This course will focus on the study of fundamental theorems and applications of multivariable calculus, extending the calculus of one-dimension studied in AP Calculus BC to Euclidean spaces of arbitrary dimension. The course will begin with careful consideration of vectors in Rn and then move on to the theory of partial derivatives and vector fields. Multiple Riemann integrals and their applications will be covered in term 2, as well as important theorems of vector calculus including the theorems of Green, Gauss, and Stokes. A nontrivial amount of real analysis and point-set topology will be studied to facilitate the development of certain multivariable calculus concepts. This increased sophistication will allow students to see more clearly how multivariable calculus is a beautiful generalization of single-variable calculus.

This course requires weekly engagement but is primarily asynchronous which allows students to work around their school schedule. There is a synchronous meeting that will take place one evening per week that is optional for students to attend. Meeting times to be determined at the beginning of the term. One-on-one support is also available by appointment.