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Functional analysis in applied mathematics and engineering / Michael Pedersen.

By: Material type: TextTextSeries: Studies in advanced mathematicsPublication details: Boca Raton, Fla : Chapman & Hall/CRC Press, c2000.Description: 298 p. : ill. ; 24 cmISBN:
  • 9780367399412
Subject(s): DDC classification:
  • 515.7 21 PED
LOC classification:
  • QA320 .P394 2000
Online resources:
Contents:
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
Summary: 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 topology Banach's fixed point theorem with applications L^p-spaces density theorems for testfunctions infinite dimensional spaces bounded linear operators Fourier series open mapping and closed graph theorems compact and differential operators Hilbert-Schmidt operators Volterra equations Sobolev spaces control theory and variational analysis Hilbert Uniqueness Method boundary element methods 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.
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Item type Current library Collection Call number Status Date due Barcode
Project book Project book CUTN Central Library Sciences Non-fiction 515.7 PED (Browse shelf(Opens below)) Checked out to Renuka Devi V (20019T) 31/01/2024 48830

Includes bibliographical references (p. 291-293) and index.

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

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 topology
Banach's fixed point theorem with applications
L^p-spaces
density theorems for testfunctions
infinite dimensional spaces
bounded linear operators
Fourier series
open mapping and closed graph theorems
compact and differential operators
Hilbert-Schmidt operators
Volterra equations
Sobolev spaces
control theory and variational analysis
Hilbert Uniqueness Method
boundary element methods

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.

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