Advertisement
| vector and tensor analysis book: Vector and Tensor Analysis George E. Hay, 1953-01-01 Remarkably comprehensive, concise and clear. — Industrial Laboratories Considered as a condensed text in the classical manner, the book can well be recommended. — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book. |
| vector and tensor analysis book: Tensor and Vector Analysis C. E. Springer, 2013-09-26 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. |
| vector and tensor analysis book: A Brief on Tensor Analysis James G. Simmonds, 2012-10-31 There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor. |
| vector and tensor analysis book: Vector and Tensor Analysis Eutiquio C. Young, 2017-12-19 Revised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved. |
| vector and tensor analysis book: Tensor Analysis on Manifolds Richard L. Bishop, Samuel I. Goldberg, 2012-04-26 DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div |
| vector and tensor analysis book: Introduction to Tensor Analysis and the Calculus of Moving Surfaces Pavel Grinfeld, 2013-09-24 This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem. |
| vector and tensor analysis book: Introduction to Vector and Tensor Analysis Robert C. Wrede, 1972-06-01 Text for advanced undergraduate and graduate students covers the algebra, differentiation, and integration of vectors, and the algebra and analysis of tensors, with emphasis on transformation theory |
| vector and tensor analysis book: Vector and Tensor Analysis Harry Lass, 1950 |
| vector and tensor analysis book: Tensor Algebra and Tensor Analysis for Engineers Mikhail Itskov, 2007-05-04 There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area. |
| vector and tensor analysis book: A History of Vector Analysis Michael J. Crowe, 1994-01-01 Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis. |
| vector and tensor analysis book: Vector and Tensor Analysis Eutiquio C. Young, 1978 |
| vector and tensor analysis book: Vector and Tensor Analysis Louis Brand, 1947 |
| vector and tensor analysis book: Vectors, Tensors and the Basic Equations of Fluid Mechanics Rutherford Aris, 2012-08-28 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. |
| vector and tensor analysis book: Tensor Calculus for Physics Dwight E. Neuenschwander, 2015 It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher American Journal of Physics |
| vector and tensor analysis book: Vector analysis with an introduction to tensor analysis Albert P. Wills, 1949 |
| vector and tensor analysis book: Introduction to Vectors and Tensors Ray M. Bowen, Chao-cheng Wang, 1976-05-31 To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further. |
| vector and tensor analysis book: Manifolds, Tensor Analysis, and Applications Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu, 2012-12-06 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. |
| vector and tensor analysis book: Tensor and Vector Analysis A.T. Fomenko, V.V. Trofimov, O V Manturnov, 1998-11-26 Reflecting the significant contributions of Russian mathematicians to the field, this book contains a selection of papers on tensor and vector analysis. It is divided into three parts, covering Hamiltonian systems, Riemannian geometry and calculus of variations, and topology. The range of applications of these topics is very broad, as many modern geometrical problems recur across a wide range of fields, including mechanics and physics as well as mathematics. Many of the approaches to problems presented in this volume will be novel to the Western reader, although questions are of global interest. The main achievements of the Russian school are placed in the context of the development of each individual subject. |
| vector and tensor analysis book: Tensors for Physics Siegfried Hess, 2015-04-25 This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity. |
| vector and tensor analysis book: Vector Analysis Louis Brand, 1967 |
| vector and tensor analysis book: Tensor Analysis and Continuum Mechanics Wilhelm Flügge, 2013-11-11 Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming vectorized (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject. |
| vector and tensor analysis book: A Student's Guide to Vectors and Tensors Daniel A. Fleisch, 2011-09-22 Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author. |
| vector and tensor analysis book: From Vectors to Tensors Juan R. Ruiz-Tolosa, Enrique Castillo, 2004-11-29 This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet. |
| vector and tensor analysis book: Vector and Tensor Analysis Louis Brand, 2020-04-15 An outstanding introduction to tensor analysis for physics and engineering students, this text admirably covers the expected topics in a careful step-by-step manor. In addition to the standard vector analysis of Gibbs, including dyadic or tensors of valence two, the treatment also supplies an introduction to the algebra of motors. The entire theory is illustrated by many significant applications. Surface geometry and hydrodynamics are treated at length in separate chapters. Nearly all of the important results are formulated as theorems, in which the essential conditions are explicitly stated. Each chapter concludes with a selection of problems that develop students' technical skills and introduce new and important applications. The material may be adapted for short courses in either vector analysis or tensor analysis. |
| vector and tensor analysis book: Vector and tensor analysis Eutiquio C. Young, 1980 |
| vector and tensor analysis book: Manifolds, Tensors and Forms Paul Renteln, 2014 Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences. |
| vector and tensor analysis book: Tensor Analysis Liqun Qi, Ziyan Luo, 2017-04-19 Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. |
| vector and tensor analysis book: Mathematical Techniques for Engineers and Scientists Larry C. Andrews, Ronald L. Phillips, 2003 This self-study text for practicing engineers and scientists explains the mathematical tools that are required for advanced technological applications, but are often not covered in undergraduate school. The authors (University of Central Florida) describe special functions, matrix methods, vector operations, the transformation laws of tensors, the analytic functions of a complex variable, integral transforms, partial differential equations, probability theory, and random processes. The book could also serve as a supplemental graduate text.--Memento. |
