, (3) parametric surfaces and scalar and vector fields in three dimensions. This course builds on the concept of parametrization, showing that if components of a curve's parametrization are known, then one can prove some powerful theorems to analyse such systems. Here, you will study Green's theorem, Stokes theorem, and divergence/Gauss' theorem. Between these three, there lies a considerable amount of abstract conceptual imagery.
Math 200 and 317 are key for the study of topics in classical mechanics and electrodynamics, and are useful for modelling systems in all practically all fields of Physics. I would consider Math 200 a survey course in mathematical concepts, akin to first year Math courses (at least the way I was taught it anyhow), while Math 317 delves deeper into analytical theory. Much of Math 317 follows a "theorem-proof" format, more suggestive of higher level Math courses.
Both courses are central to the study of Physics, and I found them both interesting. I found Math 200 a little dry, but that may have been because I took it as a first year student and was finding my way around the University. Math 317, on the other hand, is the last Math course I've taken (and the last one I'll probably ever take). It has been an absolute pleasure to be in Dr. Ed Perkins's class. His manner of teaching is crystal clear and well-paced, and this course not only was enjoyable and relaxing, but helped to elucidate concepts which I had long grappled with.
