ABSTRACT
A vector may be a function of one or more scalars and vectors. There are, for example, many important vectors in mechanics that are functions of time and position variables. A vector field associates a vector to each point, such as the wind velocity or the strength of the electric or magnetic field. Physically and geometrically important concepts in connection with scalar and vector fields are the ‘gradient’, ‘divergence’, ‘curl’ and the corresponding ‘integral theorems’. The directional derivative is a tool that generalises the concept of partial derivative of a function of several variables, by extending it to any direction identified by a vector. Vector differential operations on vector fields are more complicated because of vector nature of both the operator and the field on which it operates. The divergence operator is useful in determining whether there is a source or a well in the space areas where vector fields exist.
