{"product_id":"tensor-analysis-with-applications-in-mechanics-paperback","title":"Tensor Analysis with Applications in Mechanics - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eLeonid P. Lebedev\u003c\/b\u003e (Author), \u003cb\u003eMichael J. Cloud\u003c\/b\u003e (Author), \u003cb\u003eVictor A. Eremeyev\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e \u003cp\u003eThe 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 \u003cem\u003ecovariant\u003c\/em\u003e and \u003cem\u003econtravariant\u003c\/em\u003e terminology encountered in tensor discussions.\u003c\/p\u003e \u003cp\u003eA 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.\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 380\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.78 x 9 x 6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 20, 2010\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337110765817,"sku":"9789813203648","price":93.96,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/qeF-lL6P3F9789813203648.webp?v=1769675009","url":"https:\/\/bookscloud.io\/products\/tensor-analysis-with-applications-in-mechanics-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}