Tensor Calculus With Applications

by Maks A. Akivis

Publisher: World Scientific Publishing Company

Written in English
Cover of: Tensor Calculus With Applications | Maks A. Akivis
Published: Pages: 380 Downloads: 462
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Subjects:

  • Mathematics for scientists & engineers,
  • Vector & tensor analysis,
  • Science/Mathematics,
  • Geometry - General,
  • Mathematics,
  • Algebra - Linear,
  • Topology - General,
  • Calculus,
  • Mathematical Physics
The Physical Object
FormatHardcover
Number of Pages380
ID Numbers
Open LibraryOL9196442M
ISBN 109812385053
ISBN 109789812385055

For some mathematical applications, a more abstract approach is sometimes useful. This can be achieved by defining tensors in terms of elements of tensor products of vector spaces, which in turn are defined through a universal property.A type (p, q) tensor is defined in this context as an element of the tensor product of vector spaces, ∈ ⊗ ⋯ ⊗ ⏟ ⊗ ∗ ⊗ ⋯ ⊗ ∗ ⏟. An introductory Tensor Calculus for Physics book is a. tensor arising from applying a stress to solid bodies: the three- Chapter 2 on simple applications of. Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. ng may be from multiple locations in the US or from the UK, depending on stock availability. pages. /5(19). 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.

tensor algebra and calculus. I assume a basic knowledge of calculus and linear algebra with some commonly used mathematical terminology. I tried to be as clear as possible and to highlight the key issues of the subject at an introductory level in a concise form. I hopeFile Size: KB.   This book is a relatively easy-to-read and carefully motivated text on tensor calculus, a subject that does tend to lead to that eye-glazing-over effect because of the numerous indices. It does a very good job of keeping the focus on the concepts, without getting too bogged down in the equations - most of the time.5/5(3). definition of a tensor comes only in Chap. 6—when the reader is ready for it. Part III of this book is devoted to the calculus of moving surfaces (CMS). One of the central applications of tensor calculus is differential geometry, and there is probably not one book about tensors in which a major portion is not devoted to Size: KB. The figure is done when the basis e 1, e 2 consists of normed vectors. By identification, one can also note that e* 1 = e 1, e* 2 = e 2, and the dual basis is thus not normed!. Remark. If e 2 ⊥ e 1, then the dual basis is identical to the initial basis, {e i} = {e* i}.We shall then see later on that the notion of variance is no longer necessary.

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 Foundations of the Calculus of Moving Surfaces Extension to Arbitrary Tensors Applications of the Calculus of Moving Surfaces Index: Absolute . Buy Tensor Calculus (Dover Pictorial Archives) (Dover Books on Mathematics) New edition by Synge, John L., Schild, A. (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.4/5(15).

Tensor Calculus With Applications by Maks A. Akivis Download PDF EPUB FB2

The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some Cited by: 9.

This book includes elementary matrix and tensor calculus with some applications. The book is brief and concise Tensor Calculus With Applications book an update to typesetting and markings may be Cited by: 6.

In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of Tensor Calculus With Applications book calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).

Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his theory of general sted with the infinitesimal calculus, tensor calculus allows.

A Student's Guide to Vectors and Tensors by Daniel A. Fleisch Tensor calculus by John Lighton Synge Tensor is usually discussed in Riemannian Geometry Riemannian Geometry by Manfredo Perdigao do Carmo & Francis Flaherty There is also good discussi. Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity, Electromagnetic Theory and many other disciplines of Science and Engineering.

This book has been presented in such a clear and easy way that the students will have no difficulty in understanding Size: 1MB. This book provides a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and relativity.

This well-written text gives the origin and nature of the tensor along with the scope of the tensor calculus. Tensor product states arising in quantum information theory and algebraic statistics are then introduced as they are typical of applications where one studies subvarieties of spaces of tensors.

I conclude by briefly mentioning how the geometry and representation theory that occupies much of the first part of the book will be useful for future. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some.

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and 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. definition of a tensor comes only in Chap. 6—when the reader is ready for it.

