Functional Analysis in Applied Mathematics and Engineering / Edition 1

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Overview

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
  • Lp-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.

"...discusses rudimentary topology, Banach's fixed point theorem with applications, L^p spaces, density theorems & much more that will be useful to control engineers in the electrical, mechanical & aerospace fields."

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Editorial Reviews

Booknews
Begins with an introduction to the 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. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780849371691
  • Publisher: Taylor & Francis
  • Publication date: 9/29/1999
  • Series: Studies in Advanced Mathematics Series, #31
  • Edition number: 1
  • Pages: 312
  • Product dimensions: 6.40 (w) x 9.50 (h) x 0.98 (d)

Table of 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

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