Search Results for Wish - Narrowed by: Cloud, Michael J.

Tensor analysis with applications in mechanics [electronic resource] / Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev.

2024-05-18T06:10:25Z

by Lebedev, L. P.
Call Number 515.63 22
Publication Date 2010
Summary "The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems - most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book"--Provided by publisher.
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The calculus of variations and functional analysis [electronic resource] : with optimal control and applications in mechanics / Leonid P. Lebedev, Michael J. Cloud.

2024-05-18T06:10:25Z

by Lebedev, L. P.
Call Number 515.64 23
Publication Date 2003
Summary This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "the calculus of variations") and more modern topics (under the heading of "optimal control"). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.
Format: Electronic Resources
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Advanced engineering analysis [electronic resource] : the calculus of variations and functional analysis with applications in mechanics / Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev.

2024-05-18T06:10:25Z

by Lebedev, L. P.
Call Number 621
Publication Date 2012
Summary Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study.
Format: Electronic Resources
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