Differential Geometry and Electromagnetism - Tapa blanda

These lecture notes correspond to a short course on Mathematics focusing on the differential geometry of compact manifolds, the exterior Clifford algebra of differential forms and their applications to the classical and relativist theories of electromagnetism in Physics. It is assumed that the reader already knows the definitions and techniques of the exterior calculus and the integration theorems of differential forms on manifolds and submanifolds of euclidean spaces. The text is divided in four chapters. Except Chapter 1, which is an introduction, each chapter is independent from the others. Chapter 2 studies the integration theorems that are obtained from the differential statements of classical Maxwell's equations. In Chapter 3, the Lorentz transformations are introduced to prove the relativist theorems of electromagnetism. Finally, in Section 4, Poisson's equation is introduced and solved by global integration.

Eleonora Catsigeras has born in Montevideo (Uruguay) in 1956. She is PhD in Mathematics and Professor at the Universidad de la República (Uruguay). Her area of research is the mathematical theory of Dynamical Systems and its applications.