This class will cover multivariable calculus at an advanced level: vector spaces, div, grad and curl, differential forms, and Stokes’ theorems. The coverage will be at the level of Loomis and Sternberg’s Advanced Calculus. The course will also provide an introduction to the rudiments of differential geometry: connections, curvature, and the Gauss-Bonnet theorem. Applications will be made to Maxwell’s equations and to general relativity.