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Title: Geometrical Methods of Mathematical Physics by Bernard Schutz ISBN: 0-521-29887-3 Publisher: Cambridge University Press Pub. Date: 28 January, 1980 Format: Paperback Volumes: 1 List Price(USD): $36.95 |
Average Customer Rating: 3.5 (6 reviews)
Rating: 3
Summary: Integrability conditions discussed
Comment: Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.
Rating: 3
Summary: Not as good as "a first course in general relativity"
Comment: I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
Eventhough its not the worst book out there its not the best either.My advise,buy a better book.
Rating: 4
Summary: A Very Accessible Book ! Buy It !
Comment: This is a very enjoyable and clearly written book. From a physics point of view the approach is rather abstract, so although differential geometry is developed from 'scratch', it is probably better to have studied a more elementary text on the theory of 2-surfaces in 3-space first (eg Faber's book Differential Geometry and Relativity Theory ). The first chapter sets the mathematical background expected of the reader. The rudiments of analysis, topology, calculus of many variables and basic linear algebra is reviewed.The ensuing chapters cover differential geometry from a 'modern' viewpoint but the style is quite relaxed and the links to 'co-ordinate approach' are well explained. The exercises concentrate on the abstract approach. Throughout the book the underlying structure of manifolds is concentrated upon. No extra 'structure' eg connections and 'distance' concepts are added until the final chapter on Riemannian spaces. For example the metric tensor throughout the body of the book is merely used as a map between a tangent space and its dual space. It is only used as a 'distance' operator in the final chapter.For the purposes of independent study this is a sound book, there are hints and partial solutions for many of the exercises, which is always a welcome feature for those studying entirely on their own.
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Pubns Pub. Date: 01 April, 1989 List Price(USD): $15.95 |
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Title: A First Course in General Relativity by Bernard F. Schutz ISBN: 0521277035 Publisher: Cambridge University Press Pub. Date: 31 January, 1985 List Price(USD): $45.00 |
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Title: General Relativity by Robert M. Wald ISBN: 0226870332 Publisher: University of Chicago Press Pub. Date: July, 1984 List Price(USD): $37.00 |
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Title: Tensor Analysis on Manifolds by Samuel I. Goldberg, Richard L. Bishop ISBN: 0486640396 Publisher: Dover Pubns Pub. Date: 01 December, 1980 List Price(USD): $12.95 |
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Title: Problem Book in Relativity and Gravitation by A. Lightman, R. H. Price ISBN: 069108162X Publisher: Princeton Univ Pr Pub. Date: 01 December, 1975 List Price(USD): $50.00 |
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