The aim of this chapter is to give the reader the necessary mathematical tool for the study
of electromagnetism..
Differential operators applied to scalar functions or vector functions in Cartesian, cylindrical
and spherical coordinates will be introduced. These operators allow the description of physical
concept in a condensed manner and are usable in other physics fields such as mechanics, fluid mechanics,
plasma physics, etc.
Vectors and scalars
\bullet A vector \mathbf{v} is a quantity which has both a direction and a magnitude. It is
often represented as a directed line segment. Physical quantities, such as a velocity and a force, are
vectors. Vectors can be decomposed into components in a given \emph{basis} which is formed, in three dimension by any three
non coplanar vectors. A useful basis is the Cartesian basis which consists of three mutually
orthogonal elementary vectors of unit length \mathbf{\hat{\boldsymbol{\imath}}}, \mathbf{\hat{\boldsymbol{\jmath}}}, and \mathbf{\hat{k}}
which have the same direction at all points in space (Fig.~??.
In such basis the components of \mathbf{v} are: