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.