Problems And Solutions In Differential Geometry Lie Series Differential Forms Relativity And Applications PDF Download
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Author | : W. -H Steeb |
Publisher | : World Scientific Publishing Company |
Total Pages | : 300 |
Release | : 2017-10-24 |
Genre | : Science |
ISBN | : 9789813230828 |
Download Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity, and Applications Book in PDF, ePub and Kindle
A collection of problems and solutions in differential geometry, with applications.
Author | : Willi-Hans Steeb |
Publisher | : World Scientific Publishing Company |
Total Pages | : 296 |
Release | : 2017-10-20 |
Genre | : Mathematics |
ISBN | : 9813230843 |
Download Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications Book in PDF, ePub and Kindle
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 | : Marián Fecko |
Publisher | : Cambridge University Press |
Total Pages | : 11 |
Release | : 2006-10-12 |
Genre | : Science |
ISBN | : 1139458035 |
Download Differential Geometry and Lie Groups for Physicists Book in PDF, ePub and Kindle
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 | : Tevian Dray |
Publisher | : CRC Press |
Total Pages | : 315 |
Release | : 2014-10-20 |
Genre | : Mathematics |
ISBN | : 1466510323 |
Download Differential Forms and the Geometry of General Relativity Book in PDF, ePub and Kindle
Requiring little more than calculus and some linear algebra, this book provides readers with a coherent path to understanding relativity. It helps readers learn just enough differential geometry to grasp the basics of general relativity. The first half of the book describes some of the surprising implications of relativity without introducing more formalism than necessary. The second half takes a more detailed look at the mathematics of differential forms, showing how they are used to describe key geometric ideas in general relativity.
Author | : Bernard F. Schutz |
Publisher | : Cambridge University Press |
Total Pages | : 272 |
Release | : 1980-01-28 |
Genre | : Science |
ISBN | : 1107268141 |
Download Geometrical Methods of Mathematical Physics Book in PDF, ePub and Kindle
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 | : Loring W. Tu |
Publisher | : Springer |
Total Pages | : 347 |
Release | : 2017-06-01 |
Genre | : Mathematics |
ISBN | : 3319550845 |
Download Differential Geometry Book in PDF, ePub and Kindle
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.
Author | : Mikio Nakahara |
Publisher | : Taylor & Francis |
Total Pages | : 596 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 1420056948 |
Download Geometry, Topology and Physics Book in PDF, ePub and Kindle
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 | : |
Publisher | : Elsevier |
Total Pages | : 484 |
Release | : 2009-06-17 |
Genre | : Mathematics |
ISBN | : 9780080875248 |
Download Differential Forms in Mathematical Physics Book in PDF, ePub and Kindle
Differential Forms in Mathematical Physics
Author | : Ta-tsien Li |
Publisher | : World Scientific |
Total Pages | : 302 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9812771476 |
Download Differential Geometry Book in PDF, ePub and Kindle
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 | : Hongyu Guo |
Publisher | : World Scientific |
Total Pages | : 246 |
Release | : 2021-06-16 |
Genre | : Mathematics |
ISBN | : 9811241031 |
Download What Are Tensors Exactly? Book in PDF, ePub and Kindle
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.