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Author: Hung Nguyen-Schäfer
Publisher: Springer
ISBN: 366243444X
Category : Technology & Engineering
Languages : en
Pages : 250
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Book Description
Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics and cybernetics. This book comprehensively presents topics, such as bra-ket notation, tensor analysis and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. 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 and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists and practicing engineers.
Author: Hung Nguyen-Schäfer
Publisher: Springer
ISBN: 366243444X
Category : Technology & Engineering
Languages : en
Pages : 250
Get Book Here
Book Description
Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics and cybernetics. This book comprehensively presents topics, such as bra-ket notation, tensor analysis and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. 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 and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists and practicing engineers.
Author: Hung Nguyen-Schafer
Publisher:
ISBN: 9783662434451
Category :
Languages : en
Pages : 256
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Book Description
Author: Hung Nguyen-Schäfer
Publisher: Springer
ISBN: 3662484978
Category : Technology & Engineering
Languages : en
Pages : 389
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Book Description
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.
Author: Mikhail Itskov
Publisher: Springer Science & Business Media
ISBN: 3540939075
Category : Technology & Engineering
Languages : en
Pages : 253
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Book Description
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.
Author: David Lovelock
Publisher: Courier Corporation
ISBN: 048613198X
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Author: Chris J. Isham
Publisher: Allied Publishers
ISBN: 9788177643169
Category : Geometry, Differential
Languages : en
Pages : 308
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Book Description
Author: Emil de Souza Sánchez Filho
Publisher: Springer
ISBN: 331931520X
Category : Technology & Engineering
Languages : en
Pages : 370
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Book Description
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: Paul Renteln
Publisher: Cambridge University Press
ISBN: 1107042194
Category : Mathematics
Languages : en
Pages : 343
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Book Description
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author: Alain Bretto
Publisher: Springer Science & Business Media
ISBN: 3319000802
Category : Mathematics
Languages : en
Pages : 129
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Book Description
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.
Author: Ilka Agricola
Publisher: American Mathematical Soc.
ISBN: 0821829513
Category : Mathematics
Languages : en
Pages : 362
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Book Description
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.
