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Sinopsis
Designed for a first year graduate course in Mechanics, this text brings together never before collected works on linear vector spaces, on which the author is a world renowned authority. It is primarily concerned with finite dimensional real Euclidean spaces, with Cartesian tensors viewed as linear transformations of such a space into itself, and with applications of these notions, especially in mechanics. The geometric content of the theory and the distinction between matrices and tensors are emphasized, and absolute- and component- notation are both employed. Problems and solutions are included.
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Designed for a first year graduate course in Mechanics, this text brings together never before collected works on linear vector spaces, on which the author is a world renowned authority. It is primarily concerned with finite dimensional real Euclidean spaces, with Cartesian tensors viewed as linear transformations of such a space into itself, and with applications of these notions, especially in mechanics. The geometric content of the theory and the distinction between matrices and tensors are emphasized, and absolute- and component- notation are both employed. Problems and solutions are included.
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Linear Vector Spaces and Cartesian Tensors
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Oxford University Press, 1997
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ISBN 13: 9780195112542
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Linear Vector Spaces and Cartesian Tensors
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Oxford University Press, New York, 1998
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Linear Vector Spaces and Cartesian Tensors
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Linear Vector Spaces and Cartesian Tensors
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Oxford University Press, 1997
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Linear Vector Spaces and Cartesian Tensors
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Linear Vector Spaces and Cartesian Tensors
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Hardcover. Condición: new. Hardcover. 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- andcomponent-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 oftensors 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 isotropicmaterials, 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 Spacesand 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 usefulas a self-study guide. This text brings together works on Linear Vector Spaces. It is primarily concerned with finite dimensional real Euclidean spaces, with Cartesian tensors viewed as linear transformations of such a space into itself, and with applications of these notions, especially in mechanics. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Nº de ref. del artículo: 9780195112542
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