# MATH 725 (Applied) Functional Analysis

Graduate course, *University of Massachusetts Amherst, Department of Mathematics and Statistics*, 2024

- Course time:
**TBA** - Course text:
**Elements of Applied Functional Analysis**by Thomas Hillen.

## Topics

This is a one-semester introduction to Functional Analysis: I plan to cover most of the chapters in Hillen (as time permits), as well as some uses for functional analysis in Neural Networks, and numerical tools to explore functional analysis.

- Function Spaces;
- Linear Operators and Subspaces;
- Duality;
- Sobolev Spaces and Distributions;
- Calculus: Integration and Differentiation;
- Fixed Point Theorems;
- Calculus of Variations;
- Spectral theory;
- Semigroup theory;
- Applications of functional analysis:
- Reaction-diffusion equations.
- Bifurcation theory;
- Numerical tools (as time permits);
- Neural-networks;