Vector Analysis

The mathematical description of much of physics and engineering, including mechanics, continuum and fluid mechanics, and electromagnetism, depends heavily on the language of vectors, particularly in three dimensions. In this course we will develop the theory of vector analysis, the differential and integral calculus of scalar and vector functions in one and several dimensions, leading us to the great theorems of Green, Gauss and Stokes and some of their applications. We will aim for an appreciation both of the underlying mathematics as well as of some of the applications that have historically motivated this theory. As time permits, we will explore how one can extend the linear structure of vector algebra to more general vector spaces of polynomials and functions, including an introduction to Fourier series.