Part III of this book is devoted to the calculus of moving surfaces (CMS). One of the central applications of tensor calculus is differential geometry, and there is probably not one book about tensors in which a major portion is not devoted to Size: 1MB.

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 : Bhaben Chandra Kalita.

The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and 4/5(2).

Tensor calculus and applications: simplified tools and techniques | Kalita, Bharat Chandra | download | B–OK. Download books for free.

Find books. Tensor calculus with applications. [M A Akivis; V V Golʹdberg] Print book: EnglishView all editions and formats: Summary: The general theory of second-degree surfaces -- 6. Applications of tensor calculus to some problem of mechanics and physics -- 7. Tensor Calculus contains eight chapters.

The first four deal with the basic concepts of tensors, Riemannian spaces, Riemannian curvature, and spaces of constant curvature. The next three chapters are concerned with applications to classical dynamics, hydrodynamics, elasticity, electromagnetic radiation, and the theorems of Stokes and Green.

The title, The Poor Man’s Introduction to Tensors, is a reference to Gravitation by Misner, Thorne and Wheeler, which characterizes simplified approaches to a problem as “the poor man’s way to do X.” Originally, these notes were.

Automata Studies Edited by C. SHANNON and J. Linear Inequalities and Related Syst Edited by H. KUHN and A. Book Description. 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. more. Second, tensor theory, at the most elementary level, requires only linear algebra and some calculus as prerequisites.

Proceeding a small step further, tensor theory requires background in multivariate calculus. For a deeper understanding, knowledge of. Introduction to Tensor Calculus Kees Dullemond & Kasper Peeters c This booklet contains an explanation about tensor calculus for students of physics and engineering with a basic knowledge of linear algebra.

The focus lies mainly onFile Size: KB. This volume offers a working knowledge of the fundamentals of matrix and tensor calculus that can be applied to a variety of fields, particularly scientific aeronautical engineering.

Mathematicians, physicists, and meteorologists as well as engineers will benefit from its skillful combination of mathematical statements and immediate practical /5(3).

The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and 5/5(1).

A Some Basic Rules of Tensor Calculus give a brief guide to notations and rules of the tensor calculus applied through-out this work. For more comprehensive overviews on tensor calculus we recom-mend [54, 96, ]. The calculus of matrices is File Size: KB.

"This book is an excellent classroom text, since it is clearly written, contains numerous problems and exercises, and at the end of each chapter has a summary of the significant results of the chapter." — Quarterly of Applied Mathematics.

Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to 2/5(1). This is a well designed, pedagogically inspired and comprehensive introduction to a fundamental branch of applied mathematics: tensor and vector calculus.

Designed for the upper undergraduate or graduate student, this textbook is probably one of the most lucid, clear /5. 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.

Recommend a book for self-learning tensor calculus. I recently graduated with a bs in mathematics and physics, and in my undergrad education I had a brief encounter with the very basics of tensor calculus, just enough to understand what I needed for the time being.

of the mathematical concepts associated with tensor calculus and (ii) develop the basic equations of tensor calculus, di erential geometry and continuum mechanics which arise in engineering applications. From these basic equations one can go on to develop more sophisticated models of applied mathematics.

The material is presented in an informal. proves useful for higher-order tensor analysis of anisotropic media. In addition to reviewing basic matrix and vector analysis, the concept of a tensor is cov-ered by reviewing and contrasting numerous. different.

definition one might see in the literature for the term. Tensor Calculus The Metric Tensor in Curved Spaces for Measuring Arc Length by eigenchris.

Tensor Calculus Gradient vs "d" operator (exterior derivative/differential). textbook of tensor calculus and differential geometry Download textbook of tensor calculus and differential geometry or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get textbook of tensor calculus and differential geometry book now. This site is like a library, Use search box in the widget to.Tensor analysis, branch of mathematics concerned with relations or laws that remain valid regardless of the system of coordinates used to specify the quantities.

Such relations are called covariant. Tensors were invented as an extension of vectors to formalize the manipulation of geometric entities arising in the study of mathematical manifolds. A vector is an entity that has both magnitude. 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.

With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some.