Functional analysis is the study of infinite-dimensional vector spaces equipped with extra structure. Such spaces arise naturally as spaces of functions. As well as being a beautiful subject in its own right,
functional-analysis has numerous applications in other areas of both pure and applied mathematics, including Fourier analysis, the study of the solutions of certain differential equations, stochastic processes, quantum physics, ordinary and partial differential equations,
numerical analysis, calculus of variations, approximation theory, integral equations, optimization and approximation theory and much more. Apart from an introductory chapter, where we review basic concepts used in functional analysis, the module develops the theory of metric spaces, normed spaces, Hilbert spaces, linear operators, and linear functionals. The module will deal with these topics at a basic level appropriate for undergraduates students in Applied Mathematics.