This new edition is intended for third and fourth year undergraduates in Engineering, Physics, Mathematics, and the Applied Sciences, and can serve as a springboard for further work in Continuum Mechanics or General Relativity. Starting from a basic knowledge of calculus and matrix algebra, together with fundamental ideas from mechanics and geometry, the text gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics. The mathematics of tensor analysis is introduced in well-separated stages: the concept of a tensor as an operator; the representation of a tensor in terms of its Cartesian components; the components of a tensor relative to a general basis, tensor notation, and finally, tensor calculus. The physical interpretation and application of vectors and tensors are stressed throughout. Though concise, the text is written in an informal, non-intimidating style enhanced by worked-out problems and a meaningful variety of exercises. The new edition includes more exercises, especially at the end of chapter IV. Furthermore, the author has appended a section on Differential Geometry, the essential mathematical tool in the study of the 2-dimensional structural shells and 4-dimensional general relativity.
The ideal review for your tensor calculus course More than 40 million students have trusted Schaum´s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum´s Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. * 300 solved problems * Coverage of all course fundamentals * Effective problem-solving techniques * Complements or supplements the major logic textbooks * Supports all the major textbooks for tensor calculus courses
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Tensor Analysis with Applications in Mechanics:
This textbook represents an extensive and easily understood introduction to tensor analysis, which is to be construed here as the generic term for classical tensor analysis and tensor algebra, and which is a requirement in many physics applications and in engineering sciences. The book is primarily directed at students on various engineering study courses. It imparts the required algebraic aids and contains numerous exercises with answers, making it eminently suitable for self study. Dieses Lehrbuch stellt eine umfassende und leicht verständliche Einführung in die Tensoranalysis dar, die hier als Oberbegriff von klassischer Tensoranalysis und Tensoralgebra zu verstehen ist und die in vielen Anwendungen der Physik und der Ingenieurwissenschaften benötigt wird. Es vermittelt die nötigen algebraischen Hilfsmittel und enthält zahlreiche Übungsaufgaben mit Lösungen, so dass es sich auch für ein Selbststudium eignet.
Tensor Analysis and Nonlinear Tensor Functions: Yuriy I. Dimitrienko