MATH 725 Applied Functional Analysis

Instructor¶

This is a course given by Andreas Buttenschoen at the University of Massachusetts Amherst.

Description¶

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 (and nonlinear functional analysis);

• Calculus of Variations;

• Spectral theory;

• Semigroup theory;

• Applications of functional analysis:

  • Reaction-diffusion equations.

  • Bifurcation theory;

  • Numerical tools (as time permits);

  • Neural-networks;

If you have any topics of interest please let me know. I have already found some texts that nicely connect functional analysis with stochastic theory, so I might be able to do some examples in that direction.

Course Text¶

• Elements of Applied Functional Analysis by Thomas Hillen.

Learning Goals¶

• Learn functional analysis.

• To be confirmed.

Construction Warning¶

These notes are under heavy construction, and for the time being will be sequential.

Mathematical Python resources¶

• Mathematical Python is a great resource to get started with mathematical python.

Course Grading tools¶

• PLOM Grading will be used to grade quizzes and exams.

License¶

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.