Classical vector analysis deals with vector fields - the gradient, divergence, and curl operators line, surface, and volume integrals and the integral theorems of Gauss, Stokes, and Green. Modern vector analysis distills these into the Cartan calculus and a general form of Stokes' theorem. This text develops vector analysis on manifolds and reinterprets it from the classical viewpoint (and with the classical notation) for three-dimensional Euclidean space, then goes on to introduce de Rham cohomology and Hodge theory. The material is accessible to an undergraduate student with calculus, linear algebra, and some topology as prerequisites. The many figures, exercises with detailed hints, and tests with answers make this book suitable for anyone studying the subject independently.This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory.
|Author||:||Klaus Jänich, L. Kay|
|Publisher||:||Springer Science & Business Media - 2001-02-16|