Linear Vector Spaces and Cartesian Tensors by Knowles (English) Hardcover Book

Description: Linear Vector Spaces and Cartesian Tensors by Knowles 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher 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- 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. Author Biography Professor James K. Knowles is the William R. Kenan, Jr. Professor of Applied Mechanics. He received his Ph.D. from the Massachusetts Institute of Technology, D.Sc.h.c., National University of Ireland, and has received the following awards: Goodwin Medal for Effective Teaching, MIT (1955), Award of the Associated Students of Caltech for Excellence in Teaching (1984, 1985), Award of the Caltech Graduate Student Council for Exceptional Teaching (1993); Fellow, American Academy of Mechanics; Fellow, American Society of Mechanical Engineers; President of the American Academy of Mechanics, 1985-86; Table of Contents 1: Linear Vector Spaces2: Linear Transformations3: Finite Dimensional Euclidean Spaces and Cartesian Tensors4: Four-Tensors5: ApplicationsAppendix A: BackgroundAppendix B: Solutions for Selected Problems Long 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- 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 itselfis 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 onapplications 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. Twoappendices 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 usefulas a self-study guide. Review Text 1. Linear Vector Spaces 2. Linear Transformations 3. Finite Dimensional Euclidean Spaces and Cartesian Tensors 4. Four-Tensors 5. Applications Appendix A. Background Appendix B. Solutions for Selected Problems Feature Careful distinction between real and complex spaces, with emphasis on the real case.Careful distinction between matrices and tensors, between basis-independent and basis-dependent results, and between absolute- and component-notation.Emphasis on the geometric content of the theory.Many unusual examples and applications.Written in such a way as to facilitate self-study. Details ISBN0195112547 Short Title LINEAR VECTOR SPACES & CARTESI Language English ISBN-10 0195112547 ISBN-13 9780195112542 Media Book Format Hardcover DEWEY 512.52 Year 1997 Country of Publication United States Illustrations line drawings Imprint Oxford University Press Inc Place of Publication New York Pages 128 AU Release Date 1997-09-25 NZ Release Date 1997-09-25 US Release Date 1997-09-25 UK Release Date 1997-09-25 Author Knowles Publisher Oxford University Press Inc Publication Date 1997-09-25 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:127216471;

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