Spring 2024 - APMA 905 G100
Applied Functional Analysis (4)
Class Number: 3954
Delivery Method: In Person
Infinite dimensional vector spaces, convergence, generalized Fourier series. Operator Theory; the Fredholm alternative. Application to integral equations and Sturm-Liouville systems. Spectral theory.
In this course we will cover topics in functional analysis that are useful tools for PDE analysis and numerical analysis. After a quick review of metric spaces and normed space, we will cover various fixed point theorems and their applications to differential equations. The rest of the course will focus on the theory of Banach spaces, Hilbert spaces, and linear operators.
Prerequisites: A good (advanced undergraduate/beginning graduate) background in linear algebra and real analysis. You should be comfortable with notions of linear spaces, linear independence, eigenvalues/eigenfunctions, and metric spaces. Measure theory and graduate PDE would be useful courses to have had, but are not mandatory prerequisites.
- 10 Assessments 100%
- Final exam (depending on the success of the assignments) 0%
Assessments: There will be 4 hours of lecture, and 1 hour of problem session (for a total of 5 hours of contact time) per week. There will be 10 equally-weighted weekly assignments. Students will present their solutions in the problem sessions, have an opportunity to correct their own work, and the assessment will be based on the oral and written solutions. Note that we may, based on the success of these problem sessions, change the method of assessment to include a final examination.
• Alberto Bressan, Lecture Notes on Functional Analysis with Applications to Linear Partial Differential Equations, AMS, 2013.
• H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer 2011.
• Kreyszig, E., Introductory Functional Analysis with Applications, Wiley & Sons.
• D.H. Griffel, Applied Functional Analysis, Dover 1985.
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html