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#
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.
