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Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers
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Book Synopsis Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by : Hung Nguyen-Schafer
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:
Book Synopsis Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by : Hung Nguyen-Schäfer
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.
Book Synopsis Tensor Analysis by : Leonid P Lebedev
Download or read book Tensor Analysis written by Leonid P Lebedev and published by World Scientific. This book was released on 2003-04-24 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuum description. This concise text offers a straightforward treatment of the subject suitable for the student or practicing engineer. The final chapter introduces the reader to differential geometry, including the elementary theory of curves and surfaces. A well-organized formula list, provided in an appendix, makes the book a very useful reference. A second appendix contains full hints and solutions for the exercises.
Book Synopsis Tensor Analysis and Continuum Mechanics by : Y.R. Talpaert
Download or read book Tensor Analysis and Continuum Mechanics written by Y.R. Talpaert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..
Book Synopsis Tensor Calculus for Engineers and Physicists by : Emil de Souza Sánchez Filho
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 345 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.
Book Synopsis Tensor Algebra and Tensor Analysis for Engineers by : Mikhail Itskov
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.
Book Synopsis Elements of Advanced Mathematical Analysis for Physics and Engineering by : Filippo Gazzola
Download or read book Elements of Advanced Mathematical Analysis for Physics and Engineering written by Filippo Gazzola and published by Società Editrice Esculapio. This book was released on 2013-09-23 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep comprehension of applied sciences requires a solid knowledge of Mathematical Analysis. For most of high level scientific research, the good understanding of Functional Analysis and weak solutions to differential equations is essential. This book aims to deal with the main topics that are necessary to achieve such a knowledge. Still, this is the goal of many other texts in advanced analysis; and then, what would be a good reason to read or to consult this book? In order to answer this question, let us introduce the three Authors. Alberto Ferrero got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Universit`a del Piemonte Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano. Maurizio Zanotti got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano. The three Authors, for the variety of their skills, decided to join their expertises to write this book. One of the reasons that should encourage its reading is that the presentation turns out to be a reasonable compromise among the essential mathematical rigor, the importance of the applications and the clearness, which is necessary to make the reference work pleasant to the readers, even to the inexperienced ones. The range of treated topics is quite wide and covers the main basic notions of the scientific research which is based upon mathematical models. We start from vector spaces and Lebesgue integral to reach the frontier of theoretical research such as the study of critical exponents for semilinear elliptic equations and recent problems in fluid dynamics. This long route passes through the theory of Banach and Hilbert spaces, Sobolev spaces, differential equations, Fourier and Laplace transforms, before which we recall some appropriate tools of Complex Analysis. We give all the proofs that have some didactic or applicative interest, while we omit the ones which are too technical or require too high level knowledge. This book has the ambitious purpose to be useful to a broad variety of readers. The first possible beneficiaries are of course the second or third year students of a scientific course of degree: in what follows they will find the topics that are necessary to approach more advanced studies in Mathematics and in other fields, especially Physics and Engineering. This text could be also useful to graduate students who want to start a Ph.D. course: indeed it contains the matter of a multidisciplinary Ph.D. course given by Filippo Gazzola for several years at Politecnico di Milano. Finally, this book could be addressed also to the ones who have already left education far-back but occasionally need to use mathematical tools: we refer both to university professors and their research, and to professionals and designers who want to model a certain phenomenon, but also to the nostalgics of the good old days when they were students. It is precisely for this last type of reader that we have also reported some elementary topics, such as the properties of numerical sets and of the integrals; moreover, every chapter is provided with examples and specific exercises aimed at the involvement of the reader. Let us start immediately inviting the reader to find an “anomaly” among the six formulas appearing in the cover. This book is the translation from Italian of the book ”Elementi di Analisi Superiore per la Fisica e l’Ingegneria”. The translation is due to Ilaria Lucardesi.
Book Synopsis Tensor Calculus and Differential Geometry for Engineers by : Shahab Sahraee
Download or read book Tensor Calculus and Differential Geometry for Engineers written by Shahab Sahraee and published by Springer Nature. This book was released on 2023-12-12 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.
