MATH495B

The famous theorems of Gauss, Green, and Stokes in multivariable calculus have many important applications in the study of electromagnetic fields, heat diffusion, fluid dynamics, and complex analysis. Moreover, they are all generalizations of the (one dimensional) Fundamental Theorem of Calculus. These results assert that a certain (k dimensional) integral over a region is the (k-1 dimensional) integral over the boundary of the region, culminating in the so-called Generalized Stokes Theorem. This seminar aims to explore this general form of the classical Stokes Theorem and related topics, including the concept of differential forms.