Tensors and Manifolds: With Applications to Physics

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Oxford University Press, 2004 - Foreign Language Study - 447 pages
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This book is a new edition of "Tensors and Manifolds: With Applications to Mechanics and Relativity" which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialized courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. He existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigor combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.
 

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Contents

VECTOR SPACES
1
TENSOR PRODUCT SPACES
25
SYMMETRIC AND SKEWSYMMETRIC TENSORS
46
EXTERIOR GRASSMANN ALGEBRA
71
THE TANGENT MAP OF REAL CARTESIAN SPACES
84
TOPOLOGICAL SPACES
102
DIFFERENTIABLE MANIFOLDS
108
SUBMANIFOLDS
131
MECHANICS
248
ADDITIONAL TOPICS IN MECHANICS
268
A SPACETIME
282
SOME PHYSICS ON MINKOWSKI SPACETIME
306
EINSTEIN SPACETIMES
326
SPACETIMES NEAR AN ISOLATED STAR
339
NONEMPTY SPACETIMES
356
LIE GROUPS
369

DIFFERENTIATION AND INTEGRATION
153
THE FLOW AND THE LIE DERIVATIVE OF
168
INTEGRABILITY CONDITIONS
186
PSEUDORIEMANNIAN GEOMETRY
198
CONNECTION 1FORMS
212
CONNECTIONS ON MANIFOLDS
230
FIBER BUNDLES
384
CONNECTIONS ON FIBER BUNDLES
394
GAUGE THEORY
409
References
423
Index
435
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About the author (2004)

Robert H. Wasserman is Professor Emeritus of Mathematics at Michigan State University, USA.

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