tensor analysis and elementary differential geometry for physicists and engineers

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Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers

Author : Hung Nguyen-Schäfer
ISBN : 9783662484975
Genre : Technology & Engineering
File Size : 36. 70 MB
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This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum mechanics, cosmology, electrodynamics, computational fluid dynamics (CFD), and continuum mechanics. The target audience of this all-in-one book primarily comprises graduate students in mathematics, physics, engineering, research scientists, and engineers.

Tensor Algebra And Tensor Analysis For Engineers

Author : Mikhail Itskov
ISBN : 9783319163420
Genre : Technology & Engineering
File Size : 38. 13 MB
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This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Introduction To Vector And Tensor Analysis

Author : Robert C. Wrede
ISBN : 9780486137117
Genre : Mathematics
File Size : 53. 83 MB
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Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Tensor Analysis

Author : Leonid P Lebedev
ISBN : 9789814486071
Genre : Technology & Engineering
File Size : 79. 15 MB
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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. Contents:PreliminariesTransformations and VectorsTensorsTensor FieldsElements of Differential Geometry Readership: Undergraduates and graduate students in engineering and physics, engineers, physicists and applied mathematicians. Keywords:Vectors;Tensors;Transformations;Curves and Surfaces;Differential GeometryReviews:“The book gives a brief, clear, and comprehensive introduction to the theory … A particularly nice feature is a well-organized appendix containing compact listings of all the principal formulas required in applications — these 18 pages alone are worth the price of the book … it should be of interest to both undergraduate and graduate students of physics and engineering, as well as to practicing physicists and engineers.”ZAMM

Tensor Analysis On Manifolds

Author : Richard L. Bishop
ISBN : 9780486139234
Genre : Mathematics
File Size : 25. 78 MB
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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div


ISBN : 9788120350885
Genre : Mathematics
File Size : 46. 42 MB
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The principal aim of analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book. This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.

Vector And Tensor Analysis With Applications

Author : A. I. Borisenko
ISBN : 9780486131900
Genre : Mathematics
File Size : 23. 6 MB
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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.

Geometrical Methods Of Mathematical Physics

Author : Bernard F. Schutz
ISBN : 9781107268142
Genre : Science
File Size : 60. 13 MB
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In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

Differential Geometry Of Manifolds

Author : Stephen T. Lovett
ISBN : 9781439865460
Genre : Mathematics
File Size : 75. 73 MB
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From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra. Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.

Differential Geometry

Author : Erwin Kreyszig
ISBN : 9780486318622
Genre : Mathematics
File Size : 77. 60 MB
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An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

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