Funktionalanalysis, Wintersemester 2020-21, HU Berlin

Funktionalanalysis, Wintersemester 2020-21

Inhaltsbeschreibung / course description and syllabus

Moodle: https://moodle.hu-berlin.de/course/view.php?id=99581
WICHTIG: Die Lehrveranstaltung findet online per Zoom statt, und Sie müssen sich beim Moodle-Kurs anmelden, um die Zugangsdaten für die Zoom-Meetings zu erhalten. HU-Angehörige haben mit ihrem HU-Benutzernamen und Passwort automatisch Zugang zum Moodle. Nicht HU-Angehörige haben Zugang, indem sie auf den Link oben klicken und dann ein HU-Moodle-Konto erstellen mit der externen Mailadresse als Benutzername. Es gibt neuerdings einen Einschreibeschlüssel für den Moodle-Kurs; wer noch nicht eingeschrieben ist, kann mir per E-mail nach dem Einschreibeschlüssel fragen.
IMPORTANT: The course will be conducted online via Zoom, and you will need to join the moodle for the course in order to obtain the Zoom links for online lectures. HU students can access moodle using their HU username and password. Non-HU users can access it by following the above link and then setting up a HU Moodle Account with their external e-mail address as a username. There is now an enrolment key for the moodle; if you haven't joined yet, you can e-mail me to ask for the key.

Lecture notes on L^p spaces etc. (last update: 11.11.20221)
These notes concern topics mainly from weeks 4 through 9 of the semester.

Lecture notes on Fredholm operators (uploaded 27.01.2021, last update 11.02 at 11:40)
These are typed notes for the contents of Lectures 22 and 23 (which are not covered in Reed and Simon). They have now been revised to correct some errors in the discussion of the Laplace operator in the original version.

Whiteboard notes:
Week 1: Lecture 1 (3.11.2020) Lecture 2 (5.11.2020) Problem session 1 (5.11.2020)
Week 2: Lecture 3 (10.11.2020) Lecture 4 (12.11.2020) Problem session 2 (12.11.2020)
Week 3: Lecture 5 (17.11.2020) Lecture 6 (19.11.2020) Problem session 3 (19.11.2020)
Week 4: Lecture 7 (24.11.2020) Lecture 8 (26.11.2020) Problem session 4 (26.11.2020)
Week 5: Lecture 9 (1.12.2020) Lecture 10 (3.12.2020) Problem session 5 (3.12.2020)
Week 6: Lecture 11 (8.12.2020) Lecture 12 (10.12.2020) Problem session 6 (10.12.2020)
Week 7: Lecture 13 (15.12.2020) Lecture 14 (17.12.2020) Problem session 7 (17.12.2020)
Week 8: Lecture 15 (5.01.2021) Lecture 16 (7.01.2021) Problem session 8 (7.01.2021)
Week 9: Lecture 17 (12.01.2021) Lecture 18 (14.01.2021) Problem session 9 (14.01.2021)
Week 10: Lecture 19 (19.01.2021) Lecture 20 (21.01.2021) Problem session 10 (21.01.2021)
Week 11: Lecture 21 (26.01.2021) Lecture 22 (28.01.2021)
Week 12: Lecture 23 (2.02.2021) Lecture 24 (4.02.2021) Problem session 12 (4.02.2021) (includes take-home midterm solutions!)
Week 13: Lecture 25 (9.02.2021) Lecture 26 (11.02.2021) Problem session 13 (11.02.2021)
Week 14: Lecture 27 (16.02.2021) Lecture 28 (18.02.2021) Problem session 14 (18.02.2021)
Week 15: Lecture 29 (23.02.2021) Lecture 30 (25.02.2021) Problem session 15 (25.02.2021) (includes nearly complete solutions for Problem Set 12)

Ankündigungen / Announcements

17.12.2020: The two dates for the final exam in this course have now been fixed. They are:
- Wednesday, 3.03.2021 from 9:00 to 12:00
- Friday, 9.04.2021 from 9:00 to 12:00
For both dates, the exam will be a take-home exam that is made available via the moodle at 9:00 sharp, with 12:30 as the deadline for uploading solutions. (The extra half-hour is added as a buffer in case of technical problems.) The exam problems will be conceived to be doable within two hours, so time pressure should not be a major factor. The deadline to register with the Prüfungsbüro is (as usual) 14 days ahead of the exam. For information on administrative matters such as how to register, here is the webpage of the Prüfungsbüro Mathematik.

previous announcements (no longer relevant)

Übungsblätter / Problem sets

Problem sets will normally be posted in this spot every Thursday and can be submitted via the moodle until 15:15 on the following Thursday; solutions will then be discussed in the Übung. (See the moodle for more on the technical details of how to submit solutions.) You are welcome to work on the problems in groups, but must write up solutions (in German or English) individually -- group submissions are not accepted.

The corrected submissions are posted on the moodle about a week after the due date. Questions about the grading can be directed to the grader, Laurenz Upmeier zu Belzen (upmeibel at mathematik dot hu dash berlin dot de).

Probelm Set 1 (due 12.11.2020)
Problem Set 2 (due 19.11.2020)
Problem Set 3 (due 26.11.2020)
Problem Set 4 (due 3.12.2020)
Problem Set 5 (due 10.12.2020)
Problem Set 6 (due 17.12.2020)
Problem Set 7 (due 7.01.2021)
Problem Set 8 (due 14.01.2021)
Problem Set 9 (due 21.01.2021)
Take-Home Midterm (due 4.02.2021)
Problem Set 10 (due 11.02.2021)
Problem Set 11 (due 18.02.2021)
Problem Set 12 (due 25.02.2021)

Exam info (NEW)

Here is some advice for the final exam.
Important: The document behind that link gives the details of a new moodle page, separate from the usual moodle page for this course, which you must enrol in if you are taking the exam. Please do so as soon as possible.