Overview
Introduces differentiable manifolds using a theoretical physics approach; unique book in the literature
Provides a collection of exercises of varying degrees of difficulty
Includes applications to differential geometry and general relativity
Includes supplementary material: sn.pub/extras
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Table of contents (8 chapters)
Keywords
About this book
This textbook explores the theory behind differentiable manifolds and investigates various physics applications along the way. Basic concepts, such as differentiable manifolds, differentiable mappings, tangent vectors, vector fields, and differential forms, are briefly introduced in the first three chapters. Chapter 4 gives a concise introduction to differential geometry needed in subsequent chapters. Chapters 5 and 6 provide interesting applications to connections and Riemannian manifolds. Lie groups and Hamiltonian mechanics are closely examined in the last two chapters. Included throughout the book are a collection of exercises of varying degrees of difficulty.
Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics.
Reviews
From the reviews:
“The purpose of this book is to present some fundamental notions of differentiable geometry of manifolds and some applications in physics. The topics developed in the book are of interest of advanced undergraduate and graduate students in mathematics and physics. The author succeeded to connect differential geometry with mechanics. The computations are clearly explained and the theory is supported by several examples. Throughout the book there is a large collection of exercises … which help the reader to fix the obtained knowledge.” (Marian Ioan Munteanu, Zentralblatt MATH, Vol. 1237, 2012)
“This book presents an introduction to differential geometry and the calculus on manifolds with a view on some of its applications in physics. … The book is primarily oriented towards advanced undergraduate and graduate students in mathematics and physics … . the present author has succeeded in writing a book which has its own flavor and its own emphasis, which makes it certainly a valuable addition to the literature on the subject.” (Frans Cantrijn, Mathematical Reviews, Issue 2012 k)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Differentiable Manifolds
Book Subtitle: A Theoretical Physics Approach
Authors: Gerardo F. Torres del Castillo
DOI: https://doi.org/10.1007/978-0-8176-8271-2
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
eBook ISBN: 978-0-8176-8271-2Published: 09 October 2011
Edition Number: 1
Number of Pages: VIII, 275
Number of Illustrations: 20 b/w illustrations
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Classical Mechanics, Mathematical Methods in Physics, Topological Groups, Lie Groups