Book Synopsis Concepts from Tensor Analysis and Differential Geometry by : Tracy Yerkes Thomas
Download or read book Concepts from Tensor Analysis and Differential Geometry written by Tracy Yerkes Thomas and published by . This book was released on 2013-08 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by : Uwe Mühlich
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 125 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.
Book Synopsis Geometry, Physics, and Systems by : Robert Hermann
Download or read book Geometry, Physics, and Systems written by Robert Hermann and published by . This book was released on 1973 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Differential Geometry with Tensor Applications by : Dipankar De
Download or read book Introduction to Differential Geometry with Tensor Applications written by Dipankar De and published by John Wiley & Sons. This book was released on 2022-05-24 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student
Book Synopsis Tensor Algebra And Analysis For Engineers: With Applications To Differential Geometry Of Curves And Surfaces by : Paolo Vannucci
Download or read book Tensor Algebra And Analysis For Engineers: With Applications To Differential Geometry Of Curves And Surfaces written by Paolo Vannucci and published by World Scientific. This book was released on 2023-02-27 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In modern theoretical and applied mechanics, tensors and differential geometry are two almost essential tools. Unfortunately, in university courses for engineering and mechanics students, these topics are often poorly treated or even completely ignored. At the same time, many existing, very complete texts on tensors or differential geometry are so advanced and written in abstract language that discourage young readers looking for an introduction to these topics specifically oriented to engineering applications.This textbook, mainly addressed to graduate students and young researchers in mechanics, is an attempt to fill the gap. Its aim is to introduce the reader to the modern mathematical tools and language of tensors, with special applications to the differential geometry of curves and surfaces in the Euclidean space. The exposition of the matter is sober, directly oriented to problems that are ordinarily found in mechanics and engineering. Also, the language and symbols are tailored to those usually employed in modern texts of continuum mechanics.Though not exhaustive, as any primer textbook, this volume constitutes a coherent, self-contained introduction to the mathematical tools and results necessary in modern continuum mechanics, concerning vectors, 2nd- and 4th-rank tensors, curves, fields, curvilinear coordinates, and surfaces in the Euclidean space. More than 100 exercises are proposed to the reader, many of them complete the theoretical part through additional results and proofs. To accompany the reader in learning, all the exercises are entirely developed and solved at the end of the book.
Book Synopsis Tensor Analysis for Engineers and Physicists - With Application to Continuum Mechanics, Turbulence, and Einstein’s Special and General Theory of Relativity by : Meinhard T. Schobeiri
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.
Book Synopsis Tensors, Differential Forms, and Variational Principles by : David Lovelock
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 400 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.
Book Synopsis Tensor Analysis by : Fridtjov Irgens
Download or read book Tensor Analysis written by Fridtjov Irgens and published by Springer. This book was released on 2018-12-15 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tensors and tensor analysis as primary mathematical tools for engineering and engineering science students and researchers. The discussion is based on the concepts of vectors and vector analysis in three-dimensional Euclidean space, and although it takes the subject matter to an advanced level, the book starts with elementary geometrical vector algebra so that it is suitable as a first introduction to tensors and tensor analysis. Each chapter includes a number of problems for readers to solve, and solutions are provided in an Appendix at the end of the text. Chapter 1 introduces the necessary mathematical foundations for the chapters that follow, while Chapter 2 presents the equations of motions for bodies of continuous material. Chapter 3 offers a general definition of tensors and tensor fields in three-dimensional Euclidean space. Chapter 4 discusses a new family of tensors related to the deformation of continuous material. Chapter 5 then addresses constitutive equations for elastic materials and viscous fluids, which are presented as tensor equations relating the tensor concept of stress to the tensors describing deformation, rate of deformation and rotation. Chapter 6 investigates general coordinate systems in three-dimensional Euclidean space and Chapter 7 shows how the tensor equations discussed in chapters 4 and 5 are presented in general coordinates. Chapter 8 describes surface geometry in three-dimensional Euclidean space, Chapter 9 includes the most common integral theorems in two- and three-dimensional Euclidean space applied in continuum mechanics and mathematical physics.
Book Synopsis Advances in Fractional Calculus by : J. Sabatier
Download or read book Advances in Fractional Calculus written by J. Sabatier and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
