Download or read book Covariant Differentiation of Geometric Objects written by A. Szybiak and published by . This book was released on 1967 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Basic Concepts of the Theory of Geometric Objects written by M. Kucharzewski and published by . This book was released on 1964 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Differential Geometry A New Approach Using D Differentiation written by Donal J. Hurley and published by Springer Science & Business Media. This book was released on 2002 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-differentiation is a unified operation that enables aspects of differential geometry to be developed and presented from a new perspective. This book is the first comprehensive and self-contained treatment of this new method. It demonstrates, concisely but without sacrificing rigour or intelligibility, how even elementary concepts in differential geometry can be reformulated to obtain new and valuable insights. In addition, D-differentiation has applications in several areas of physics, such as classical mechanics, solid-state physics and general relativity. This book will prove useful to all users of D-differentiation - from advanced graduate students onwards - and to those researching into new approaches to some branches of physics and mathematics.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Download or read book Global Differential Geometry of Surfaces written by A. Svec and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (ü) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one book covering this area of research: the Lecture Notes [3] written in the tensor slang. In my book, I am using the machinary of E. Cartan's calculus. It should be equivalent to the tensor calculus; nevertheless, using it I get better results (but, honestly, sometimes it is too complicated). It may be said that almost all results are new and belong to myself (the exceptions being the introductory three chapters, the few classical results and results of my post graduate student Mr. M. ÄFWAT who proved Theorems V.3.1, V.3.3 and VIII.2.1-6).

Download or read book Natural Operations in Differential Geometry written by Ivan Kolar and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.

Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Encyclopaedia of Mathematics set written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.

Download or read book Applied Differential Geometry written by William L. Burke and published by Cambridge University Press. This book was released on 1985-05-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Download or read book The Shapes of Things written by Shawn W. Walker and published by SIAM. This book was released on 2015-06-25 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.

Download or read book The Foundations of Spacetime Physics written by Antonio Vassallo and published by Taylor & Francis. This book was released on 2022-09-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date overview of the foundations of spacetime physics. It features original essays written by world-class experts in the physics and philosophy of spacetime. The foundational questions regarding the origin and nature of spacetime are branching into new and exciting directions. These questions are not restricted to the quantum gravity program but also arise in the context of a well-established theory like general relativity. Against the background of these quick and diverse developments, this volume features a broad range of perspectives on spacetime. Part I focuses on the nature of spacetime in non-quantum theories, such as Newtonian mechanics and relativity. Part II explores some intriguing conceptual implications of developing a quantum theory of spacetime. The Foundations of Spacetime Physics is an essential resource for scholars and advanced students working in philosophy of physics, philosophy of science, and scientific metaphysics.

Download or read book Handbook of Differential Geometry Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Download or read book Analysis and Mathematical Physics written by H. Triebel and published by Springer Science & Business Media. This book was released on 1987-01-31 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Differential Geometry And Kinematics Of Continua written by John D Clayton and published by World Scientific. This book was released on 2014-07-31 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.

Download or read book Relativistic Celestial Mechanics of the Solar System written by Sergei Kopeikin and published by John Wiley & Sons. This book was released on 2011-10-25 with total page 897 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.

Download or read book How Energy Considerations Have Shaped Our Fundamental Modern Theories of Physics written by E. B. Manoukian and published by Springer Nature. This book was released on with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fundamentals of Differential Geometry written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER