Graduate Studies in Mathematics 2002; 343 pp; hardcover Volume: 52 ISBN10: 0821829513 ISBN13: 9780821829516 List Price: US$68 Member Price: US$54.40 Order Code: GSM/52
 This book is an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. Wellwritten and with plenty of examples, this textbook originated from courses on geometry and analysis and presents a widelyused mathematical technique in a lucid and very readable style. The authors introduce readers to the world of differential forms while covering relevant topics from analysis, differential geometry, and mathematical physics. The book begins with a selfcontained introduction to the calculus of differential forms in Euclidean space and on manifolds. Next, the focus is on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology. The authors then discuss the integrability conditions of a Pfaffian system (Frobenius's theorem). Chapter 5 is a thorough exposition of the theory of curves and surfaces in Euclidean space in the spirit of Cartan. The following chapter covers Lie groups and homogeneous spaces. Chapter 7 addresses symplectic geometry and classical mechanics. The basic tools for the integration of the Hamiltonian equations are the moment map and completely integrable systems (LiouvilleArnold Theorem). The authors discuss Newton, Lagrange, and Hamilton formulations of mechanics. Chapter 8 contains an introduction to statistical mechanics and thermodynamics. The final chapter deals with electrodynamics. The material in the book is carefully illustrated with figures and examples, and there are over 100 exercises. Readers should be familiar with firstyear algebra and advanced calculus. The book is intended for graduate students and researchers interested in delving into geometric analysis and its applications to mathematical physics. Readership Graduate students, research mathematicians, and mathematical physicists. Table of Contents  Elements of multilinear algebra
 Differential forms in \({\mathbb{R}}^n\)
 Vector analysis on manifolds
 Pfaffian systems
 Curves and surfaces in Euclidean 3space
 Lie groups and homogeneous spaces
 Symplectic geometry and mechanics
 Elements of statistical mechanics and thermodynamics
 Elements of electrodynamics
 Bibliography
 Symbols
 Index
