Differential Forms In Mathematical Physics
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Differential Forms In Mathematical Physics
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Author : C. Von Westenholz
language : en
Publisher: North Holland
Release Date : 1981
Differential Forms In Mathematical Physics written by C. Von Westenholz and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Differential Geometry And Mathematical Physics
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Author : Gerd Rudolph
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09
Differential Geometry And Mathematical Physics written by Gerd Rudolph and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Science categories.
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.
Differential Forms In Mathematical Physics
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Author : C. von Westenholtz
language : en
Publisher:
Release Date : 1986
Differential Forms In Mathematical Physics written by C. von Westenholtz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Geometrical Methods Of Mathematical Physics
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Author : Bernard F. Schutz
language : en
Publisher: Cambridge University Press
Release Date : 1980-01-28
Geometrical Methods Of Mathematical Physics written by Bernard F. Schutz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-28 with Science categories.
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
A Visual Introduction To Differential Forms And Calculus On Manifolds
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Author : Jon Pierre Fortney
language : en
Publisher: Springer
Release Date : 2018-11-03
A Visual Introduction To Differential Forms And Calculus On Manifolds written by Jon Pierre Fortney and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
Differential Forms And Applications
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Author : Manfredo P. Do Carmo
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-05-20
Differential Forms And Applications written by Manfredo P. Do Carmo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-20 with Mathematics categories.
An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
Partial Differential Equations And Mathematical Physics
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Author : Kunihiko Kajitani
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-13
Partial Differential Equations And Mathematical Physics written by Kunihiko Kajitani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-13 with Mathematics categories.
The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs---are presented in the areas of partial differential equations, complex analysis, and mathematical physics. Key subjects are: * Treated from the mathematical physics viewpoint: nonlinear stability of an expanding universe, the compressible Euler equation, spin groups and the Leray--Maslov index, * Linked to the Cauchy problem: an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy--Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem. Additional articles examine results on: * Local solvability for a system of partial differential operators, * The hypoellipticity of second order operators, * Differential forms and Hodge theory on analytic spaces, * Subelliptic operators and sub- Riemannian geometry. Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet- Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K. Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji, S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi The book is suitable as a reference text for graduate students and active researchers.
Modern Differential Geometry For Physicists
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Author : Chris J. Isham
language : en
Publisher: Allied Publishers
Release Date : 2002
Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometry, Differential categories.
Differential Forms With Applications To The Physical Sciences
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Author : Harley Flanders
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Differential Forms With Applications To The Physical Sciences written by Harley Flanders and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
"To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." — T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.
Differential Geometry For Physicists
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Author : Bo-yu Hou
language : en
Publisher: World Scientific Publishing Company
Release Date : 1997-10-31
Differential Geometry For Physicists written by Bo-yu Hou and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-31 with Science categories.
This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.