Description
Functional Analysis in Applied Mathematics and Engineering
Studies in Advanced Mathematics Series
Author: Pedersen Michael
Language: EnglishSubjects for Functional Analysis in Applied Mathematics and Engineering:
Keywords
Ordinary Differential Equation; Pure Point Spectrum; banach; Infinite Dimensional Hilbert Spaces; spaces; Banach Space; hilbert; Compact Self-Adjoint Operators; space; Normed Vector Space; cauchy; Volterra Integral Equation; sequence; Hilbert Spaces; orthonormal; Cauchy Sequence; basis; Orthonormal Basis; normed; Orthonormal Sequence; vector; Unbounded Operator; Continuous Linear Mapping; Hilbert Schmidt Operators; Self-adjoint Operator; Fredholm Integral Equation; Linear Operators; Vector Space; Bounded Linear Operators; Sesquilinear Form; Sobolev Spaces; Metric Space; Infinitesimal Generator; Interpolation Spaces; Spectral Theorem
· 15.6x23.4 cm · Paperback
Description
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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:
Functional 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.
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