Book Description
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"
Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 21,60 MB
Release : 2015
Category : Mathematics
ISBN : 142141564X
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"
Author : Dwight E. Neuenschwander
Publisher : Johns Hopkins University Press
Page : 244 pages
File Size : 21,29 MB
Release : 2014-10-20
Category : Mathematics
ISBN : 1421415658
It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.
Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 41,45 MB
Release : 2014-10-20
Category : Mathematics
ISBN : 1421415666
Using a clear, step-by-step approach, this book explains one of the more difficult—yet crucial—topics in physics. Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism, they encounter the "polarization tensor." However, this piecemeal approach can set students up for misconceptions when they have to learn about tensors in more advanced physics and mathematics studies (e.g., while enrolled in a graduate-level general relativity course or when studying non-Euclidean geometries in a higher mathematics class). Dwight E. Neuenschwander's Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. Using a clear, step-by-step approach, the book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.
Author : Emil de Souza Sánchez Filho
Publisher : Springer
Page : 370 pages
File Size : 35,31 MB
Release : 2016-05-20
Category : Technology & Engineering
ISBN : 331931520X
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.
Author : Derek Frank Lawden
Publisher :
Page : 184 pages
File Size : 29,92 MB
Release : 2013-08
Category :
ISBN : 9781258787417
Author : J. L. Synge
Publisher : Courier Corporation
Page : 340 pages
File Size : 49,93 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 048614139X
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.
Author : Pavel Grinfeld
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 38,38 MB
Release : 2013-09-24
Category : Mathematics
ISBN : 1461478677
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.
Author : Richard L. Bishop
Publisher : Courier Corporation
Page : 290 pages
File Size : 38,43 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486139239
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author : Jan Arnoldus Schouten
Publisher : Courier Corporation
Page : 322 pages
File Size : 21,49 MB
Release : 1989-01-01
Category : Science
ISBN : 0486655822
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.
Author : Uwe Mühlich
Publisher : Springer
Page : 134 pages
File Size : 50,48 MB
Release : 2017-04-18
Category : Science
ISBN : 3319562649
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.