Vector Spaces, Matrices and Tensors in Physics PDF Download
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Author: M. C. Jain
Publisher:
ISBN: 9781783323760
Category : Technology & Engineering
Languages : en
Pages : 284
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Book Description
Vector spaces, matrices, and tensors in physics form an essential part of the mathematical background required by physicists. This book is written primarily as textbook for undergraduate and postgraduate students and as a reference book for working physicists. Special emphasis is given to topics relevant to physics, for example linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors, diagonalization of matrices, expressing various physical quantities as tensors, tensorial formulation of vector algebra, calculus and geometry. The role of orthogonal, hermitian and unitary matrices in physics is highlighted.
Author: M. C. Jain
Publisher:
ISBN: 9781783323760
Category : Technology & Engineering
Languages : en
Pages : 284
Get Book Here
Book Description
Vector spaces, matrices, and tensors in physics form an essential part of the mathematical background required by physicists. This book is written primarily as textbook for undergraduate and postgraduate students and as a reference book for working physicists. Special emphasis is given to topics relevant to physics, for example linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors, diagonalization of matrices, expressing various physical quantities as tensors, tensorial formulation of vector algebra, calculus and geometry. The role of orthogonal, hermitian and unitary matrices in physics is highlighted.
Author: Sharma
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120338669
Category : Science
Languages : en
Pages : 498
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Book Description
They have wide applications in a number of subjects ranging from solid state physics, solid/fluid mechanics to relativity and electromagnetics. This well-written book gives, in an easy-to-read style, a step-by-step and comprehensive understanding about the various concepts, theories and applications of vector spaces, matrices and tensors. The book equips the reader with the fundamental knowledge in such subjects as matrix theory, linear algebraic equations, applications of eigenvalues and eigenvectors, diagonalisation process, quadratic forms, Cartesian tensors and more.
Author: Dwight E. Neuenschwander
Publisher: JHU Press
ISBN: 142141564X
Category : Mathematics
Languages : en
Pages : 244
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Book Description
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"
Author: A. W. Joshi
Publisher:
ISBN: 9780852264386
Category : Calculus of tensors
Languages : en
Pages : 289
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Book Description
Author: M. C. Jain
Publisher: CRC Press
ISBN: 9780849309786
Category : Mathematics
Languages : en
Pages : 184
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Book Description
The theory of vector spaces and matrices is an essential part of the mathematical background required by physicists. Most books on the subject, however, do not adequately meet the requirements of physics courses-they tend to be either highly mathematical or too elementary. Books that focus on mathematical theory may render the subject too dry to hold the interest of physics students, while books that are more elementary tend to neglect some topics that are vital in the development of physical theories. In particular, there is often very little discussion of vector spaces, and many books introduce matrices merely as a computational tool. Vector Spaces and Matrices in Physics fills the gap between the elementary and the heavily mathematical treatments of the subject with an approach and presentation ideal for graduate-level physics students. After building a foundation in vector spaces and matrix algebra, the author takes care to emphasize the role of matrices as representations of linear transformations on vector spaces, a concept of matrix theory that is essential for a proper understanding of quantum mechanics. He includes numerous solved and unsolved problems, and enough hints for the unsolved problems to make the book self-sufficient. Developed through many years of lecture notes, Vector Spaces and Matrices in Physics was written primarily as a graduate and post-graduate textbook and as a reference for physicists. Its clear presentation and concise but thorough coverage, however, make it useful for engineers, chemists, economists, and anyone who needs a background in matrices for application in other areas.
Author: Hongyu Guo
Publisher: World Scientific
ISBN: 9811241031
Category : Mathematics
Languages : en
Pages : 246
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Book Description
Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.
Author: James Kenyon Knowles
Publisher: Oxford University Press on Demand
ISBN: 9780195112542
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Linear Vector Spaces and Cartesian Tensors is primarily concerned with the theory of finite dimensional Euclidian spaces. It makes a careful distinction between real and complex spaces, with an emphasis on real spaces, and focuses on those elements of the theory that are especially important in applications to continuum mechanics. The geometric content of the theory and the distinction between matrices and tensors are emphasized, and absolute- and component-notation are both employed. While the mathematics is rigorous, the style is casual. Chapter 1 deals with the basic notion of a linear vector space; many examples of such spaces are given, including infinite-dimensional ones. The idea of a linear transformation of a vector space into itself is introduced and explored in Chapter 2. Chapter 3 deals with linear transformations on finite dimensional real Euclidean spaces (i.e., Cartesian tensors), focusing on symmetric tensors, orthogonal tensors, and the interaction of both in the kinetically important polar decomposition theorem. Chapter 4 exploits the ideas introduced in the first three chapters in order to construct the theory of tensors of rank four, which are important in continuum mechanics. Finally, Chapter 5 concentrates on applications of the earlier material to the kinematics of continua, to the notion of isotropic materials, to the concept of scalar invariant functions of tensors, and to linear dynamical systems. Exercises and problems of varying degrees of difficulty are included at the end of each chapter. Two appendices further enhance the text: the first is a short list of mathematical results that students should already be familiar with, and the second contains worked out solutions to almost all of the problems. Offering many unusual examples and applications, Linear Vector Spaces and Cartesian Tensors serves as an excellent text for advanced undergraduate or first year graduate courses in engineering mathematics and mechanics. Its clear writing style also makes this work useful as a self-study guide.
Author: William Byers
Publisher: Princeton University Press
ISBN: 0691145997
Category : Mathematics
Languages : en
Pages : 424
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Book Description
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 0486131904
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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.
Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 0486139239
Category : Mathematics
Languages : en
Pages : 290
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Book Description
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
