Differentiable Manifolds - A Theoretical Physics Approach - Castillo - 2011 - 0817682708.pdf

Gerardo F. Torres del Castillo
Differentiable
Manifolds
ATheoreticalPhysicsApproach
Gerardo F. Torres del Castillo
Instituto de Ciencias
Universidad Autónoma de Puebla
Ciudad Universitaria
72570 Puebla, Puebla, Mexico
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ISBN 978-0-8176-8270-5 e-ISBN 978-0-8176-8271-2
DOI -0-8176-8271-2
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2011939950
Mathematics Subject Classification (2010): 22E70, 34C14, 53B20, 58A15, 70H05
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Preface
The aim of this book is to present in an elementary manner the basic notions related
with differentiable manifolds and some of their applications, especially in physics.
The book is aimed at advanced undergraduate and graduate students in physics and
mathematics, assuming a working knowledge of calculus in several variables, linear
algebra, and differential equations. For the last chapter, which deals with Hamilto-
nian mechanics, it is useful to have some previous knowledge of analytical mechan-
ics. Most of the applications of the formalism considered here are related to dif-
ferential equations, differen