MA8105 Distribusjonsteori og Sobolevrom med anvendelser
Lecturer: Helge Holden Email: holden [at] math [dot] ntnu [dot] no
Textbook: H. Holden: "Tools from the Toolbox. Functional Analysis for Partial Differential Equations" (notes will handed out to the students taking the course).
Lectures: (the lectures will be in English)
- Tuesday 8:15-10:00, room 734, Sentralbygg 2
- Thursday 10:15-12:00, room 734, Sentralbygg 2
- (Back up times: Monday 14:15-16 and Friday 14:15-16)
Plan for lectures:
- Tue, Jan 15: pages 5-8
- Thu, Jan 17: pages 9-10, Exercise 4
- Tue, Jan 22: pages 11-13
- Thu, Jan 24: pages 14-17
- Tue, Jan 29: pages 18-20
- Thu, Jan 31: pages 21-23. Pages from Brezis: "Functional Analysis, Sobolev Spaces and Partial Differential Equations", p. 136-7
- Tue, Feb 5: pages 24-25, 35-36
- Thu, Feb 7: pages 36-40
- Tue, Feb 12: pages 40-43, Exercises 5,7
- Thu, Feb 14: pages 43-45
- Tue, Feb 19: pages 45-49
- Thu, Feb 21: pages 51-54, Exercises 4,5
- Tue, Feb 26: pages 54-58
- Thu, Feb 28: pages 59-62
- Tue, March 5: New room: room 822. pages 63-69 (proof of Thm. 4.15 skipped)
- Thu, March 7: pages 69-72, Exercises 10 (Example 4.22), 11 (Example 4.23)
- Tue, March 12: pages 93-95
- Thu, March 14: pages 95-100
- Tue, March 19: pages 100-102
- Thu, March 21: No lecture.
- Thu, April 4: pages 102-104
- Tue, April 9: pages 104-107
- Thu, April 11: pages 107-110
- Tue, April 16: pages 111-113, Exercise
- Thu, April 18: Pages from Larsson and Thomee: "Partial Differential Equations with Numerical Methods", p. 51-55. Exercise: Show equations (5.7) and (5.8).
- Tue, April 23: Exercises
- Thu, April 25: p. 153-157
- Tue, April 30: p. 157-159
Exam: The exam is oral.
Curriculum: pages 1-25, 35-72 (not proof of Thm. 4.15), 93-112, 143-147,161-172. (pages refer to the latest version of the manuscript.)
Regulations concerning the exam:
For the first 20 min the candidate presents a lecture using blackboard only on one of the topics given below. Notes are allowed. It should be a lecture presenting the main parts of the topic, or if the topic is big, a selected part of it. Proofs are encouraged. After that, and for approximately 25 min the candidate will be asked questions about all of the curriculum. Here there will of course be no notes. The topic is decided at the beginning of the exam.
Topics: (A) Sections 2.1-2.2; (B) Ch. 3; (C) Sections 4.1-4.4; (D) Sections 5.1-5.3; (E) Sections 5.4-5.8; (F) Sections 7.5, App. D.