Introduction to continuum mechanics: an incursion into computational mechanics self-study

This work is part of a series on self-study. The series of self-study aims to teach programming, mathematical analysis, continuum mechanics, and numerical methods for boundary value problems to a wide range of students, from an undergraduate background to the graduate student, as a supplementary material. The main objective is to allow the reader to teach him or herself with little to no external help. This objective is framed by the use of analogies and a conversational prose, as well as a stronger basis on mathematics. 

We believe that undergraduate courses on mechanical engineering lack disciplines on continuum mechanics, which, in turn, hinders the analytical ability of students to tackle real-world problems. Numerical methods, such as the finite element method are widely available through commercial softwares, such as \textit{Ansys} and \textit{Nastran}. Nonetheless, the understanding of the users is too little to critically analyze numerical results. This undesirable reality might even pose risk to the practice of engineering and design activities.

Given this context, we aim to introduce the reader to the underlying principles that govern physics and numerical analysis.  We attempt to present each and every concept as amenable as possible, without losing physical and mathematical precision. The next text of the series will be dedicated to introduce the finite element method as means to approximate solutions to boundary value problems stemming from the physical principles here defined.

Mathematical derivations were reordered (when compared to classical literature) to highlight the style of this series---mathematics are fundamental tools to understanding the underlying physics, hence it must be seen alongside physics; not apart from it. Exercises and challenges are proposed throughout and sprinkled around the text. Therefore, the reader might test his or her skills as he or she progresses over the text.