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's theorem. This essentially modern text carefully 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 particularly suitable for anyone studying the subject independently. Read more ISBN10 1441931449 ISBN13 978-1441931443 Edition Softcover reprint of hardcover 1st ed. 2001 Language English Publisher Springer Dimensions 7.01 x 0.68 x 10 inches Item Weight 1.25 pounds Print length 298 pages Part of series Undergraduate Texts in Mathematics Publication date December 1, 2010