Download or read book Tensor Calculus for Engineers and Physicists written by Emil de Souza Sánchez Filho and published by Springer. This book was released on 2016-05-20 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds written by Uwe Mühlich and published by Springer. This book was released on 2017-04-18 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Download or read book Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers written by Hung Nguyen-Schäfer and published by Springer. This book was released on 2016-08-16 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Vector and Tensor Analysis with Applications written by A. I. Borisenko and published by Courier Corporation. This book was released on 2012-08-28 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Algebra and Tensor Analysis for Engineers written by Mikhail Itskov and published by Springer Science & Business Media. This book was released on 2009-04-30 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Calculus with Applications written by Maks A?zikovich Akivis and published by World Scientific. This book was released on 2003 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, sincesuch tensors are important in applications to physics and engineering. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book p
Download or read book Tensor Calculus written by J. L. Synge and published by Courier Corporation. This book was released on 2012-04-26 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensors Differential Forms and Variational Principles written by David Lovelock and published by Courier Corporation. This book was released on 2012-04-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Vectors And Tensors In Engineering And Physics written by Donald Danielson and published by Westview Press. This book was released on 2003-01-29 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vectors and Tensors in Engineering and Physics develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications. The book provides equations for predicting: the rotations of gyroscopes and other axisymmetric solids, derived from Euler's equations for the motion of rigid bodies; the temperature decays in quenched forgings, derived from the heat equation; the deformed shapes of twisted rods and bent beams, derived from the Navier equations of elasticity; the flow fields in cylindrical pipes, derived from the Navier-Stokes equations of fluid mechanics; the trajectories of celestial objects, derived from both Newton's and Einstein's theories of gravitation; the electromagnetic fields of stationary and moving charged particles, derived from Maxwell's equations; the stress in the skin when it is stretched, derived from the mechanics of curved membranes; the effects of motion and gravitation upon the times of clocks, derived from the special and general theories of relativity. The book also features over 100 illustrations, complete solutions to over 400 examples and problems, Cartesian components, general components, and components-free notations, lists of notations used by other authors, boxes to highlight key equations, historical notes, and an extensive bibliography.
Download or read book Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers written by Hung Nguyen-Schafer and published by . This book was released on 2014-07-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Manifolds Tensor Analysis and Applications written by Ralph Abraham and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Calculus Made Simple written by Taha Sochi and published by Taha Sochi. This book was released on 2022-08-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about tensor calculus. The language and method used in presenting the ideas and techniques of tensor calculus make it very suitable for learning this subject by the beginners who have not been exposed previously to this elegant branch of mathematics. Considerable efforts have been made to reduce the dependency on foreign texts by summarizing the main concepts needed to make the book self-contained. The book also contains a significant number of high-quality graphic illustrations to aid the readers and students in their effort to visualize the ideas and understand the abstract concepts. Furthermore, illustrative techniques, such as coloring and highlighting key terms by boldface fonts, have been employed. The book also contains extensive sets of exercises which cover most of the given materials. These exercises are designed to provide thorough revisions of the supplied materials. The solutions of all these exercises are provided in a companion book. The book is also furnished with a rather detailed index and populated with hyperlinks, for the ebook users, to facilitate referencing and connecting related subjects and ideas.
Download or read book Tensor Analysis for Engineers and Physicists With Application to Continuum Mechanics Turbulence and Einstein s Special and General Theory of Relativity written by Meinhard T. Schobeiri and published by Springer Nature. This book was released on 2021-12-13 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.
Download or read book Tensor Analysis for Physicists written by Jan Arnoldus Schouten and published by Courier Corporation. This book was released on 1989-01-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.
Download or read book Mathematical Methods for Engineers and Scientists 2 written by Kwong-Tin Tang and published by Springer Science & Business Media. This book was released on 2006-11-30 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
Download or read book Math Refresher for Scientists and Engineers written by John R. Fanchi and published by John Wiley & Sons. This book was released on 2006-06-12 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanded coverage of essential math, including integral equations, calculus of variations, tensor analysis, and special integrals Math Refresher for Scientists and Engineers, Third Edition is specifically designed as a self-study guide to help busy professionals and students in science and engineering quickly refresh and improve the math skills needed to perform their jobs and advance their careers. The book focuses on practical applications and exercises that readers are likely to face in their professional environments. All the basic math skills needed to manage contemporary technology problems are addressed and presented in a clear, lucid style that readers familiar with previous editions have come to appreciate and value. The book begins with basic concepts in college algebra and trigonometry, and then moves on to explore more advanced concepts in calculus, linear algebra (including matrices), differential equations, probability, and statistics. This Third Edition has been greatly expanded to reflect the needs of today's professionals. New material includes: * A chapter on integral equations * A chapter on calculus of variations * A chapter on tensor analysis * A section on time series * A section on partial fractions * Many new exercises and solutions Collectively, the chapters teach most of the basic math skills needed by scientists and engineers. The wide range of topics covered in one title is unique. All chapters provide a review of important principles and methods. Examples, exercises, and applications are used liberally throughout to engage the readers and assist them in applying their new math skills to actual problems. Solutions to exercises are provided in an appendix. Whether to brush up on professional skills or prepare for exams, readers will find this self-study guide enables them to quickly master the math they need. It can additionally be used as a textbook for advanced-level undergraduates in physics and engineering.
Download or read book Applied Mathematics for Engineers and Physicists written by Louis A. Pipes and published by Courier Corporation. This book was released on 2014-06-10 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.
