MATH 725 (Applied) Functional Analysis

• 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;