Exterior Analysis

Preface

Exterior forms come into existence at its inception as elements of the exterior algebra, which is in essence a Grassmann algebra, formed by defining an operation of exterior product over a linear vector space. However in early 20th century, works of Poincaré, and particularly of Cartan make it possible to extend this algebraic structure as to include the exterior differential forms by employing exterior products of differentials of coordinates. Nevertheless the main impetus to the elaboration of the theory of exterior differential forms has been the development of the concept of differentiable manifolds that are topological spaces equipped with an appropriate structure which blends topological properties with some kind of differentiability. ...