While most students of vector analysis are no doubt familiar with grad, div, and curl, geometric algebra provides a unified treatment of all these differential operators and extends them to arbitrary manifolds in an arbitrary number of dimensions. As a nice bonus, we recover all of complex analysis in the special case of 2-dimensions - and discover that since, unlike div and curl, the vector derivative is invertible, Cauchy's integral formula results directly upon applying the inverse of the vector derivative to an analytic function. Furthermore, Stoke's theorem, Green's theorem, etc... are all seen to be nothing more than special cases of the Fundamental Theorem of Calculus applied to directed integrals (line and surface integrals). It seems that these approaches force a complete reassessment of the way in which these topics are generally approached in the standard curriculum. Since looking into these ideas I've been forced to question the very foundations of complex analysis and, more generally, the calculus on manifolds. I'm trying to put together an online study group to discuss these topics and other applications of geometric algebra. If anyone is interested, please let me know. All that is required is a little curiosity, a bit of motivation, and an open mind. Join the fun!