Functional Analysis in Applied Mathematics and Engineering

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:

3. rudimentary topology
4. Banach's fixed point theorem with applications
5. L^p-spaces
6. density theorems for testfunctions
7. infinite dimensional spaces
8. bounded linear operators
9. Fourier series
10. open mapping and closed graph theorems
11. compact and differential operators
12. Hilbert-Schmidt operators
13. Volterra equations
14. Sobolev spaces
15. control theory and variational analysis
16. Hilbert Uniqueness Method
17. boundary 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.