Geometry and Physics (University of Groningen)
Geometry and Physics (Meetkunde en Natuurkunde) was an elective course for University of Groningen students in the programs BSc Mathematics, BSc Applied Mathematics, BSc Astronomy, BSc Physics & Mathematics, MSc Physics, and MSc Applied Physics. I taught this course from 2005 to 2007 in small classes.
Gauss and Riemann, among others, studied the properties of manifolds: curved, non-Euclidean spaces. But it was Einstein’s theory of General Relativity that familiarized physicists with such spaces. Differential forms are a powerful tool for computing on manifolds, while at the same time they offer a beautiful geometric abstraction. After introducing the concept of a submanifold of a Euclidean space we discuss vector fields and differential forms in Euclidean space. Finally, we generalize these concepts to manifolds. We show how the generalized Stokes theorem expressed in the language of differential forms unifies the, well-known from vector calculus, theorems of Gauss and Stokes. Finally, we discuss applications of differential forms in electromagnetism and dynamical systems.
Meetkunde en fysica, met differentiaalvormen en integraalstellingen, H. W. Broer, Epsilon Uitgaven, 1999.