Introduction to Functional Analysis with Applications

As science and technology are increasingly refined and interrelated, the demand for mathematical concepts beyond vector algebra and differential and integral calculus has greatly increased. There are four fundamental theorems dealing with properties of functionals and operators called Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem and Closed graph theorem. Notions of differentiability and integrability of operators are also studied in functional analysis. Applications of functional analysis to operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control and wavelets are all discussed at length, reflecting current trends in the study of functional analysis. This book introduces the above concepts in a way accessible to readers having minimum possible prerequisite of undergraduate mathematics.