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Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201) download epub

by Shigeyuki Morita


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Series: Translations of Mathematical Monographs (Book 201). The use of differential forms is indispensible

Series: Translations of Mathematical Monographs (Book 201). Paperback: 321 pages. Publisher: American Mathematical Society (August 28, 2001). The use of differential forms is indispensible. Perhaps the most satisfying aspect of this book is that it clarifies the notions of connection, connection form, curvature, curvature form for manifolds and fibre bundles. There are plenty of exercises to boot.

Volume 201. z c:: Geometry of Differential Forms.

This books gives a very direct explanation of the main concepts in differential forms. I would recommend it for anyone wanting to get to the main concepts quickly and cleanly. Download (djvu, . 8 Mb) Donate Read.

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Shigeyuki Morita Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201). ISBN 13: 9780821810453. Geometry of Differential Forms (Translations of Mathematical Monographs, Vol.

Translations of MATHEMATICAL MONOGRAPHS Volume 199 Geometry of Characteristic Classes Shigeyuki . TRANSLATIONS OF MATHEMATICAL MONOGRAPHS Volume 29 LINEAR DIFFERENTIAL EQUATIONS IN BANACH SPACE b. .

Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties (Translations of Mathematical Monographs) lHAJibHhiE c)QPMbl, OPTOrOHAJibHbiE rOJIOMOPr}, !EM diam M sup Ir - z I. r,zEM CM denotes the .Report "Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201)".

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Morita S. - Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. Читать книгу бесплатно. Скачать книгу с нашего сайта нельзя. This books gives a very direct explanation of the main concepts in differential forms.

It begins with a quick presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and. the theory of characteristic classes. Among the less traditional topics treated in the book is a detailed description of the Chern-Weil theory.

MODULAR FORMS AND HECKE OPERATORS (Translations of Mathematical Monographs 145) .

MODULAR FORMS AND HECKE OPERATORS (Translations of Mathematical Monographs 145) By A. N. Andrianov .July 1997 · Bulletin of the London Mathematical Society. Peter Swinnerton-Dyer. August 2006 · Bulletin of the London Mathematical Society. 00, ISBN 0-8218-3810-5 (American Mathematical Society, 2005) - - Volume 38 Issue 4 - Christopher Lance.

Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. <P>The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. <P>The book can serve as a textbook for undergraduate students and for graduate students in geometry.

Comments: (7)

Anen
This must be surely one of the bests if not the best introduction into the world of differential geometry (and some aspects of algebraic topology) that has been written. The author does a marvelous job of teaching and explaining the concepts for an audience that goes from mathematicians to physicists. As another reviewer pointed out it is a mathematical text but written with enough informality at some places which eases the lecture of the whole material, providing further insight and even some historical notes (like for example the fact that Ehresmann made the last contribution to date in the definition of a connection in fiber bundles). Among the things that I like to point out are that with this book I finally understood the concept of paracompactness, the support of a function, the concept of a partition of unity, etc. The clarity in the presentation of material is throughout cristal clear, I found no better place for the definition of a manifold for example or the demonstration of Stoke's theorem. Also it gives the best motivation for the equation of a geodesic, i.e. that the covariant derivative of its tangent vector must vanish, this is motivated from the case of a surface embedded in R^3, where it is explained that geodesics in the surface are the ones whose accelerator vector are normal to the surface which means that the derivative of its velocity vector tangential to the surface is zero, so the covariant derivative equal zero for the tangent vector (the velocity vector) is the generalization of this situation for a general manifold which may not be embedded in a higher dimensional space. I also like the discussion or presentation if you like of the Riemann curvature tensor. Finally I would like to comment another spot which I am very grateful to the author and is that with this book I finally saw why the connection defined in fiber bundles is a matrix which I found helped me to see that it is a Lie algebra valued function. I proceed now to briefly describe the contents of the book. The first chapter is about manifolds, where it gives the definition, examples and then goes to define functions and vector fields on them. The second chapter is concerned with differential forms, it gives all you need ending with Frobenius theorem both in the vector and differential forms case. The third chapter introduces Homology (simplicial and singular) and then the de Ram and Cech Cohomology. Chapter four is about Hodge theory for the Laplacian and Harmonic forms and finally chapter five and six are about Vector bundles and fiber bundles and Characteristics Classes which are nothing else than global invariant forms (polynomials of the curvature) which by their properties are useful in the topology and classification of the bundles.
All in all, a wonderful book, but a word of caution, beware, reading to much of this book may make you fall in love with it!...so my advice, buy it you will be making a full worth investment, only take care of not making your girlfriend jealous by giving to much time to it despite of her!
Marige
It's a perfect book for a non-math-major student to learn differential form.
Gianni_Giant
Very, very good! Thank you!
Atineda
This is a wonderful book. It is an insightful and careful introduction to differential forms and to the geometry they describe. The author is properly rigorous in his approach, but is kind enough to incorporate some informal discussion that gives much improved guidance. So, I find this a very much better learning opportunity than Flanders or Cartan or even Lovelock and Rund. I think it is a very helpful balance between correctness and full regard of the formalism and insight. On the other hand, there is a flavor that I would want included in such a book. The "phone book" version of Gravitation, by Misner, Thorne, and Wheeler, offers pictorial guidance in places. An improved version of that style of guidance would, I think, make this a perfect book. As it is, it would be absurd to criticize Misner, Thorne, and Wheeler. It has been a classic for years and will continue to be. It is well above my poor power to add or detract, for sure. Still, I find the phone book to be too loosely organized. It is encyclopaedic, but not crisp, insightful, and to the point. If just a bit of it could be incorporated here properly, we wouldn't need the phone book, because we'd already have the number.
Skillet
Textbook wl solutions, oh my!
Deeroman
This text is phenomenally easy to read and well organized. The author starts you on a journey by first explaining the importance and power of classifying manifolds namely by certain invariants preserved by certain mappings ( diffeomorphisms ).

For example, like Euler, we could count the number of holes in the surface and using this combinatorial method we are led to homology theory.

Or like Gauss, we could use a differentiation and integration to come up with the idea of curvature as an intrinsic feature of the surface.

Modern approaches use differential forms to represent homology and cohomoly groups.

The author also deals with fibre bundles demonstrating their importance in analyzing manifolds specifically how the number of fibre bundles possible with given Lie groups as structure groups over the manifold can be answered by characteristic classes such as the Chern and Pontrjagin classes. The use of differential forms is indispensible.

Perhaps the most satisfying aspect of this book is that it clarifies the notions of connection, connection form, curvature, curvature form for manifolds and fibre bundles.

There are plenty of exercises to boot.
Xaluenk
An excellent introduction to calculus on manifolds and its application to geometry of Yang-Mills fields and topology. What I like about this book is that it covers the topics which are the most important ones from the viewpoint of a high-energy theoretical physicist. Most introductory books written for mathematicians do not cover principal bundles, connections on them, and characteristic classes. This book does.
This is probably the most clearly written self-contained book on the basics of differential geometry. The author does a great job explaining the ideas behind purely mathematical 'dry' constructions. On the other hand, everything is defined correctly and precisely. A very readable and useful book with the perfect combination of formal math. and intuition. I would recommend it to students in theoretical physics area, together with the Nakahara's fantastic book.
Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201) download epub
Mathematics
Author: Shigeyuki Morita
ISBN: 0821810456
Category: Science & Math
Subcategory: Mathematics
Language: English
Publisher: American Mathematical Society (August 28, 2001)
Pages: 321 pages