Applied Exterior Calculus

This is a reprint of the 1985 edition pubished by John Wiley & Sons. Edelen (mathematics emeritus, Lehigh U.) believes the exterior calculus is essential, if not for its intrinsic value, then because in the quantified sciences it has become an expository vehicle. He proves his point by examining the exterior calculus in terms of its vectors and forms, such as vector fields, exterior forms, exterior derivatives, Lie derivatives, and integration, and its antiexact differential forms and homotopy operators. He then examines the exterior calculus as it is applied to mathematics, such as in isovector methods for second-order partial differential equations and in the calculus of variations. He also examines its applications to physics, as in modern thermodynamics, electrodynamics with electric and magnetic changes, and gauge theories. Readers should be upper-level undergraduate and graduate students with upper-division algebra and analysis courses. Annotation c2004 Book News, Inc., Portland, OR (booknews.com)