Differential Geometry Differential Equations And Mathematical Physics

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Differential Geometry, Differential Equations, and Mathematical Physics

Maria Ulan,Eivind Schneider
Differential Geometry Differential Equations and Mathematical Physics Book PDF

Author : Maria Ulan,Eivind Schneider
Publisher : Springer Nature
Page : 231 pages
File Size : 40,8 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.

Seminar on Differential Geometry

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

Author : Shing-Tung Yau,Institute for Advanced Study (Princeton, N.J.)
Publisher : Princeton University Press
Page : 720 pages
File Size : 44,7 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.

Differential Equations on Manifolds and Mathematical Physics

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

Author : Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Publisher : Springer Nature
Page : 349 pages
File Size : 50,8 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.

Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics

Molin Ge,Jiaxing Hong,Tatsien Li,Weiping Zhang
Frontiers in Differential Geometry Partial Differential Equations and Mathematical Physics Book PDF

Author : Molin Ge,Jiaxing Hong,Tatsien Li,Weiping Zhang
Publisher : World Scientific
Page : 372 pages
File Size : 43,8 Mb
Release : 2014-03-18
Category : Science
ISBN : 9789814578103

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Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics by Molin Ge,Jiaxing Hong,Tatsien Li,Weiping Zhang Pdf

This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime. All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects. Contents:A Profile of the Late Professor Gu Chaohao (Tatsien Li)List of Publications of Gu ChaohaoIn Memory of Professor Gu Chaohao (Xiaqi Ding)In Memory of Professor Gu Chaohao (Gongqing Zhang (Kung-Ching Chang))Stability of E-H Mach Configuration in Pseudo-Steady Compressible Flow (Shuxing Chen)Incompressible Viscous Fluid Flows with Slip Boundary Conditions and Their Numerical Simulations (Ben-yu Guo)Global Existence and Uniqueness of the Solution for the Generalized Schrödinger-KdV System (Boling Guo, Bolin Ma & Jingjun Zhang)Anomaly Cancellation and Modularity (Fei Han, Kefeng Liu & Weiping Zhang)On Interior Estimates for Mean Curvature of Convex Surfaces in R3 and Its Applications (Jiaxing Hong)Geometric Invariant Theory of the Space — A Modern Approach to Solid Geometry (Wu-Yi Hsiang)Optimal Convergence Rate of the Binomial Tree Scheme for American Options and Their Free Boundaries (Lishang Jiang & Jin Liang)Rademacher Φ Function, Jacobi Symbols, Quantum and Classical Invariants of Lens Spaces (Bang-He Li & Tian-Jun Li)Historical Review on the Roles of Mathematics in the Study of Aerodynamics (Jiachun Li)Toward Chern–Simons Theory of Complexes on Calabi–Yau Threefolds (Jun Li)Exact Boundary Synchronization for a Coupled System of Wave Equations (Tatsien Li)Scaling Limit for Compressible Viscoelastic Fluids (Xianpeng Hu & Fang-Hua Lin)Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds (Ngaiming Mok)The Application of Conditional Nonlinear Optimal Perturbation to Targeted Observations for Tropical Cyclone Prediction (Mu Mu, Feifan Zhou, Xiaohao Qin & Boyu Chen)Isometric Immersions in Minkowski Spaces (Yi-Bing Shen)Remarks on Volume Growth for Minimal Graphs in Higher Codimension (Yuanlong Xin)Separation of Variables for the Lax Pair of the Bogomolny Equation in 2+1 Dimensional Anti-de Sitter Space-Time (Zi-Xiang Zhou) Readership: Mathematicians and advanced graduate students in mathematics. Key Features:In memory of the highly distinguished mathematician Gu ChaohaoThe contributors are excellent experts, including 9 members of the CASProvides some important information on Differential Geometry, Partial Differential Equations, Mathematical Physics, etcKeywords:Differential Geometry;Partial Differential Equations;Mathematical Physics

Differential Geometry: Geometry in Mathematical Physics and Related Topics

Robert Everist Greene,Shing-Tung Yau
Differential Geometry Geometry in Mathematical Physics and Related Topics Book PDF

Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 681 pages
File Size : 48,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821814956

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Differential Geometry: Geometry in Mathematical Physics and Related Topics by Robert Everist Greene,Shing-Tung Yau Pdf

The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

Yuri E. Gliklikh
Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics Book PDF

Author : Yuri E. Gliklikh
Publisher : Springer
Page : 192 pages
File Size : 41,6 Mb
Release : 1996-08-31
Category : Mathematics
ISBN : 9780792341543

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Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics by Yuri E. Gliklikh Pdf

The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

Differential Geometry and Mathematical Physics

Gerd Rudolph,Matthias Schmidt
Differential Geometry and Mathematical Physics Book PDF

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 52,6 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457

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Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics

Stancho Dimiev
Topics in Contemporary Differential Geometry Complex Analysis and Mathematical Physics Book PDF

Author : Stancho Dimiev
Publisher : World Scientific
Page : 350 pages
File Size : 42,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812709806

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Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics by Stancho Dimiev Pdf

This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas. Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

Differential Geometry, Differential Equations, and Mathematical Physics

Maria Ulan,Eivind Schneider
Differential Geometry Differential Equations and Mathematical Physics Book PDF

Author : Maria Ulan,Eivind Schneider
Publisher : Unknown
Page : 0 pages
File Size : 43,5 Mb
Release : 2021
Category : Electronic
ISBN : 3030632547

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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.

