The Very Basics of Tensors

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Author: Nils K. Oeijord

Publisher: iUniverse

ISBN: 059535694X

Category: Mathematics

Page: 137

View: 6773

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.

TensorFlow für Dummies

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Author: Matthew Scarpino

Publisher: John Wiley & Sons

ISBN: 3527818960

Category: Computers

Page: 324

View: 7887

TensorFlow ist Googles herausragendes Werkzeug für das maschinelle Lernen, und dieses Buch macht es zugänglich, selbst wenn Sie bisher wenig über neuronale Netze und Deep Learning wissen. Sie erfahren, auf welchen Prinzipien TensorFlow basiert und wie Sie mit TensorFlow Anwendungen schreiben. Gleichzeitig lernen Sie die Konzepte des maschinellen Lernens kennen. Wenn Sie Softwareentwickler sind und TensorFlow in Zukunft einsetzen möchten, dann ist dieses Buch der richtige Einstieg für Sie. Greifen Sie auch zu, wenn Sie einfach mehr über das maschinelle Lernen erfahren wollen.

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

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Author: Hung Nguyen-Schäfer,Jan-Philip Schmidt

Publisher: Springer

ISBN: 3662484978

Category: Technology & Engineering

Page: 376

View: 7276

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

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Author: Emil de Souza Sánchez Filho

Publisher: Springer

ISBN: 331931520X

Category: Technology & Engineering

Page: 345

View: 7775

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.

Why Minus Times Minus Is Plus

The Very Basic Mathematics of Real and Complex Numbers

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Author: Nils K. Oeijord

Publisher: N.A

ISBN: 9781450240635

Category: Mathematics

Page: 136

View: 778

MATHEMATICS / ALGEBRA This book is written for a very broad audience. There are no particular prerequisites for reading this book. We hope students of High Schools, Colleges, and Universities, as well as hobby mathematicians, will like and benefit from this book. The book is rigorous and self-contained. All results are proved (or the proofs are optional exercises) and stated as theorems. Important points are covered by examples and optional exercises. Additionally there are also two sections called "More optional exercises (with answers)." Modern technology uses complex numbers for just about everything. Actually, there is no way one can formulate quantum mechanics without resorting to complex numbers. Leonard Euler (1707-1786) considered it natural to introduce students to complex numbers much earlier than we do today. Even in his elementary algebra textbook he uses complex numbers throughout the book. Nils K. Oeijord is a science writer and a former assistant professor of mathematics at Tromsoe College, Norway. He is the author of The Very Basics of Tensors, and several other books in English and Norwegian. Nils K. Oeijord is the discoverer of the general genetic catastrophe (GGC).

The General Genetic Catastrophe

On the Discovery and the Discoverer

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Author: Nils K. Oeijord

Publisher: iUniverse

ISBN: 9781450297653

Category: Health & Fitness

Page: 244

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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).

Vectors, Tensors and the Basic Equations of Fluid Mechanics

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Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 048613489X

Category: Mathematics

Page: 320

View: 7489

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.

Fundamentals of Electroceramics

Materials, Devices, and Applications

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Author: R. K. Pandey

Publisher: John Wiley & Sons

ISBN: 1119057280

Category: Technology & Engineering

Page: 304

View: 2596

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.

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

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Author: Yorck Sommerhauser,Yorck Sommerhäuser

Publisher: Springer Science & Business Media

ISBN: 9783540437994

Category: Mathematics

Page: 157

View: 3783

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.

Tensors and Manifolds

With Applications to Physics

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Author: Robert Wasserman

Publisher: Oxford University Press on Demand

ISBN: 9780198510598

Category: Foreign Language Study

Page: 447

View: 3655

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.

Tensors, Differential Forms, and Variational Principles

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Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 1176

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.

Transport Phenomena in Newtonian Fluids - A Concise Primer

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Author: Per Olsson

Publisher: Springer Science & Business Media

ISBN: 3319013092

Category: Science

Page: 94

View: 5748

This short primer provides a concise and tutorial-style introduction to transport phenomena in Newtonian fluids , in particular the transport of mass, energy and momentum. The reader will find detailed derivations of the transport equations for these phenomena, as well as selected analytical solutions to the transport equations in some simple geometries. After a brief introduction to the basic mathematics used in the text, Chapter 2, which deals with momentum transport, presents a derivation of the Navier-Stokes-Duhem equation describing the basic flow in a Newtonian fluid. Also provided at this stage are the derivations of the Bernoulli equation, the pressure equation and the wave equation for sound waves. The boundary layer, turbulent flow and flow separation are briefly reviewed. Chapter 3, which addresses energy transport caused by thermal conduction and convection, examines a derivation of the heat transport equation. Finally, Chapter 4, which focuses on mass transport caused by diffusion and convection, discusses a derivation of the mass transport equation.

Energy Momentum Tensors

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Author: Robert Hermann

Publisher: Math Science Press

ISBN: 9780915692033

Category: Calculus of tensors

Page: 120

View: 1796

Introduction to Diffusion Tensor Imaging

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Author: Susumu Mori

Publisher: Elsevier

ISBN: 9780080495767

Category: Science

Page: 190

View: 1635

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

Introduction to Vectors and Tensors

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Author: Ray M. Bowen,Chao-cheng Wang

Publisher: Courier Corporation

ISBN: 048646914X

Category: Mathematics

Page: 520

View: 5771

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.

Tensor Analysis with Applications in Mechanics

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Author: L. P. Lebedev

Publisher: World Scientific

ISBN: 9814313998

Category: Mathematics

Page: 380

View: 734

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.

Angewandte Mathematik: Body and Soul

Band 2: Integrale und Geometrie in IRn

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Author: Kenneth Eriksson,Donald Estep,Claes Johnson

Publisher: Springer-Verlag

ISBN: 3540269509

Category: Mathematics

Page: 362

View: 9548

"Angewandte Mathematik: Body & Soul" ist ein neuer Grundkurs in der Mathematikausbildung für Studienanfänger in den Naturwissenschaften, der Technik, und der Mathematik, der an der Chalmers Tekniska Högskola in Göteborg entwickelt wurde. Er besteht aus drei Bänden sowie Computer-Software. Das Projekt ist begründet in der Computerrevolution, die ihrerseits völlig neue Möglichkeiten des wissenschaftlichen Rechnens in der Mathematik, den Naturwissenschaften und im Ingenieurwesen eröffnet hat. Es besteht aus einer Synthese der mathematischen Analysis (Soul) mit der numerischen Berechnung (Body) sowie den Anwendungen. Die Bände I-III geben eine moderne Version der Analysis und der linearen Algebra wieder, einschließlich konstruktiver numerischer Techniken und Anwendungen, zugeschnitten auf Anfängerprogramme im Maschinenbau und den Naturwissenschaften. Weitere Bände behandeln Themen wie z.B. dynamische Systeme, Strömungsdynamik, Festkörpermechanik und Elektromagnetismus. Dieser Band entwickelt das Riemann-Integral, um eine Funktion zu einer gegebenen Ableitung zu bestimmen. Darauf aufbauend werden Differentialgleichungen und Anfangswertprobleme mit einer Vielzahl anschaulicher Anwendungen behandelt. Die lineare Algebra wird auf n-dimensionale Räume verallgemeinert, wobei wiederum dem praktischen Umgang und numerischen Lösungstechniken besonderer Platz eingeräumt wird. Die Autoren sind führende Experten im Gebiet des wissenschaftlichen Rechnens und haben schon mehrere erfolgreiche Bücher geschrieben. "[......] Oh, by the way, I suggest immediate purchase of all three volumes!" The Mathematical Association of America Online, 7.7.04