TMA4305 Partial Differential Equations 2018

• Here is a link to the official examination information. Quick summary: The exam is at 09:00 on Tuesday 11 December. The location is published three days earlier. That would normally be three workdays, which would hopefully be on Thursday, 6 December. (If not, try again on Friday.) My understanding is that you need to look in your “studweb” page to find out where you'll be. But as I have no access to studweb, I am not too sure about it.
• The written exam is given in English Only. You may answer it in English or a Scandinavian language, or a mixture thereof. Although I really would like Norwegian speaking students to know Norwegian terminology, you will not be marked down on this exam for not knowing it.
• You may bring to the exam One yellow A4-sized sheet of paper stamped by the Department of Mathematical Sciences. On this sheet you may write whatever is desired. You can get these sheets at the department office on the 7th floor of Sentralbygg 2. Also, a simple calculator is allowed, as specified in the exam regulations (though I really don't know what you would use it for, in this course).

From Borthwick's book (see further below for bibliographic detail) – but note that the introductory sections on model problems for the various equations are for information only; you are not expected to have detailed knowledge of these models or how they are derived.

This is the final syllabus.

• Ch 1 (self study)
• Ch 2 (background material for much of the book)
• Ch 3
• Ch 4
• Ch 6
• Ch 7 background material, no proofs
• Ch 9
• Ch 10
• Ch 11 (but only the first half of 11.7)
• Ch 12

And these notes (which may be updated and/or supplemented with more notes):

• On first-order quasilinear equations (A5 for the screen, A4 for printing; updated 2018-08-27)
• The energy method for wave equations. (A5 for the screen, A4 for printing); updated 2018-11-20
  (misprint in the second displayed formula on p. 1: \(u_tu_tt\) should be \(u_tu_{tt}\))
• Weak maximum principle for the heat equation (A5 for the screen, A4 for printing); updated 2018-09-17)
• Harmonicfunctionology (A5 for the screen, A4 for printing); updated 2018-10-02)
• Boundary traces (A5 for the screen, A4 for printing); new 2018-10-21

Note that there is quite a bit of overlap between the notes and the textbook.

General course information / Generell kursinformasjon (course description, schedule, exam)

The lecturer for this term is Harald Hanche-Olsen.

The course will be taught in English, assuming at least one student requires it (which is quite likely). I will try to provide some guidance to proper Norwegian mathematics terminology, however, since there seems to be a lot of confusion about it. My current pet peeve: The Norwegian for bounded is begrenset, not “bundet”. And a set is called en mengde in Norwegian, not “et sett”. Enough for now.

The textbook is David Borthwick: Introduction to partial differential equations.

• Errata list from the author's home page.
• Note that you can get the PDF from Springerlink (you must be inside the NTNU network, either physically or via VPN, to get it).

I will supplement this book with a few notes and material from other sources.

Some other good PDE books include:

• Michael Shearer and Rachel Levy: Partial differential equations. Used as a textbook in 2016; fairly elementary, but quite insightful
• Peter Olver: Introduction to partial differential equations. Used as a textbook previously; available on Springerlink
• L. C. Evans: Partial differential equations. Widely used textbook, advanced
• Fritz John: Partial differential equations. Used for this course in the distant past, advanced; available on Springerlink.

I may use Blackboard for announcements, especially in case of cancelled lectures (heaven forbid!) or other information that does not need to be visible to the entire world.

The first lecture is on Tuesday, 21 August.

The first exercise session is on Friday, 31 August (i.e., the second week of the term).

<schedule> <daytitles>Monday|Tuesday|Wednesday|Thursday|Friday</daytitles> <timeslots>09:15–10:00|10:15–12:00|12:15–14:00</timeslots> <entry day:Tu start:2 color:innsida1>Lecture
R73</entry> <entry day:Th start:1 color:innsida1>Lecture
K26</entry> <entry day:Fr start:0 color:innsida2>Exercices
R60</entry> </schedule>

The rooms, in Mazemap: R73 · K26 · R60