Differential Geometric Methods in Theoretical Physics

Ling-Lie Chau,Werner Nahm
Differential Geometric Methods in Theoretical Physics Book PDF

Author : Ling-Lie Chau,Werner Nahm
Publisher : Springer Science & Business Media
Page : 795 pages
File Size : 49,8 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9781468491487

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Differential Geometric Methods in Theoretical Physics by Ling-Lie Chau,Werner Nahm Pdf

After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit ful again. Many of the leading specialists of both fields became involved in this devel opment. This process even led to the discovery of previously unsuspected connections between various subfields of physics and mathematics. In mathematics this concerns in particular knots von Neumann algebras, Kac-Moody algebras, integrable non-linear partial differential equations, and differential geometry in low dimensions, most im portantly in three and four dimensional spaces. In physics it concerns gravity, string theory, integrable classical and quantum field theories, solitons and the statistical me chanics of surfaces. New discoveries in these fields are made at a rapid pace. This conference brought together active researchers in these areas, reporting their results and discussing with other participants to further develop thoughts in future new directions. The conference was attended by SO participants from 15 nations. These proceedings document the program and the talks at the conference. This conference was preceded by a two-week summer school. Ten lecturers gave extended lectures on related topics. The proceedings of the school will also be published in the NATO-AS[ volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to thank the many people who have made the conference a success. Furthermore, ·we appreciate the excellent talks. The active participation of everyone present made the conference lively and stimulating. All of this made our efforts worth while.

Differential Equations, Asymptotic Analysis, and Mathematical Physics

Michael Demuth,Bert-Wolfgang Schulze
Differential Equations Asymptotic Analysis and Mathematical Physics Book PDF

Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : John Wiley & Sons
Page : 436 pages
File Size : 44,8 Mb
Release : 1997
Category : Mathematics
ISBN : 3055017692

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Differential Equations, Asymptotic Analysis, and Mathematical Physics by Michael Demuth,Bert-Wolfgang Schulze Pdf

This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.

Differential Forms in Mathematical Physics

Anonim
Differential Forms in Mathematical Physics Book PDF

Author : Anonim
Publisher : Elsevier
Page : 484 pages
File Size : 46,8 Mb
Release : 2009-06-17
Category : Mathematics
ISBN : 0080875246

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Differential Forms in Mathematical Physics by Anonim Pdf

Differential Forms in Mathematical Physics

Partial Differential Equations III

Michael E. Taylor
Partial Differential Equations III Book PDF

Author : Michael E. Taylor
Publisher : Springer Nature
Page : 774 pages
File Size : 40,5 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9783031339288

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Partial Differential Equations III by Michael E. Taylor Pdf

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)

Differential Geometric Methods in Mathematical Physics

S. Sternberg
Differential Geometric Methods in Mathematical Physics Book PDF

Author : S. Sternberg
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 40,9 Mb
Release : 2001-11-30
Category : Science
ISBN : 1402003412

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Differential Geometric Methods in Mathematical Physics by S. Sternberg Pdf

The following pages represent the Proceedings of the XI Annual Conference on Differential Geometric Methods in Mathematical Physics which was held in Jerusalem from August 5 through 11, 1982 under the auspices of the Tel Aviv University and the Israel Academy of Sciences and Humanities. In addition to the above mentioned institutions, partial financial support was received form the Bank Leumi Lelsrael Fund for International Conferences, the American Friends of the Tel Aviv Institute of Mathematical Sciences and the Mathematics and Physics Branch of the United States Army Research, Development and Standardization Group (UK). We are grateful to all of these organizations for their financial support. GAUGE THEORY AND NUCLEAR STRUCTURE K. Bleuler Institut fur Theoretische Kernphysik der Universitat Bonn NuBallee 14-16, D-5300 Bonn, West-Germany I. INTRODUCTION The recent, most impressive verification of the Salam­ -Weinberg theory of electro-weak interactions through the experimental discovery of the so-called inter­ mediate bosons represents, at the same time, a success of the general gauge theoretical viewpoints in modern particle physics (quantum chromodynamics, 0CD). This theory leads to a deeper and by far more natural inter­ pretation of particle interaction and induces, as we shall see, also a profound change in our understanding of nuclear structure.

Differentiable Manifolds

Gerardo F. Torres del Castillo
Differentiable Manifolds Book PDF

Author : Gerardo F. Torres del Castillo
Publisher : Springer Nature
Page : 447 pages
File Size : 51,7 Mb
Release : 2020-06-23
Category : Mathematics
ISBN : 9783030451936

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Differentiable Manifolds by Gerardo F. Torres del Castillo Pdf

This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics.