ABSTRACT
Many of the basic problems of applied mathematics share the property of linearity, and linear spaces along with linear operators provide a very generalised framework of the analysis of such problems. In this chapter, the authors dish out a concised account of functional analysis with special reference to differential operators. A common feature of linear subspaces is that they all contain the zero element. The concept of linear maps is associated with only the linear spaces. In theory of differential equations, the differential operator is often required to be approximated by a sequence of operators having simpler form. In such circumstances, it is very useful to consider the limits of convergent sequence of bounded linear operators.
