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| Author | : Dwight E. Neuenschwander |
| Publisher | : JHU Press |
| Total Pages | : 244 |
| Release | : 2015 |
| Genre | : 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 | : J. L. Synge |
| Publisher | : Courier Corporation |
| Total Pages | : 340 |
| Release | : 2012-04-26 |
| Genre | : 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 |
| Total Pages | : 303 |
| Release | : 2013-09-24 |
| Genre | : 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 | : Derek Frank Lawden |
| Publisher | : |
| Total Pages | : 184 |
| Release | : 2013-08 |
| Genre | : |
| ISBN | : 9781258787417 |
| Author | : Richard L. Bishop |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486139239 |
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
| Author | : Emil de Souza Sánchez Filho |
| Publisher | : Springer |
| Total Pages | : 370 |
| Release | : 2016-05-20 |
| Genre | : 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 | : John G. Papastavridis |
| Publisher | : Routledge |
| Total Pages | : 444 |
| Release | : 2018-12-12 |
| Genre | : Mathematics |
| ISBN | : 1351411616 |
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.
| Author | : Wolfgang Hackbusch |
| Publisher | : Springer Nature |
| Total Pages | : 622 |
| Release | : 2019-12-16 |
| Genre | : Mathematics |
| ISBN | : 3030355543 |
Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.
| Author | : Bhaben Chandra Kalita |
| Publisher | : CRC Press |
| Total Pages | : 186 |
| Release | : 2019-03-11 |
| Genre | : Technology & Engineering |
| ISBN | : 0429647565 |
The aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject -tensor, and can be used in many fields of research. Special applications are discussed in the book, to remove any confusion, and for absolute understanding of the subject. In most books, they emphasize only the theoretical development, but not the methods of presentation, to develop concepts. Without knowing how to change the dummy indices, or the real indices, the concept cannot be understood. This book takes it down a notch and simplifies the topic for easy comprehension. Features Provides a clear indication and understanding of the subject on how to change indices Describes the original evolution of symbols necessary for tensors Offers a pictorial representation of referential systems required for different kinds of tensors for physical problems Presents the correlation between critical concepts Covers general operations and concepts
| Author | : Jan Arnoldus Schouten |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 535 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662129272 |
This is an entirely new book. The first edition appeared in 1923 and at that time it was up to date. But in 193 5 and 1938 the author and Prof. D. J. STRUIK published a new book, their Einführung I and li, and this book not only gave the first systematic introduction to the kernel index method but also contained many notions that had come into prominence since 1923. For instance densities, quantities of the second kind, pseudo-quantities, normal Coordinates, the symbolism of exterior forms, the LIE derivative, the theory of variation and deformation and the theory of subprojective connexions were included. Now since 1938 there have been many new developments and so a book on RICCI cal culus and its applications has to cover quite different ground from the book of 1923. Though the purpose remains to make the reader acquainted with RICCI's famous instrument in its modern form, the book must have quite a different methodical structure and quite different applica tions have to be chosen. The first chapter contains algebraical preliminaries but the whole text is modernized and there is a section on hybrid quantities (quantities with indices of the first and of the second kind) and one on the many abridged notations that have been developed by several authors. In the second chapter the most important analytical notions that come before the introduction of a connexion aredealt with in full.
