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 ...
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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.
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Add this copy of Linear Vector Spaces and Cartesian Tensors to cart. $7.92, very good condition, Sold by ThriftBooks-Baltimore rated 4.0 out of 5 stars, ships from Halethorpe, MD, UNITED STATES, published 1997 by Oxford University Press, USA.
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Fine. 0195112547. First edition (same 1998 date on title and copyright pages with no additional printings listed); first printing (all numbers present). Original laminated boards, 6 ¼ x 9 ½ inches, index, viii + 120 pp. Hardcover, fine. Previous owner's name and address rubber stamped on title page, otherwise tight, clean, paper crisp, unmarked and apparently never read. Mathematics; geometry; 128 pages.
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Good. Name stamped on book edge. Ships from UK in 48 hours or less (usually same day). Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Shows some signs of wear but in good overall condition. 100% money back guarantee. We are a world class secondhand bookstore based in Hertfordshire, United Kingdom and specialize in high quality textbooks across an enormous variety of subjects. We aim to provide a vast range of textbooks, rare and collectible books at a great price. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions. We provide a 100% money back guarantee and are dedicated to providing our customers with the highest standards of service in the bookselling industry.
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