# TMA4305 Partial Differential Equations 2018

## Exam

- 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).

## Syllabus / reading list (pensumliste)

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):

- 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)

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

## General information

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.

## Schedule

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>