ACM 105 Applied Real and Functional Analysis
2023 Winter
type: Graduate course
where: Caltech, CMS
date: 2023 Winter
Instructor
======
Oscar Leong
Course Description
======
Previously ACM 105, this course is now ACM/CMS 107 part b.
Continuation of ACM 107a, developing new material and providing further details on some topics already covered. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.Topics: Review of Banach spaces, Hilbert spaces, Linear Operators, and Duality, Hahn-Banach Theorem, Open Mapping and Closed Graph Theorem, Uniform Boundedness Principle, The Fourier transform (L1, L2, Schwartz space theory), Sobolev spaces (W^s,p, H^s), Sobolev embedding theorem, Trace theorem Spectral Theorem, Compact operators, Ascoli Arzela theorem, Contraction Mapping Principle, with applications to the Implicit Function Theorem and ODEs, Calculus of Variations (differential calculus, existence of extrema, Gamma-convergence, gradient flows) Applications to Inverse Problems (Tikhonov regularization, imaging applications).
Reviews from Students
======
* Dohyeon was very helpful during office hours, I wouldn't have managed to get through the course without her help.
* Doh Yeon is one of the best TAs I have ever encountered. She is really really nice and patient with our questions, always taking time outside the class to answer questions, and provides thoughtful feedback for the homework as well. She subbed for some of the classes, and the contents she prepared was very clear and easy to understand. She is also very open to discussion and are always so kind when we come to her for questions during office hours. Thank you so much for a great term!
where: Caltech, CMS
date: 2023 Winter
Instructor
======
Oscar Leong
Course Description
======
Previously ACM 105, this course is now ACM/CMS 107 part b.
Continuation of ACM 107a, developing new material and providing further details on some topics already covered. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.Topics: Review of Banach spaces, Hilbert spaces, Linear Operators, and Duality, Hahn-Banach Theorem, Open Mapping and Closed Graph Theorem, Uniform Boundedness Principle, The Fourier transform (L1, L2, Schwartz space theory), Sobolev spaces (W^s,p, H^s), Sobolev embedding theorem, Trace theorem Spectral Theorem, Compact operators, Ascoli Arzela theorem, Contraction Mapping Principle, with applications to the Implicit Function Theorem and ODEs, Calculus of Variations (differential calculus, existence of extrema, Gamma-convergence, gradient flows) Applications to Inverse Problems (Tikhonov regularization, imaging applications).
Reviews from Students
======
* Dohyeon was very helpful during office hours, I wouldn't have managed to get through the course without her help.
* Doh Yeon is one of the best TAs I have ever encountered. She is really really nice and patient with our questions, always taking time outside the class to answer questions, and provides thoughtful feedback for the homework as well. She subbed for some of the classes, and the contents she prepared was very clear and easy to understand. She is also very open to discussion and are always so kind when we come to her for questions during office hours. Thank you so much for a great term!