Review of vector calculus

Abstract

This chapter sets the ground for the derivation of the conservation equations by providing a brief review of the continuum mechanics tools needed for that purpose while establishing some of the mathematical notations and procedures that will be used throughout the book. The review is by no mean comprehensive and assumes a basic knowledge of the fundamentals of continuum mechanics. A short introduction of the elements of linear algebra including vectors, matrices, tensors, and their practices is given. The chapter ends with an examination of the fundamental theorems of vector calculus, which constitute the elementary building blocks needed for manipulating and solving these conservation equations either analytically or numerically using computational fluid dynamics.