The objectives in Advanced Calculus are typically to add depth to your first exposure to calculus. We will cover topics ranging from vector analysis and the calculus of vector spaces through integration over vector spaces. We will begin with a review of basic multivariate calculus and expand on the theory and application of what you have already encountered in elementary calculus. As described in the catalog, this will be "a thorough study of differential and integral calculus of vector-valued functions of a vector variable. Jacobians, inverse and implicit function theorems, change of variables in multiple integrals; theorems of Green, Gauss, and Stokes; applications."

We will approach this subject in a novel way, by looking at the subject both physically and historically. We will begin with Newton and the early problem of planetary motion and possibly end with Einstein. At the same time we will look at the mathematical structure underlying the applications of calculus. You are expected to be familiar with the calculus you have seen in MAT 161, 162 and 261, though we will spend some time reviewing and going deeper into the theory and applications from the latter course.

Group Work: Some of the problems appear in groups and the computations can become tedious. Therefore, to relieve you of some of this, you will be assigned a couple of group projects. Some of these may involve using the computing facilities. This will count 10% of your grade.

Exams and Grades: Exams and Grades: There will be a two 50 minute exams and a final exam. The exams will cover the basic material up to the date of the exam. The tentative dates for the exams are below.

Your final grade will be based on the following:

More information will be posted on the web related to the topics we are studying. Links can be found with summaries to the material, study suggestions, homework assignments, etc. These will be accessible through the instructor's homepage at