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Author | : J. M. Landsberg |
Publisher | : American Mathematical Soc. |
Total Pages | : 464 |
Release | : 2011-12-14 |
Genre | : Mathematics |
ISBN | : 0821869078 |
Download Tensors: Geometry and Applications Book in PDF, ePub and Kindle
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Author | : C. T. J. Dodson |
Publisher | : Springer Science & Business Media |
Total Pages | : 449 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3642105149 |
Download Tensor Geometry Book in PDF, ePub and Kindle
This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.
Author | : C. E. Springer |
Publisher | : Courier Corporation |
Total Pages | : 256 |
Release | : 2013-09-26 |
Genre | : Mathematics |
ISBN | : 048632091X |
Download Tensor and Vector Analysis Book in PDF, ePub and Kindle
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Author | : Joseph M. Landsberg |
Publisher | : American Mathematical Soc. |
Total Pages | : |
Release | : 2012 |
Genre | : Matrices |
ISBN | : 9780821884812 |
Download Tensors: Geometry and Applications Book in PDF, ePub and Kindle
Author | : Nail H. Ibragimov |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 198 |
Release | : 2015-08-31 |
Genre | : Mathematics |
ISBN | : 3110379503 |
Download Tensors and Riemannian Geometry Book in PDF, ePub and Kindle
This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
Author | : C. T. J. Dodson |
Publisher | : Pitman Publishing |
Total Pages | : 598 |
Release | : 1979 |
Genre | : Calculus of tensors |
ISBN | : 9780273010401 |
Download Tensor Geometry Book in PDF, ePub and Kindle
Author | : Thomas Andrew Ivey |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833758 |
Download Cartan for Beginners Book in PDF, ePub and Kindle
This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.
Author | : Nazrul Islam |
Publisher | : New Age International |
Total Pages | : 6 |
Release | : 2006-12 |
Genre | : Tensor algebra |
ISBN | : 8122418384 |
Download Tensors and Their Applications Book in PDF, ePub and Kindle
The Book Is Written Is In Easy-To-Read Style With Corresponding Examples. The Main Aim Of This Book Is To Precisely Explain The Fundamentals Of Tensors And Their Applications To Mechanics, Elasticity, Theory Of Relativity, Electromagnetic, Riemannian Geometry And Many Other Disciplines Of Science And Engineering, In A Lucid Manner. The Text Has Been Explained Section Wise, Every Concept Has Been Narrated In The Form Of Definition, Examples And Questions Related To The Concept Taught. The Overall Package Of The Book Is Highly Useful And Interesting For The People Associated With The Field.
Author | : Ralph Abraham |
Publisher | : Springer Science & Business Media |
Total Pages | : 666 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461210291 |
Download Manifolds, Tensor Analysis, and Applications Book in PDF, ePub and Kindle
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
Author | : K.K. Dube |
Publisher | : I. K. International Pvt Ltd |
Total Pages | : 377 |
Release | : 2013-12-30 |
Genre | : Mathematics |
ISBN | : 9380026587 |
Download Differential Geometry and Tensors Book in PDF, ePub and Kindle
The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: " Theory of curves, envelopes and developables. " Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. " Fundamental equations of surface theory. " Geodesics. Section B deals with: " Tensor algebra. " Tensor calculus. " Christoffel symbols and their properties. " Riemann symbols and Einstein space, and their properties. " Physical components of contravariant and covariant vectors. " Geodesics and Parallelism of vectors. " Differentiable manifolds, charts, atlases.