Linear Functional Analysis

Analyzes the theory of normed linear spaces and of linear mappings between such spaces, providing the necessary foundation for further study in many areas of analysis. Strives to generate an appreciation for the unifying power of the abstract linear-space point of view in surveying the problems of linear algebra, classical analysis, and differential and integral equations.

This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics.

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa­ question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.

Functional analysis studies linear spaces provided with suitable topo- logical structures and (continuous) linear transformations between such spaces. It has far reaching applications in several disciplines. For in- stance, the modern theory of (partial) differential equations and the numerical approximation of their solutions rely a lot on functional ana- lytic techniques. Functional analysis is now an integral part of the curriculum in any post graduate course in Mathematics. Ideally it should be taught after having covered courses in linear algebra, real and complex analysis, and topology.