EXTERIOR CALCULUS theory and cases.

This Exterior Calculus ebook has been designed for third-year students of Sciences, as it contains the fundamentals related to Geometric algebra or Grassmann algebra oriented to Calculus. Without any doubt, this algebra has important implications in Science and Engineering. Here, the reader will find a clear presentation of the Geometric algebra on a plane and in space, as well as the extension of all its operators in R n . In order to make the comprehension of this important algebra easier, some examples and completely solved exercises are included. The ebook thoroughly examines the elements of Geometric algebra G over the Real field and these operators: inner product, outer product, and geometric product, their components, and their geometric representation, as well as their properties and the rigid transformations on the plane and in space. It also reviews the differentiation and the integration over Geometric algebra, including the line integral and surface integral. The Green, Stokes and Gauss theorems are also studied in detail and the Theorem of Fundamental Calculus is generalized.