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More copies of this ISBN:Geometrical Methods of Mathematical Physicsby Bernard F Schutz
Synopses & ReviewsPublisher Comments:In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions. Review:"...excellent. It would require a great deal of delving in the literature to produce equivalent treatments....a very useful introduction...." J. M. Stewart, Journal of Fluid Mechanics"...Schutz has such a mastery of tthe material that it soon becomes clear that one is in authoritative hands....this book is the most lucid I have come across at this level of exposition. It is eminently suitable for a graduate course (indeed, the more academically able undergraduates should be able to cope with most of it), and the applications should suffice to persuade any physicist or applied mathematician of its importance." Ray d'Inverno, Times Higher Education Supplement Synopsis:For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms. Table of ContentsPreface; 1. Some basic mathematics; 2. Differentiable manifolds and tensors; 3. Lie derivatives and Lie groups; 4. Differential forms; 5. Applications in physics; 6. Connections for Riemannian manifolds and gauge theories; Appendix; Notation; Index.
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