Lectures On Classical Differential Geometry

Author : Dirk Jan Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 52,9 Mb
Release : 1961-01-01
Category : Mathematics
ISBN : 0486656098

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Lectures on Classical Differential Geometry by Dirk Jan Struik Pdf

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.

Author : Dirk J. Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 44,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138183

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Lectures on Classical Differential Geometry by Dirk J. Struik Pdf

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.

Author : Dirk Jan STRUIK
Publisher : Unknown
Page : 221 pages
File Size : 40,5 Mb
Release : 1957
Category : Electronic
ISBN : OCLC:503836650

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Lectures on Classical Differential Geometry. (Second Printing.). by Dirk Jan STRUIK Pdf

Author : Liviu I. Nicolaescu
Publisher : World Scientific
Page : 606 pages
File Size : 43,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812778628

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Lectures on the Geometry of Manifolds by Liviu I. Nicolaescu Pdf

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar‚ duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-;Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand H”lder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 40,8 Mb
Release : 1961
Category : Electronic
ISBN : OCLC:1067908233

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Lectures on Classical Differential Geometry by Anonim Pdf

Author : Su Buchin
Publisher : World Scientific Publishing Company
Page : 149 pages
File Size : 50,9 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 9789813104105

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Lectures on Differential Geometry by Su Buchin Pdf

This book is a set of notes based on lectures delivered by Prof. Su Buchin at Fudan University, Shanghai in 1978 and 1979 to graduate students as well as teachers from other institutions in China. Some selected topics in global differential geometry are dealt with. Certain areas of classical differential geometry based on modern approach are presented in Lectures 1, 3 and 4. Lecture 2 is on integral geometry on the Euclidean plane. It is abridged from W Blaschke's Vorlesungen Ulber Integralgeometrie. In Lecture 5, Cartan's exterior differential forms are introduced. Fruitful applications in this area by Profs S S Chern and C C Hsiung are also discussed.

Author : Georges Valiron
Publisher : Unknown
Page : 288 pages
File Size : 52,5 Mb
Release : 1986
Category : Mathematics
ISBN : 0915692392

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The Classical Differential Geometry of Curves and Surfaces by Georges Valiron Pdf

Author : Paul A. Blaga
Publisher : Unknown
Page : 236 pages
File Size : 52,9 Mb
Release : 2005
Category : Electronic
ISBN : 9736568962

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Lectures on classical differential geometry by Paul A. Blaga Pdf

Author : Iskander Asanovich Taĭmanov
Publisher : European Mathematical Society
Page : 224 pages
File Size : 54,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190507

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Lectures on Differential Geometry by Iskander Asanovich Taĭmanov Pdf

Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. It is addressed to students as well as anyone who wants to learn the basics of differential geometry.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 7040503026

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Lectures on Differential Equations and Differential Geometry by Anonim Pdf

Author : Shiing-Shen Chern,Weihuan Chen,Kai Shue Lam
Publisher : World Scientific
Page : 370 pages
File Size : 48,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9810241828

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Lectures on Differential Geometry by Shiing-Shen Chern,Weihuan Chen,Kai Shue Lam Pdf

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Author : Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 51,8 Mb
Release : 1999
Category : Geometry, Differential
ISBN : 9780821813850

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Lectures on Differential Geometry by Shlomo Sternberg Pdf

This book is based on lectures given at Harvard University during the academic year 1960-1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. His reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.

Author : S S Chern,W H Chen,K S Lam
Publisher : World Scientific Publishing Company
Page : 368 pages
File Size : 44,7 Mb
Release : 1999-11-30
Category : Mathematics
ISBN : 9789813102989

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Lectures on Differential Geometry by S S Chern,W H Chen,K S Lam Pdf

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 53,8 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 50,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781447136965

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Elementary Differential Geometry by A.N. Pressley Pdf

Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.