The Interplay Between Differential Geometry And Differential Equations

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The Interplay between Differential Geometry and Differential Equations

Author : Valentin Vasilʹevich Lychagin
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 47,7 Mb
Release : 1995
Category : Differential equations, Nonlinear
ISBN : 0821804286

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The Interplay between Differential Geometry and Differential Equations by Valentin Vasilʹevich Lychagin Pdf

Seminar on Differential Geometry

Author : Shing-Tung Yau,Institute for Advanced Study (Princeton, N.J.)
Publisher : Princeton University Press
Page : 720 pages
File Size : 48,5 Mb
Release : 1982-03-21
Category : Mathematics
ISBN : 9780691082967

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Seminar on Differential Geometry by Shing-Tung Yau,Institute for Advanced Study (Princeton, N.J.) Pdf

This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.

The Interplay Between Differential Geometry and Differential Equations

Author : Anonim
Publisher : American Mathematical Society(RI)
Page : 294 pages
File Size : 55,8 Mb
Release : 1995
Category : Differential equations
ISBN : 0821804286

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The Interplay Between Differential Geometry and Differential Equations by Anonim Pdf

This work applies symplectic methods and discusses quantization problems to emphasize the advantage of an algebraic geometry approach to nonlinear differential equations. One common feature in most of the presentations in this book is the systematic use of the geometry of jet spaces.

Topics in Mathematical Analysis and Differential Geometry

Author : Nicolas K. Laos
Publisher : World Scientific
Page : 580 pages
File Size : 52,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9810231806

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Topics in Mathematical Analysis and Differential Geometry by Nicolas K. Laos Pdf

This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.

Differential Equations on Manifolds and Mathematical Physics

Author : Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Publisher : Springer Nature
Page : 349 pages
File Size : 42,7 Mb
Release : 2022-01-21
Category : Mathematics
ISBN : 9783030373269

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Differential Equations on Manifolds and Mathematical Physics by Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang Pdf

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.

An Introduction to Differential Geometry with Applications to Elasticity

Author : Philippe G. Ciarlet
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 44,7 Mb
Release : 2006-06-28
Category : Technology & Engineering
ISBN : 9781402042485

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An Introduction to Differential Geometry with Applications to Elasticity by Philippe G. Ciarlet Pdf

curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are “two-dimensional”, in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental “Korn inequality on a surface” and to an “in?nit- imal rigid displacement lemma on a surface”. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book “Mathematical Elasticity, Volume III: Theory of Shells”, published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].

Differential Geometric Methods in the Control of Partial Differential Equations

Author : Robert Gulliver
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 47,5 Mb
Release : 2000
Category : Boundary value problems
ISBN : 9780821819272

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Differential Geometric Methods in the Control of Partial Differential Equations by Robert Gulliver Pdf

This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on "Differential Geometric Methods in the Control of Partial Differential Equations", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic. Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects-differential geometry and control of PDEs-have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.

Differential Geometry

Author : Mladen Luksic,Clyde Martin,W. F. Shadwick
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 46,8 Mb
Release : 1987-12-31
Category : Mathematics
ISBN : 0821854070

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Differential Geometry by Mladen Luksic,Clyde Martin,W. F. Shadwick Pdf

Normally, mathematical research has been divided into ``pure'' and ``applied,'' and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas. The papers in this volume represent the proceedings of a conference entitled ``Differential Geometry: The Interface Between Pure and Applied Mathematics,'' which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis, and control theory.

Analytic, Algebraic and Geometric Aspects of Differential Equations

Author : Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik
Publisher : Birkhäuser
Page : 471 pages
File Size : 54,6 Mb
Release : 2017-06-23
Category : Mathematics
ISBN : 9783319528427

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Analytic, Algebraic and Geometric Aspects of Differential Equations by Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik Pdf

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Differential Geometry and Its Applications

Author : John Oprea
Publisher : American Mathematical Soc.
Page : 469 pages
File Size : 41,7 Mb
Release : 2019-02-06
Category : Electronic
ISBN : 9781470450502

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Differential Geometry and Its Applications by John Oprea Pdf

Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

Transformations of Manifolds and Applications to Differential Equations

Author : Keti Tenenblat
Publisher : Chapman & Hall/CRC
Page : 232 pages
File Size : 46,6 Mb
Release : 1998
Category : Differential equations
ISBN : UOM:39015043402836

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Transformations of Manifolds and Applications to Differential Equations by Keti Tenenblat Pdf

The interaction between differential geometry and partial differential equations has been studied since the last century. This relationship is based on the fact that most of the local properties of manifolds are expressed in terms of partial differential equations. The correspondence between certain classes of manifolds and the associated differential equations can be useful in two ways. From our knowledge about the geometry of the manifolds we can obtain solutions to the equations. In particular it is important to study transformations of manifolds which preserve a geometric property, since the analytic interpretation of these transformations will provide mappings between the corresponding differential equations. Conversely, we can obtain geometric properties of the manifolds or even prove the non existence of certain geometric structures on manifolds from our knowledge of the differential equation. This kind of interaction between differential geometry and differential equations is the general theme of the book. The author focuses on the role played by differential geometry in the study of differential equations, combining the geometric and analytic aspects of the theory, not only in the classical examples but also in results obtained since 1980, on integrable systems with an arbitrary number of independent variables. The book will be of interest to graduate students, researchers and mathematicians working in differential geometry, differential equations and mathematical physics.

Differential Geometry and Differential Equations

Author : Chaohao Gu,Marcel Berger,Robert L. Bryant
Publisher : Lecture Notes in Mathematics
Page : 266 pages
File Size : 52,9 Mb
Release : 1987-05-06
Category : Mathematics
ISBN : STANFORD:36105032362852

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Differential Geometry and Differential Equations by Chaohao Gu,Marcel Berger,Robert L. Bryant Pdf

The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.

Quantization, PDEs, and Geometry

Author : Dorothea Bahns,Wolfram Bauer,Ingo Witt
Publisher : Birkhäuser
Page : 314 pages
File Size : 40,8 Mb
Release : 2016-02-11
Category : Mathematics
ISBN : 9783319224077

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Quantization, PDEs, and Geometry by Dorothea Bahns,Wolfram Bauer,Ingo Witt Pdf

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics

Author : Troy L Story
Publisher : iUniverse
Page : 165 pages
File Size : 43,6 Mb
Release : 2005
Category : Geometry, Differential
ISBN : 9780595339211

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Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics by Troy L Story Pdf

Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.

Differential Geometry: The Interface between Pure and Applied Mathematics

Author : Mladen Luksic,Clyde Martin
Publisher : American Mathematical Soc.
Page : 273 pages
File Size : 41,9 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821850756

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Differential Geometry: The Interface between Pure and Applied Mathematics by Mladen Luksic,Clyde Martin Pdf

Normally, mathematical research has been divided into 'pure' and 'applied', and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas. The papers in this volume represent the proceedings of a conference entitled 'Differential Geometry: The Interface Between Pure and Applied Mathematics', which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis and control theory.