Tensor Calculus for Engineers and Physicists
Tensor Calculus for Engineers and Physicists

Author: Emil de Souza Sánchez Filho

Publisher: Springer

Published: 2016-05-20

Total Pages: 370

ISBN-13: 331931520X

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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.

Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds
Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds

Author: Uwe Mühlich

Publisher: Springer

Published: 2017-04-18

Total Pages: 134

ISBN-13: 3319562649

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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.

Tensor Algebra and Tensor Analysis for Engineers
Tensor Algebra and Tensor Analysis for Engineers

Author: Mikhail Itskov

Publisher: Springer Science & Business Media

Published: 2009-04-30

Total Pages: 253

ISBN-13: 3540939075

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There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

Tensor Calculus
Tensor Calculus

Author: J. L. Synge

Publisher: Courier Corporation

Published: 2012-04-26

Total Pages: 340

ISBN-13: 048614139X

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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 Analysis and Elementary Differential Geometry for Physicists and Engineers
Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Author: Hung Nguyen-Schäfer

Publisher: Springer

Published: 2016-08-16

Total Pages: 389

ISBN-13: 3662484978

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This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

Tensor Calculus and Differential Geometry for Engineers
Tensor Calculus and Differential Geometry for Engineers

Author: Shahab Sahraee

Publisher: Springer Nature

Published: 2023-12-12

Total Pages: 684

ISBN-13: 3031339533

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The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.

Matrix and Tensor Calculus
Matrix and Tensor Calculus

Author: Aristotle D. Michal

Publisher:

Published: 2008

Total Pages: 0

ISBN-13: 9780486462462

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This volume offers a working knowledge of the fundamentals of matrix and tensor calculus. Relevant to several fields, particularly aeronautical engineering, the text skillfully combines mathematical statements with practical applications. 1947 edition.

Vector and Tensor Analysis with Applications
Vector and Tensor Analysis with Applications

Author: A. I. Borisenko

Publisher: Courier Corporation

Published: 2012-08-28

Total Pages: 292

ISBN-13: 0486131904

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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.

Tensor Calculus and Analytical Dynamics
Tensor Calculus and Analytical Dynamics

Author: John G. Papastavridis

Publisher: Routledge

Published: 2018-12-12

Total Pages: 435

ISBN-13: 1351411624

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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
Tensor Calculus and Applications

Author: Bhaben Chandra Kalita

Publisher: CRC Press

Published: 2019-03-11

Total Pages: 123

ISBN-13: 0429647565

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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