MA2104 Differensiallikninger og kompleks funksjonsteori 2006

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Contents: Messages · Examinations · Syllabus · Exercises · Lectures

Lecturer:
Harald Hanche-Olsen
Messages (inverse chronological order)
Examinations:
A collection of earlier exam problems, including midterm tests, is available.
Midterm exam: During usual lecture hours: Thursday 26th October 12:15–14:00 in S6. Results.
Final exam: Tuesday 12th December, 09:00–13:00 at Nidarøhallen.
You may bring your HP 30S calculator. A formula sheet (two sheets, actually) will be appended to the exam.
Syllabus:

HH-O: The Cauchy integral theorem. (PDF: A5/A4.) Basically, the note gives a more fundamental definition of the path integral, and a different proof of the Cauchy integral theorem. It gives some proofs in much more detail than I expect you to absorb.

Paul R. Chernoff: Pointwise Convergence of Fourier Series. The American Mathematical Monthly, 87 (1980), 399–400. (The link requires a subscription. NTNU subscribes, so you can get the paper so long as you are within the NTNU computer network. Use the DOWNLOAD link at the top of the page, and select high quality output to get something that looks good when you print it.)

HH-O: The Riemann–Lebesgue lemma. (PDF: A5/A4.) A much simpler proof than the one in the book (on p.~504). We need it for the proof in Chernoff's paper.

HH-O: The classification of isolated singularities. (PDF: A5/A4.) Section 4.6 of the book, in very short form.

Nakhlé H. Asmar: Applied Complex Analysis with Partial Differential Equations (Prentice Hall; ISBN: 0130892394).
Some changes may occur.

Final syllabus:
Chap Read Comments
1 All  
2 1–4  
3 1–7, 9 Skip proofs in 3.5 and 3.9
4 1–6  
5 1–4 except pages 338–342 and 348–351
7 1–5  
8 1–4, 6 except pages 558–560

Note: There was a misprint in the syllabus: I had listed only sections 1–4 for Chapter 7. But don't worry, there will be no need for complex Fourier series on this year's exam. But I reserve the right to ask about it on the spring exam, for those that need to (re)take the exam then.

Exercises
There are no mandatory exercises. If you wish feedback on some of your work, you can hand in your solutions to exercises marked with an asterisk (*), preferably no later than Monday a week and a half after the exercises have been posted. I have arranged for a box on the third floor of «Nordre lavblokk», see separate map. Solutions to the first two exercises will be posted here on Monday, and then one further solution will be posted each Monday henceforth. (Both for problems with and without the asterisk.)
(Week numbers referer to the week when problems are posted.)
Lectures

Harald Hanche-Olsen Oppdatert: 2007–01–11 19:37