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Fourier analysis involves rewriting functions of position as functions of frequency. In many situations, the behaviour of a system is much simpler when it is viewed as dependent on frequency rather than position. It is therefore a Good Thing to have the output of the system written in terms of frequency. However, it is often much easier to find the values of that system in terms of position. The techniques of Fourier theory allow us to make the best of both: we can read off the values in terms of position and then use Fourier analysis to rewrite these in terms of frequency.

In this course we shall be studying the mathematical tools and ideas behind Fourier theory.

Lecturer: Andrew Stacey

Teaching Assistant: Jan-Fredrik Olsen

Fourier Analysis and Applications. Gasquet and Witomski, Texts in Applied Mathematics 30. Springer (ISBN 0-387-98485-2).

The final grade will depend entirely on the final exam, which will be held on 12th December, 9am, 4hrs.

There will be regular assignments. Although these do not count directly towards the final grade the best preparation for taking the exam is to do the assignments.

Previous exams with solutions can be found on the old course webpages 2004, 2006, 2005.

Links to official information about this course:

• Description Norsk English
• Final exam dates (scroll down a long way)
• Time plan.

Jan-Fredrik Olsen will have office hours on Wednesday December 3rd from 14:00 - 16:00. His office is 902 (9th floor) in SBII.

More Messages

Note that the homework assignments are not mandatory and will not count towards your final grade. Nevertheless I recommend that you do the homework assignments.

Each week I shall list exercises from the book that I think will help you understand the material. The list may be quite long in which case I do not recommend that you do all of them; rather you should assess (honestly!) which you think are trivial and which you do not immediately see and only write out the latter. A few will be marked with a star, these are ones that I consider particularly useful and may be handed in to get feedback on (though you are welcome to ask about any in the problem sessions).

The deadline for handing in is the Friday lecture of the week after the problems are set. There is now a box for handing in the homeworks on the 3rd floor of Nordre Lavblokk.

1. Homework assignment one; Lessons 3 - 7.

   4.1 *, 4.4, 4.5, 4.6

   5.2, 5.3, 5.6, 5.10, 5.11, 5.12 *, 5.13 *.

2. Homework assignment two; Lessons 8 - 9.

   8.1 *, 8.2, 8.3, 8.4, 8.5 *

3. Homework assignment three: Lessons 11 - 16.

   13.3 (take everything in the real line), 13.6

   Anything from 14 (though I'm unclear as to what the "converse" is in 14.2a). *'d questions: 14.6 and 14.7

   15.2, 15.4, 15.7 *

   16.2 *, 16.6, 16.7

4. Homework assignment four: Lessons 17 - 18.

   17.1, 17.2, 17.3

   18.2, 18.3, 18.4

   I would have set 18.1 but I'm not convinced I understand it. If you can figure out what it is asking, try answering it.

5. Homework assignment five: Lessons 19 & 22.

   19.2, 19.3, 19.5, 19.7 *

   22.1, 22.2, 22.3 *, 22.5 *

   (With apologies for late publication).

6. Homework assignment six: Lessons 20, 21, 23

   20.2, 20.3, 20.6, 20.7 *

   21.1, 21.2, 21.6 *, 21.7

   23.1 *, 23.2, 23.3, 23.4 *, 23.5, 23.6

7. Homework assignment seven: Lessons 24, 25

   24.2, 24.3, 24.4, 24.5 (you will need to read the chapter to understand fully what the questions are asking)

   25.2

8. Homework assignment eight: Lessons 26 - 29

   As we have approached distributions from a different angle in class, you will need to read the lessons for some of the notation and particularly for specific examples of distributions.

   27.1 *, 27.3, 27.4, 27.6

   28.7 *, 28.8 (ignore d for now), 28.9, 28.11 *, 28.12, 28.17

   29.2 *, 29.3, 29.4, 29.8, 29.9

9. Homework assignment nine: Lessons 26 - 31

   28.1, 28.2, 28.3, 28.5, 28.6, 28.8(d)

   30.1 *, 30.2

   31.4, 31.5 *, 31.6, 31.7, 31.9 *, 31.10, 31.11

10. (3rd November). No extra assignments this week - the ones from the previous two assignments are still the most relevant.

11. Homework assignment ten: Lessons 32 - 33

    32.2, 32.3, 32.8 (an inverse of T - if it exists - is S such that S * T = T * S = δ.)

    33.2, 33.3