Lectures On Differential Equations And Differential Geometry

Author : Maria Ulan,Eivind Schneider
Publisher : Springer Nature
Page : 231 pages
File Size : 49,8 Mb
Release : 2021-02-12
Category : Mathematics
ISBN : 9783030632533

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Differential Geometry, Differential Equations, and Mathematical Physics by Maria Ulan,Eivind Schneider Pdf

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 : Iskander Asanovich Taĭmanov
Publisher : European Mathematical Society
Page : 224 pages
File Size : 51,6 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 : Dirk Jan Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 46,8 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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,8 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 7040503026

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Lectures on Differential Equations and Differential Geometry by Anonim Pdf

Author : Robert Hardt,Michael Wolf
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 40,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0821886843

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Nonlinear Partial Differential Equations in Differential Geometry by Robert Hardt,Michael Wolf Pdf

This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.

Author : Peter J. Vassiliou,Ian G. Lisle
Publisher : Cambridge University Press
Page : 242 pages
File Size : 54,9 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0521775981

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Geometric Approaches to Differential Equations by Peter J. Vassiliou,Ian G. Lisle Pdf

A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.

Author : Dirk J. Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 45,5 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 : Liviu I. Nicolaescu
Publisher : World Scientific
Page : 606 pages
File Size : 43,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812708533

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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 : Xi-Ping Zhu
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 40,8 Mb
Release : 2002
Category : Flows (Differentiable dynamical systems).
ISBN : 9780821833117

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Lectures on Mean Curvature Flows by Xi-Ping Zhu Pdf

``Mean curvature flow'' is a term that is used to describe the evolution of a hypersurface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals $\pi$, the curve tends to the unit circle. In thisbook, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions. Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolutionof non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow. Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential equations, as well as in engineering, chemistry, and biology, this book can be useful to graduate students and researchers working in these areas. The book would also make a nice supplementary text for an advanced course in differential geometry.Prerequisites include basic differential geometry, partial differential equations, and related applications.

Author : V V Zharinov
Publisher : World Scientific
Page : 372 pages
File Size : 47,7 Mb
Release : 1992-03-26
Category : Mathematics
ISBN : 9789814513999

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Lecture Notes on Geometrical Aspects of Partial Differential Equations by V V Zharinov Pdf

This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text. Contents:Introduction: Internal Geometry of PDE:Differential ManifoldsLie-Backlund MappingsLie-Backlund Fields and Infinitesimal SymmetriesCartan Forms, Currents and Conservation LawsC-Spectral Sequence. Further Properties of Conservation LawsTrivial Equations. The Formal Variational CalculusEvolution EquationsExternal Geometry of PDE:Differential SubmanifoldsNormal Projection. External Fields and FormsTrivial Ambient Differential ManifoldsThe Characteristic MappingThe Green's FormulaLow-Dimensional Conservation LawsBacklund CorrespondenceFurther Studies:Lagrangian FormalismHamiltonian EquationsExample: The Nambu's StringAppendix Readership: Graduate students and researchers in mathematical physics. keywords:Differential Manifolds;Lie-Bäcklund Mappings;Cartan Forms;Currents;Conservation Laws;Lagrangian Formation;Hamiltonian Equations

Author : S S Chern,W H Chen,K S Lam
Publisher : World Scientific Publishing Company
Page : 368 pages
File Size : 48,5 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 : W. Klingenberg
Publisher : Unknown
Page : 196 pages
File Size : 45,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1461299241

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A Course in Differential Geometry by W. Klingenberg Pdf

Author : Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 50,7 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 : Richard M. Schoen,Shing-Tung Yau
Publisher : International Pressof Boston Incorporated
Page : 414 pages
File Size : 49,9 Mb
Release : 1994
Category : Mathematics
ISBN : 1571460128

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Lectures on Differential Geometry by Richard M. Schoen,Shing-Tung Yau Pdf

In 1984, the authors gave a series of lectures on differential geometry in the Institute for Advanced Studies in Princeton, USA. These lectures are published in this volume, which describes the major achievements in the field.

Author : James Johnston Stoker
Publisher : Unknown
Page : 346 pages
File Size : 54,6 Mb
Release : 1956
Category : Geometry, Differential
ISBN : STANFORD:36105032219052

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Differential Geometry by James Johnston Stoker Pdf