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Book Synopsis Lectures on Differential Equations and Differential Geometry by :
Download or read book Lectures on Differential Equations and Differential Geometry written by . This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shlomo Sternberg
Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 854/5 ( reviews)
Book Synopsis Lectures on Differential Geometry by : Shlomo Sternberg
Download or read book Lectures on Differential Geometry written by Shlomo Sternberg. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Maria Ulan
Release : 2021-02-12
Genre : Mathematics
Kind : eBook
Book Rating : 539/5 ( reviews)
Book Synopsis Differential Geometry, Differential Equations, and Mathematical Physics by : Maria Ulan
Download or read book Differential Geometry, Differential Equations, and Mathematical Physics written by Maria Ulan. This book was released on 2021-02-12. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.
Author : Dirk Jan Struik
Release : 1961-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 090/5 ( reviews)
Book Synopsis Lectures on Classical Differential Geometry by : Dirk Jan Struik
Download or read book Lectures on Classical Differential Geometry written by Dirk Jan Struik. This book was released on 1961-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Iskander Asanovich Taĭmanov
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 500/5 ( reviews)
Book Synopsis Lectures on Differential Geometry by : Iskander Asanovich Taĭmanov
Download or read book Lectures on Differential Geometry written by Iskander Asanovich Taĭmanov. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: 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.
