A Brief on Tensor Analysis (Undergraduate Texts in Mathematics) - Hardcover

This edition is intended for 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 are introduced in 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 tensor calculus. The physical interpretation and application of vectors and tensors are stressed throughout. The new edition includes more exercises, especially at the end of chapter 4. 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.