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Introduction To Differential Geometry With Applications To Navier Stokes Dynamics
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Book Synopsis Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics by : Troy L Story
Download or read book Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics written by Troy L Story and published by iUniverse. This book was released on 2005 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 and published by Springer Nature. This book was released on 2021-02-12 with total page 231 pages. 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.
Book Synopsis Introduction to Differential Geometry with Tensor Applications by : Dipankar De
Download or read book Introduction to Differential Geometry with Tensor Applications written by Dipankar De and published by John Wiley & Sons. This book was released on 2022-05-24 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student
Book Synopsis Differential Geometry with Applications to Mechanics and Physics by : Yves Talpaert
Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential
Book Synopsis An Introduction to Differential Geometry with Applications to Elasticity by : Philippe G. Ciarlet
Download or read book An Introduction to Differential Geometry with Applications to Elasticity written by Philippe G. Ciarlet and published by Springer Science & Business Media. This book was released on 2006-06-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Book Synopsis Introduction to Differential Geometry by : Joel W. Robbin
Download or read book Introduction to Differential Geometry written by Joel W. Robbin and published by Springer Nature. This book was released on 2022-01-12 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Book Synopsis Applied Differential Geometry: A Modern Introduction by : Vladimir G Ivancevic
Download or read book Applied Differential Geometry: A Modern Introduction written by Vladimir G Ivancevic and published by World Scientific. This book was released on 2007-05-21 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Book Synopsis Differential Geometry and Its Applications by : John Oprea
Download or read book Differential Geometry and Its Applications written by John Oprea and published by MAA. This book was released on 2007-09-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Book Synopsis Mathematical Modeling I by : Troy L. Story
Download or read book Mathematical Modeling I written by Troy L. Story and published by iUniverse. This book was released on 2010-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling I: kinetics, thermodynamics and statistical mechanics (MMI) features traditional topics in physical chemistry (chemical physics), but is distinguished by problem solving techniques which emphasize the assignment of mathematical models to describe physical phenomena. MMI is a starting point to unify theoretical and empirical perceptions of the following topics: Kinetics, distributions and collisions The first law of thermodynamics The second law of thermodynamics The third law of thermodynamics Statistical mechanics MMI can be used as a text on the above topics in the first semester part of a two-semester undergraduate course in physical chemistry. Since many quantum ideas are introduced in the study of kinetics, distributions, collisions, and statistical mechanics, MMI serves as a logical foundation for the study of quantum mechanics and spectroscopy in the second volume, Mathematical Modeling II: quantum mechanics and spectroscopy (to appear in the fall of 2010)."
Book Synopsis Dynamical Systems and Differential Geometry via MAPLE by : Constantin Udriste
Download or read book Dynamical Systems and Differential Geometry via MAPLE written by Constantin Udriste and published by Cambridge Scholars Publishing. This book was released on 2021-10-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of dynamical systems and differential geometry via MAPLE is a field which has become exceedingly technical in recent years. In the field, everything is structured for the benefit of optimizing evolutionary geometric aspects that describe significant physical or engineering phenomena. This book is structured in terms of the importance, accessibility and impact of theoretical notions capable of shaping a future mathematician-computer scientist possessing knowledge of evolutionary dynamical systems. It provides a self-contained and accessible introduction for graduate and advanced undergraduate students in mathematics, engineering, physics, and economic sciences. This book is suitable for both self-study for students and professors with a background in differential geometry and for teaching a semester-long introductory graduate course in dynamical systems and differential geometry via MAPLE.
Book Synopsis Introduction to Differential Geometry by : Luther Pfahler Eisenhart
Download or read book Introduction to Differential Geometry written by Luther Pfahler Eisenhart and published by Princeton University Press. This book was released on 2015-12-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Introduction to Differential Geometry for Engineers by : Brian F. Doolin
Download or read book Introduction to Differential Geometry for Engineers written by Brian F. Doolin and published by Courier Corporation. This book was released on 2012-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers. The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.
Book Synopsis Introductory Differential Geometry For Physicists by : A Visconti
Download or read book Introductory Differential Geometry For Physicists written by A Visconti and published by World Scientific Publishing Company. This book was released on 1992-10-09 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.
Book Synopsis An Introduction to Differential Geometry by : T. J. Willmore
Download or read book An Introduction to Differential Geometry written by T. J. Willmore and published by Courier Corporation. This book was released on 2013-05-13 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Book Synopsis Differential Geometry and Topology by : Keith Burns
Download or read book Differential Geometry and Topology written by Keith Burns and published by CRC Press. This book was released on 2005-05-27 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.
Book Synopsis Differential Geometry Applied To Dynamical Systems (With Cd-rom) by : Jean-marc Ginoux
Download or read book Differential Geometry Applied To Dynamical Systems (With Cd-rom) written by Jean-marc Ginoux and published by World Scientific. This book was released on 2009-04-03 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
Author :Iskander Asanovich Taĭmanov Publisher :European Mathematical Society ISBN 13 :9783037190500 Total Pages :224 pages Book Rating :4.1/5 (95 download)
Book Synopsis Lectures on Differential Geometry by : Iskander Asanovich Taĭmanov
Download or read book Lectures on Differential Geometry written by Iskander Asanovich Taĭmanov and published by European Mathematical Society. This book was released on 2008 with total page 224 pages. 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.
