Tensor Calculus Made Simple

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Tensor Calculus Made Simple

Taha Sochi
Tensor Calculus Made Simple Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 171 pages
File Size : 44,8 Mb
Release : 2022-08-23
Category : Mathematics
ISBN : 8210379456XXX

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Tensor Calculus Made Simple by Taha Sochi Pdf

This book is about tensor calculus. The language and method used in presenting the ideas and techniques of tensor calculus make it very suitable for learning this subject by the beginners who have not been exposed previously to this elegant branch of mathematics. Considerable efforts have been made to reduce the dependency on foreign texts by summarizing the main concepts needed to make the book self-contained. The book also contains a significant number of high-quality graphic illustrations to aid the readers and students in their effort to visualize the ideas and understand the abstract concepts. Furthermore, illustrative techniques, such as coloring and highlighting key terms by boldface fonts, have been employed. The book also contains extensive sets of exercises which cover most of the given materials. These exercises are designed to provide thorough revisions of the supplied materials. The solutions of all these exercises are provided in a companion book. The book is also furnished with a rather detailed index and populated with hyperlinks, for the ebook users, to facilitate referencing and connecting related subjects and ideas.

Tensor Calculus Made Simple

Taha Sochi
Tensor Calculus Made Simple Book PDF

Author : Taha Sochi
Publisher : Createspace Independent Publishing Platform
Page : 170 pages
File Size : 48,8 Mb
Release : 2016-12-09
Category : Electronic
ISBN : 1541013638

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Tensor Calculus Made Simple by Taha Sochi Pdf

This book is about tensor analysis. It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning.

Principles of Tensor Calculus

Taha Sochi
Principles of Tensor Calculus Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 189 pages
File Size : 47,7 Mb
Release : 2022-08-23
Category : Mathematics
ISBN : 8210379456XXX

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Principles of Tensor Calculus by Taha Sochi Pdf

This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.

Tensor Calculus for Physics

Dwight E. Neuenschwander
Tensor Calculus for Physics Book PDF

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 42,6 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642

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Tensor Calculus for Physics by Dwight E. Neuenschwander Pdf

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"

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Pavel Grinfeld
Introduction to Tensor Analysis and the Calculus of Moving Surfaces Book PDF

Author : Pavel Grinfeld
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 43,5 Mb
Release : 2013-09-24
Category : Mathematics
ISBN : 9781461478676

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Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld Pdf

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.

Tensor Calculus

J. L. Synge,A. Schild
Tensor Calculus Book PDF

Author : J. L. Synge,A. Schild
Publisher : Courier Corporation
Page : 336 pages
File Size : 41,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486141398

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Tensor Calculus by J. L. Synge,A. Schild Pdf

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.

Tensor Calculus for Engineers and Physicists

Emil de Souza Sánchez Filho
Tensor Calculus for Engineers and Physicists Book PDF

Author : Emil de Souza Sánchez Filho
Publisher : Springer
Page : 345 pages
File Size : 51,7 Mb
Release : 2016-05-20
Category : Technology & Engineering
ISBN : 9783319315201

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Tensor Calculus for Engineers and Physicists by Emil de Souza Sánchez Filho Pdf

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.

Solutions of Exercises of Tensor Calculus Made Simple

Taha Sochi
Solutions of Exercises of Tensor Calculus Made Simple Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 91 pages
File Size : 53,6 Mb
Release : 2024-04-20
Category : Mathematics
ISBN : 8210379456XXX

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Solutions of Exercises of Tensor Calculus Made Simple by Taha Sochi Pdf

This book contains the detailed solutions of all the exercises of my book: Tensor Calculus Made Simple. The solutions are generally very detailed and hence they are supposed to provide some sort of revision for the subject topic.

Solutions of Exercises of Principles of Tensor Calculus

Taha Sochi
Solutions of Exercises of Principles of Tensor Calculus Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 158 pages
File Size : 44,8 Mb
Release : 2022-10-10
Category : Mathematics
ISBN : 8210379456XXX

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Solutions of Exercises of Principles of Tensor Calculus by Taha Sochi Pdf

This book contains the solutions of all the exercises of my book: Principles of Tensor Calculus. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory levels.

Tensor Calculus and Analytical Dynamics

John G. Papastavridis
Tensor Calculus and Analytical Dynamics Book PDF

Author : John G. Papastavridis
Publisher : Routledge
Page : 435 pages
File Size : 51,8 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351411622

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Tensor Calculus and Analytical Dynamics by John G. Papastavridis Pdf

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.

Tensor Calculus and Applications

Bhaben Chandra Kalita
Tensor Calculus and Applications Book PDF

Author : Bhaben Chandra Kalita
Publisher : CRC Press
Page : 123 pages
File Size : 51,9 Mb
Release : 2019-03-11
Category : Technology & Engineering
ISBN : 9780429647567

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Tensor Calculus and Applications by Bhaben Chandra Kalita Pdf

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

Tensor Calculus

Uday Chand De,Absos Ali Shaikh,Joydeep Sengupta
Tensor Calculus Book PDF

Author : Uday Chand De,Absos Ali Shaikh,Joydeep Sengupta
Publisher : Alpha Science Int'l Ltd.
Page : 188 pages
File Size : 41,6 Mb
Release : 2005
Category : Computers
ISBN : 1842651900

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Tensor Calculus by Uday Chand De,Absos Ali Shaikh,Joydeep Sengupta Pdf

This work covers all the basic topics of tensor analysis in a lucid and clear language and is aimed at both the undergraduate and postgraduate in Civil, Mechanical and Aerospace Engineering and in Engineering Physics.

Tensor Spaces and Numerical Tensor Calculus

Wolfgang Hackbusch
Tensor Spaces and Numerical Tensor Calculus Book PDF

Author : Wolfgang Hackbusch
Publisher : Springer Nature
Page : 605 pages
File Size : 46,6 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9783030355548

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Tensor Spaces and Numerical Tensor Calculus by Wolfgang Hackbusch Pdf

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.

Introduction to Differential Geometry of Space Curves and Surfaces

Taha Sochi
Introduction to Differential Geometry of Space Curves and Surfaces Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 252 pages
File Size : 42,6 Mb
Release : 2022-09-14
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to Differential Geometry of Space Curves and Surfaces by Taha Sochi Pdf

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

TENSORS made easy with SOLVED PROBLEMS

Giancarlo Bernacchi
TENSORS made easy with SOLVED PROBLEMS Book PDF

Author : Giancarlo Bernacchi
Publisher : Lulu.com
Page : 302 pages
File Size : 47,9 Mb
Release : 2015-06
Category : Calculus of tensors
ISBN : 9781326292539

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TENSORS made easy with SOLVED PROBLEMS by Giancarlo Bernacchi Pdf

-- New MARCH 2021 REVISED RELEASE -- A friendly and non-formal approach to a subject of abstract mathematics that has important applications in physics, especially in General Relativity, but also in other fields. The purpose of the book is mainly didactic and requires some mathematical background (differential calculus, partial derivatives included).