| vector and tensor analysis book: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. |
| vector and tensor analysis book: Tensors, Differential Forms, and Variational Principles David Lovelock, Hanno Rund, 2012-04-20 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. |
| vector and tensor analysis book: Tensor Geometry C. T. J. Dodson, Timothy Poston, 2013-04-17 This treatment of differential geometry and the mathematics required for general relativity makes the subject of this book accessible for the first time to anyone familiar with elementary calculus in one variable and with a knowledge of some vector algebra. |
| vector and tensor analysis book: Vector Analysis Klaus Jänich, 2013-03-09 Classical vector analysis deals with vector fields; the gradient, divergence, and curl operators; line, surface, and volume integrals; and the integral theorems of Gauss, Stokes, and Green. Modern vector analysis distills these into the Cartan calculus and a general form of Stokes' theorem. This essentially modern text carefully develops vector analysis on manifolds and reinterprets it from the classical viewpoint (and with the classical notation) for three-dimensional Euclidean space, then goes on to introduce de Rham cohomology and Hodge theory. The material is accessible to an undergraduate student with calculus, linear algebra, and some topology as prerequisites. The many figures, exercises with detailed hints, and tests with answers make this book particularly suitable for anyone studying the subject independently. |
| vector and tensor analysis book: A Primer in Tensor Analysis and Relativity Ilya L. Shapiro, 2019-08-30 This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject. |
| vector and tensor analysis book: Vector and Tensor Analysis , 1950 |
| vector and tensor analysis book: Tensor Calculus J. L. Synge, A. Schild, 2012-04-26 Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more. |
| vector and tensor analysis book: Schaum's Outline of Theory and Problems of Vector Analysis and an Introduction to Tensor Analysis Murray R. Spiegel, 1959 This book introduces students to vector analysis, a concise way of presenting certain kinds of equations and a natural aid for forming mental pictures of physical and geometrical ideas. Students of the physical sciences and of physics, mechanics, electromagnetic theory, aerodynamics and a number of other fields will find this a rewarding and practical treatment of vector analysis. Key points are made memorable with the hundreds of problems with step-by-step solutions, and many review questions with answers. |
| vector and tensor analysis book: Vector Analysis and Cartesian Tensors Donald Edward Bourne, 1982 |
| vector and tensor analysis book: Ricci-Calculus Jan Arnoldus Schouten, 2014-01-15 |
| vector and tensor analysis book: Schaum's Outline of Vector Analysis, 2ed Seymour Lipschutz, Murray R. Spiegel, Dennis Spellman, 2009-05-04 The guide to vector analysis that helps students study faster, learn better, and get top grades More than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's is better than ever-with a new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study. Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved. |
| vector and tensor analysis book: Vector and Tensor Analysis with Applications Aleksandr Ivanovich Borisenko, Ivan Evgen?evich Tarapov, 1968-01-01 Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition. |
Free Vectors to Download | Freepik
Vector images for every kind of project. Explore categories of curated visuals and give your designs the perfect …
Download Free Vectors, Images, Photos & Videos | Ve…
Explore millions of royalty free vectors, images, stock photos and videos! Get the perfect background, graphic, clipart, picture or drawing …
Vector (mathematics and physics) - Wikipedia
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has …
VectorStock - Vector Art, Images, Graphics & Clipart
Royalty free vector images, vector art, graphics, clipart, illustrations and high resolution stock images. Find the vectors you want!
Download Free Vectors, Images & Backgrounds | Vecteezy
Download free backgrounds, graphics, clipart, drawings, icons, logos and more that are safe for commercial use. Vector graphics use mathematical calculations to plot points and draw connecting …
Free Vectors to Download | Freepik
Vector images for every kind of project. Explore categories of curated visuals and give your designs the perfect final touch
Download Free Vectors, Images, Photos & Videos | Vecteezy
Explore millions of royalty free vectors, images, stock photos and videos! Get the perfect background, graphic, clipart, picture or drawing for your design.
Vector (mathematics and physics) - Wikipedia
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or …
VectorStock - Vector Art, Images, Graphics & Clipart
Royalty free vector images, vector art, graphics, clipart, illustrations and high resolution stock images. Find the vectors you want!
Download Free Vectors, Images & Backgrounds | Vecteezy
Download free backgrounds, graphics, clipart, drawings, icons, logos and more that are safe for commercial use. Vector graphics use mathematical calculations to plot points and draw …
Download Free Vectors & Graphics - VectorStock.com
Download Free Vector Art, Stock Images, Free Graphic Vectors, Free Vector Clipart, High-res Vector Images, Free Symbols, Icons, Vector Silhouettes and more. New! Turn your bitmap …
Vectr – AI Logo Maker & Vector Editor | Background Remover
Whether it is vectorizing an image or saving a jpg file as a vector, converting PNG to SVG, or converting a photo into a vector silhouette, the AI-powered vector generator gives your …
Vector Icons and Stickers - PNG, SVG, EPS, PSD and CSS
Access 18.1M+ vector icons & stickers . Download Free Icons and Stickers for your projects. Resources made by and for designers. PNG, SVG, EPS, PSD and CSS formats.
SVG Repo - Free SVG Vectors and Icons
Search, explore and edit the best-fitting free icons or vectors for your projects using a wide variety vector library. Download free SVG vectors and icons for commercial use.
Royalty-Free Vectors, Clipart Graphics & Icons Downloads - Hello Vector
Download thousands of uniquely designed royalty-free vector art, clipart graphics, Aboriginal art, infographics templates, web templates & T-shirt designs.
