Functional Analysis in Applied Mathematics and Engineering

Description

Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.This text/reference discusses:rudimentary topologyBanach's fixed point theorem with applicationsL^p-spacesdensity theorems for testfunctionsinfinite dimensional spacesbounded linear operatorsFourier seriesopen mapping and closed graph theoremscompact and differential operatorsHilbert-Schmidt operatorsVolterra equationsSobolev spacescontrol theory and variational analysisHilbert Uniqueness Methodboundary element methodsFunctional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.  Read more... Abstract: Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.This text/reference discusses:rudimentary topologyBanach's fixed point theorem with applicationsL^p-spacesdensity theorems for testfunctionsinfinite dimensional spacesbounded linear operatorsFourier seriesopen mapping and closed graph theoremscompact and differential operatorsHilbert-Schmidt operatorsVolterra equationsSobolev spacescontrol theory and variational analysisHilbert Uniqueness Methodboundary element methodsFunctional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text Content: Topological and Metric Spaces -- Banach Spaces -- Bounded Operators -- Hilbert Spaces -- Operators in Hilbert Space -- Spectral Theory -- Integral Operators -- Semigroups of Evolution -- Sobolev Spaces -- Interpolation Spaces -- Linear Elliptic Operators -- Regularity of Hyperbolic Mixed Problems -- The Hilbert Uniqueness Method -- Exercises -- References.