Global Analysis: Differential Forms in Analysis, Geometry, and Physics (Graduate Studies in Mathematics, 52)

Agricola, Ilka; Friedrich, Thomas

ISBN 10: 0821829513 / ISBN 13: 9780821829516

Verlag: Amer Mathematical Society, 2002

Beschreibung

Gently used with minimal wear on the corners and cover. A few pages may contain light highlighting or writing, but the text remains fully legible. Dust jacket may be missing, and supplemental materials like CDs or codes may not be included. May be ex-library with library markings. Ships promptly!

Bestandsnummer des Verkäufers DBV.0821829513.G

Bibliografische Details

• Titel: Global Analysis: Differential Forms in Analysis, Geometry, and Physics (Graduate Studies in Mathematics, 52)
• Verlag: Amer Mathematical Society
• Erscheinungsjahr: 2002
• Sprache: Englisch
• ISBN-10: 0821829513
• ISBN-13: 9780821829516
• Einband: Hardcover
• Zustand: good

Über diesen Titel

Inhaltsangabe

This book is devoted to differential forms and their applications in various areas of mathematics and physics. Well-written and with plenty of examples, this introductory textbook originated from courses on geometry and analysis and presents a widely used 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 self-contained 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 (Liouville-Arnold 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 an Readers should be familiar with first-year 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.