Introduction to the Variational Formulation in Mechanics

Part IVector and Tensor Algebra and Analysis

The goal of the following two chapters, which comprise Part I of this book, is to provide the reader with the basic concepts and training in the area of tensor algebra (Chapter 1) and tensor analysis (Chapter 2) which will be omnipresent throughout this book. It is important to highlight here the use of compact notation (also called intrinsic notation) when invoking vector and tensors as well as algebraic and differential operations among them. That is, vectors and tensors are written independently from the adopted coordinate system. In contrast to the use of indicial notation, which puts in evidence the components of vectors and tensors in the given coordinate system, the compact notation appears as a clean and elegant form that allows the concepts to be presented without being obnubilated by the sometimes overwhelming presence of indexes.

At the end of these two chapters, some further reading material is suggested to complement and deepen the concepts presented here. However, we highlight that for the study of the rest of the book this reading is not mandatory. Moreover, the reader will also find in Appendices A and B a more detailed exposition of the topics addressed in what follows, in an attempt to make the book self‐contained.