Calculus III

MATH 2310 (UVA)

Course information


The main focus of the course will be introducing the techniques involved in the study of functions of two and three variables. An overview of the topics covered and a rough schedule of the course can be found on the syllabus.

The calculus of multiple variables, loosely speaking, uses the techniques you learned in single-variable calculus (limits, derivatives, and integrals) to explore and understand 3-dimensional — or higher-dimensional — problems. Some of these are motivated by physical questions:

  • How do we describe a magnetic field suffusing 3-dimensional space?
  • What do we mean by velocity and acceleration for a particle corkscrewing through space? How do we compute and describe these?
  • How much energy does sunlight transfer to the earth’s surface?

Other motivating questions have a more everyday feel:

  • What do the lines on a topographical map mean? How can I tell which way direction I have to go to get to the top of a mountain from a topographical map?
  • If we have an object, can we describe “how curved” the object is? What if the object is very irregular?
  • How do we compute the volume of an oddly shaped bottle?

The techniques and concepts we will study in this class are of great use in a variety of other disciplines. They are key to the understanding of modern — and not-so-modern — physics and chemistry. Unsurprisingly, they will also occur again and again in different guises throughout mathematics and statistics. Slightly further afield, many of the techniques are widely used in the study of economics. This course will aim at providing the knowledge and understanding necessary to embark upon the study of these applications, as well as the background necessary to proceed further into mathematics.

+A free textbook from a more advanced perspective is available here. +As the course goes on, I am trying to occasionally make visualizations of some concepts using Mathematica. A list of these, and links to the visualizations can be found here. +On Collab, I have enabled LaTeX, which should allow you to type mathematics more easily. A brief guide to writing equations in LaTeX is here. A short list of commands to produce specific mathematical symbols can be found here. Note that, on Collab, inline math is placed between single dollar signs, and display math is placed between double dollar signs. On Piazza, all math must be between double dollar signs.