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Author : W. -H Steeb
Publisher : World Scientific Publishing Company
Page : 300 pages
File Size : 46,9 Mb
Release : 2017-10-24
Category : Science
ISBN : 9813230827
A collection of problems and solutions in differential geometry, with applications.
Author : Willi-Hans Steeb
Publisher : World Scientific Publishing Company
Page : 296 pages
File Size : 43,9 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789813230842
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer–Cartan form, and the Lie derivative are covered. Readers will find useful applications to special and general relativity, Yang–Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry. Request Inspection Copy
Author : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 45,9 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9781466510005
Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
Author : Marián Fecko
Publisher : Cambridge University Press
Page : 11 pages
File Size : 53,6 Mb
Release : 2006-10-12
Category : Science
ISBN : 9781139458030
Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.
Author : Anonim
Publisher : Elsevier
Page : 484 pages
File Size : 41,8 Mb
Release : 2009-06-17
Category : Mathematics
ISBN : 0080875246
Differential Forms in Mathematical Physics
Author : Bo-Yu Hou,Bo-Yuan Hou
Publisher : World Scientific Publishing Company
Page : 560 pages
File Size : 41,8 Mb
Release : 1997-10-31
Category : Mathematics
ISBN : 9789813105096
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.
Author : Ta-tsien Li
Publisher : World Scientific
Page : 302 pages
File Size : 43,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812771476
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a OC classicalOCO one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.This volume will be very useful to graduate students and researchers in pure and applied mathematics."
Author : A Visconti
Publisher : World Scientific Publishing Company
Page : 424 pages
File Size : 51,5 Mb
Release : 1992-10-09
Category : Electronic
ISBN : 9789813103887
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.
Author : Bernard F. Schutz
Publisher : Cambridge University Press
Page : 272 pages
File Size : 44,6 Mb
Release : 1980-01-28
Category : Science
ISBN : 9781107268142
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.
Author : George A. Duckett
Publisher : Createspace Independent Publishing Platform
Page : 266 pages
File Size : 52,8 Mb
Release : 2015-12-24
Category : Electronic
ISBN : 152290610X
If you have a question about Differential Geometry this is the book with the answers. Differential Geometry: Questions and Answers takes some of the best questions and answers asked on the math.stackexchange.com website. You can use this book to look up commonly asked questions, browse questions on a particular topic, compare answers to common topics, check out the original source and much more. This book has been designed to be very easy to use, with many internal references set up that makes browsing in many different ways possible. Topics covered include: differential topology, manifolds, riemannian gemoetry, differential forms and many more."
Author : Mikio Nakahara
Publisher : Taylor & Francis
Page : 596 pages
File Size : 46,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781420056945
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Author : R. W. R. Darling
Publisher : Cambridge University Press
Page : 288 pages
File Size : 52,5 Mb
Release : 1994-09-22
Category : Mathematics
ISBN : 0521468000
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.
Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 52,8 Mb
Release : 2021-06-16
Category : Mathematics
ISBN : 9789811241031
Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.
Author : George M. Rassias,Themistocles M. Rassias
Publisher : CRC Press
Page : 544 pages
File Size : 40,9 Mb
Release : 2023-05-31
Category : Mathematics
ISBN : 9781000943948
This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Author : Theodore Frankel
Publisher : Cambridge University Press
Page : 749 pages
File Size : 50,7 Mb
Release : 2011-11-03
Category : Mathematics
ISBN : 9781139505611
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.