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**

A vector 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 , , and

which have the same direction at all points in space (Fig.~??.

In such basis the components of are: