The Very Basics of Tensors

Author: Nils K. Oeijord

Publisher: iUniverse

ISBN: 059535694X

Category: Mathematics

Page: 137

View: 4091


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.

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: 8910


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.

Tensor Calculus for Engineers and Physicists

Author: Emil de Souza Sánchez Filho

Publisher: Springer

ISBN: 331931520X

Category: Technology & Engineering

Page: 345

View: 1013


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.

Fundamentals of Electroceramics

Materials, Devices, and Applications

Author: R. K. Pandey

Publisher: John Wiley & Sons

ISBN: 1119057280

Category: Technology & Engineering

Page: 304

View: 4748


The first textbook to provide in-depth treatment of electroceramics with emphasis on applications in microelectronics, magneto-electronics, spintronics, energy storage and harvesting, sensors and detectors, magnetics, and in electro-optics and acousto-optics Electroceramics is a class of ceramic materials used primarily for their electrical properties. This book covers the important topics relevant to this growing field and places great emphasis on devices and applications. It provides sufficient background in theory and mathematics so that readers can gain insight into phenomena that are unique to electroceramics. Each chapter has its own brief introduction with an explanation of how the said content impacts technology. Multiple examples are provided to reinforce the content as well as numerous end-of-chapter problems for students to solve and learn. The book also includes suggestions for advanced study and key words relevant to each chapter. Fundamentals of Electroceramics: Materials, Devices and Applications offers eleven chapters covering: 1.Nature and types of solid materials; 2. Processing of Materials; 3. Methods for Materials Characterization; 4. Binding Forces in Solids and Essential Elements of Crystallography; 5. Dominant Forces and Effects in Electroceramics; 6. Coupled Nonlinear Effects in Electroceramics; 7. Elements of Semiconductor; 8. Electroceramic Semiconductor Devices; 9. Electroceramics and Green Energy; 10.Electroceramic Magnetics; and 11. Electro-optics and Acousto-optics. Provides an in-depth treatment of electroceramics with the emphasis on fundamental theoretical concepts, devices, and applications with focus on non-linear dielectrics Emphasizes applications in microelectronics, magneto-electronics, spintronics, energy storage and harvesting, sensors and detectors, magnetics and in electro-optics and acousto-optics Introductory textbook for students to learn and make an impact on technology Motivates students to get interested in research on various aspects of electroceramics at undergraduate and graduate levels leading to a challenging career path. Includes examples and problem questions within every chapter that prepare students well for independent thinking and learning. Fundamentals of Electroceramics: Materials, Devices and Applications is an invaluable academic textbook that will benefit all students, professors, researchers, scientists, engineers, and teachers of ceramic engineering, electrical engineering, applied physics, materials science, and engineering.

Vectors, Tensors and the Basic Equations of Fluid Mechanics

Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 048613489X

Category: Mathematics

Page: 320

View: 3192


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.

The General Genetic Catastrophe

On the Discovery and the Discoverer

Author: Nils K. Oeijord

Publisher: iUniverse

ISBN: 9781450297653

Category: Health & Fitness

Page: 244

View: 5088


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).

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: 6741


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.

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


Category: Optical materials

Page: 241

View: 4186


Basics of Modern Cosmology

Author: Aleksandr Dmitrievich Dolgov,Mikhail Vasilʹevich Sazhin

Publisher: Atlantica Séguier Frontières

ISBN: 9782863320846

Category: Cosmologie

Page: 247

View: 7042


Introduction to Diffusion Tensor Imaging

Author: Susumu Mori

Publisher: Elsevier

ISBN: 9780080495767

Category: Science

Page: 190

View: 3445


The concept of Diffusion Tensor Imaging (DTI) is often difficult to grasp, even for Magnetic Resonance physicists. Introduction to Diffusion Tensor Imaging uses extensive illustrations (not equations) to help readers to understand how DTI works. Emphasis is placed on the interpretation of DTI images, the design of DTI experiments, and the forms of application studies. The theory of DTI is constantly evolving and so there is a need for a textbook that explains how the technique works in a way that is easy to understand - Introduction to Diffusion Tensor Imaging fills this gap. * Uses extensive illustrations to explain the concept of Diffusion Tensor Imaging * Easy to understand, even without a background in physics * Includes sections on image interpretation, experimental design and applications

Grid Generation Methods

Author: Vladimir D. Liseikin

Publisher: Springer Science & Business Media

ISBN: 9048129125

Category: Science

Page: 390

View: 4783


This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.

Tensors, Differential Forms, and Variational Principles

Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 6919


Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Structural Geology Algorithms

Vectors and Tensors

Author: Richard W. Allmendinger,Nestor Cardozo,Donald M. Fisher

Publisher: Cambridge University Press

ISBN: 1139505009

Category: Science

Page: N.A

View: 4633


State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also provide professional structural geologists with a valuable reference and refresher for calculations.

Geodynamics of the Lithosphere

An Introduction

Author: Kurt Stüwe

Publisher: Springer Science & Business Media

ISBN: 3540712372

Category: Science

Page: 493

View: 5995


This second edition of the important introductory text for earth scientists has been thoroughly revised and extended. It is required reading for all those interested in learning about the quantitative description of geological problems. It contains chapters on heat flow, sedimentary basin modeling, the mechanics of continental deformation, PT path modeling, geomorphology, mass transfer and more. The book is aimed at the field oriented geologist who wants to begin by learning about the quantitative description of problems. The new edition features yet more illustrations and maps as well as almost 100 corrections of scientific problems.

Visualization and Processing of Tensor Fields

Author: Joachim Weickert,Hans Hagen

Publisher: Springer Science & Business Media

ISBN: 3540312722

Category: Mathematics

Page: 481

View: 1866


Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Potential Theory in Applied Geophysics

Author: Kalyan Kumar Roy

Publisher: Springer Science & Business Media

ISBN: 354072334X

Category: Science

Page: 651

View: 2737


This book introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.

Introduction to Vectors and Tensors

Author: Ray M. Bowen,Chao-cheng Wang

Publisher: Courier Corporation

ISBN: 048646914X

Category: Mathematics

Page: 520

View: 4056


This convenient single-volume compilation of two texts offers both an introduction and an in-depth survey. Geared toward engineering and science students rather than mathematicians, its less rigorous treatment focuses on physics and engineering applications. A practical reference for professionals, it is suitable for advanced undergraduate and graduate students. 1976 edition.