Anastasios Matzavinos

Course Description

Math 520 is a continuation of Math 519. Topics include linear operator theory, spectral theory of differential and integral operators, Green's functions and boundary value problems, weak solutions of partial differential equations, variational methods, and calculus in Banach spaces.

The ISU course catalog description for this course (including course requirements)  can be found here.

References

Grading Policy

The final grade will be based on homework assignments, a midterm exam (see below for dates) and one final exam, and it will be determined as follows:

Homework assignments Midterm Exam Final Exam

40% 30% 30%

Homework Assignments

Homework problems will be handed out by the instructor on a regular basis. Discussion of homework assignments with other students is encouraged, but what is handed in should be your own work. You are strongly encouraged to ask the instructor to go over those exercises that you find difficult.

The homework assignments and due dates are posted here.

Important Dates

Midterm exam Final Exam

Monday, March 1 TBA

Announcements box:

WEDNESDAY, APRIL 21: The fifth homework assignment has been posted online. MONDAY, MARCH 8: The fourth homework assignment has been posted online. MONDAY, MARCH 1: The midterm exam will be held this Monday. FRIDAY, FEBRUARY 26: We discussed specific examples of compact operator equations, and we introduced variational principles for the spectrum of compact self-adjoint operators. WED, FEB 17 - WED, FEB 24: We proved a sequence of lemmas and theorems that led us to a complete characterization of the spectrum of compact operators on Hilbert spaces. FRI, FEB 12 - MON FEB 15: We defined weak convergence in Hilbert spaces and proved a number of related properties. We introduced the Banach-Alaoglu theorem. FRIDAY, FEBRUARY 12: The third homework assignment has been posted online. MON, FEB 8 - WED, FEB 10: We focused on the spectral properties of self-adjoint and unitary operators. We also introduced the notion of a compact operator (section 9.3). FRIDAY, FEBRUARY 5: We discussed bounded perturbations of densely defined operators and proved that the spectrum of a bounded operator is compact. FRI, JAN 29 - WED, FEB 3: We defined the resolvent and spectrum of a densely defined operator and introduced the notions of strong and uniform convergence of operators. MONDAY, FEBRUARY 1: The second homework assignment has been posted online. MON, JAN 25 - WED, JAN 27: We defined closed linear operators, and we introduced the adjoint of a densely defined unbounded operator (section 10.1 of the text). MONDAY, JANUARY 25: The first homework assignment has been posted online. WED, JAN 20 - FRI, JAN 22: We proved various properties of the adjoint of a bounded operator. We defined Fredholm operators and proved the Fredholm alternative theorem. FRIDAY, JANUARY 15: We proved the existence of the adjoint of a bounded linear operator, and we discussed briefly the solvability of operator equations. MON, JAN 11 - WED, JAN 13: We focused on examples of linear bounded operators in Hilbert spaces, and we proved that Hilbert-Schmidt integral operators are bounded. MONDAY, JANUARY 11: Classes begin.

Disability Resources

Iowa State University complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act. If you have a disability and require accommodations, please contact the instructor early in the semester so that your learning needs may be appropriately met. You should contact the Disability Resources office for information on appropriate policies and procedures. The Disability Resources office is located on the main floor of the Student Services Building, Room 1076; their phone is 515-294-6624.