Applications of Functional Analysis and Operator Theory

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

Key Features

- Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
- Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
- Introduces each new topic with a clear, concise explanation.
- Includes numerous examples linking fundamental principles with applications.
- Solidifies the reader’s understanding with numerous end-of-chapter problems.

· Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
· Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
· Introduces each new topic with a clear, concise explanation.
· Includes numerous examples linking fundamental principles with applications.
· Solidifies the reader's understanding with numerous end-of-chapter problems.

1. Banach Spaces
2. Lebesgue Integration and the Lp Spaces
3. Foundations of Linear Operator Theory
4. Introduction to Nonlinear Operators
5. Compact Sets in Banach Spaces
6. The Adjoint Operator
7. Linear Compact Operators
8. Nonlinear Compact Operators and Monotonicity
9. The Spectral Theorem
10. Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations
11. Linear Elliptic Partial Differential Equations
12. The Finite Element Method
13. Introduction to Degree Theory
14. Bifurcation Theory