The Very Basics of Tensors

Author: Nils K. Oeijord

Publisher: iUniverse

ISBN: 059535694X

Category: Mathematics

Page: 137

View: 8586

DOWNLOAD NOW »

Tensor calculus is a generalization of vector calculus, and comes near of being a universal language in physics. Physical laws must be independent of any particular coordinate system used in describing them. This requirement leads to tensor calculus. The only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra, and some knowledge of differential equations.
Release

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Author: Hung Nguyen-Schäfer,Jan-Philip Schmidt

Publisher: Springer

ISBN: 3662484978

Category: Technology & Engineering

Page: 376

View: 8179

DOWNLOAD NOW »

This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Release

Tensor Calculus for Engineers and Physicists

Author: Emil de Souza Sánchez Filho

Publisher: Springer

ISBN: 331931520X

Category: Technology & Engineering

Page: 345

View: 6739

DOWNLOAD NOW »

This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.
Release

Vectors, Tensors and the Basic Equations of Fluid Mechanics

Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 048613489X

Category: Mathematics

Page: 320

View: 1216

DOWNLOAD NOW »

Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
Release

The General Genetic Catastrophe

On the Discovery and the Discoverer

Author: Nils K. Oeijord

Publisher: iUniverse

ISBN: 9781450297653

Category: Health & Fitness

Page: 244

View: 7233

DOWNLOAD NOW »

Nils K. Oeijord’s research since 1999 shows that we have a worldwide general genetic catastrophe (GGC) due to general local and global manmade mutagenic pollution. The GGC began in the 1700s, increased in the 1800s, and exploded in the 1900s. The HIGH and INCREASING prevalence and the HIGH and INCREASING incidence of gene damage and genetic diseases all over the world logically prove the existence of the GGC. Nils K. Oeijord is a science writer, a former researcher (plant production), a former assistant professor (mathematics), and a former science and mathematics lecturer (high school). He is the discoverer of the general genetic catastrophe, and has earned a place in Who’s Who in the World (28th Edition), in Great Minds of the 21st Century (5th Edition), and in 2000 Outstanding Intellectuals of the 21st Century (2011 Edition).
Release

Tensor Analysis with Applications in Mechanics

Author: L. P. Lebedev

Publisher: World Scientific

ISBN: 9814313998

Category: Mathematics

Page: 380

View: 9260

DOWNLOAD NOW »

The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book.
Release

Yetter-Drinfel'd Hopf Algebras Over Groups of Prime Order

Author: Yorck Sommerhauser,Yorck Sommerhäuser

Publisher: Springer Science & Business Media

ISBN: 9783540437994

Category: Mathematics

Page: 157

View: 9128

DOWNLOAD NOW »

Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.
Release

Basic Optical Properties of Materials

Summaries of Papers Presented at the Topical Conference on Basic Optical Properties of Materials, Held at the National Bureau of Standards, Gaithersburg, Maryland, May 5-7, 1980

Author: Albert Feldman

Publisher: N.A

ISBN: N.A

Category: Optical materials

Page: 241

View: 3663

DOWNLOAD NOW »

Release

Basics of Modern Cosmology

Author: Aleksandr Dmitrievich Dolgov,Mikhail Vasilʹevich Sazhin

Publisher: Atlantica Séguier Frontières

ISBN: 9782863320846

Category: Cosmologie

Page: 247

View: 9844

DOWNLOAD NOW »

Release

Tensors and Manifolds

With Applications to Physics

Author: Robert H. Wasserman,Robert Wasserman

Publisher: Oxford University Press on Demand

ISBN: 9780198510598

Category: Foreign Language Study

Page: 447

View: 5999

DOWNLOAD NOW »

The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics."--Jacket.
Release