# TMA4305 Partial Differential Equations 2019

(General information moved down to make room for exam and syllabus info.)

## Exam

- Here is a link to the official examination information. Quick summary: The exam is at 15:00 on Wednesda 4 December. The exact location is published three days earlier. That would normally be three
*workdays*, which would hopefully be on Friday, 30 November. (If not, try again on Monday.) 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 don't know anything 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

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.

- 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 §11.7 only up to and including Theorem 11.11)
- Ch 12

Additionally, these notes:

- Collisions of characteristics (A5 for the screen, A4 for printing
- On the energy method for wave equations (A5 for the screen, A4 for printing

These notes may be thought of as an alternative to, and expansion of, §4.7) - Weak maximum principle for the heat equation (A5 for the screen, A4 for printing)

These notes are an alternative to §9.5 - Harmonicfunctionology (A5 for the screen, A4 for printing)

These notes are related to §§9.1–9.4.

Lebesgue's example, in small print at the end of the note, is not required reading. - Boundary traces.</color> (A5 for the screen, A4 for printing)
- Compactness in Banach spaces

*Cursory*, background knowledge. Handwritten note meant to cover a possible gap in students' background knowledge .

Note that there is quite a bit of overlap between the notes and the book. Sometimes, I just wanted to present the material in a different way. Other times, the notes contain material that is not in the book.

One major change from last year: We drop treatment of the general quasilinear equation \(a(t,x,u)u_x+b(t,x,u)u_y=c(t,x,u)\). This topic was covered by a note, not in the book.

## General information

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

Correction made 2019-10-10: The above links now point to the information for the *current* year. Until now, it pointed to the previous year's information. (Blame copy/paste syndrome.) In particular, note that this year's exam is on 4 December, in the afternoon.

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.