Fourier Series and Integral Transforms. Information for Students

WELCOME TO FOURIER SERIES AND INTEGRAL TRANSFORMS

( OLD PAGE FROM SPRING SEMESTER 2000/01 ) I wish you all a very pleasant and successful semester.
To go to the "official" website of the course, which contains ESSENTIAL INFORMATION including a text book, click here.
To go directly to download or read the text book for this course, written by Allan Pinkus and Sami Zafrani, click here.
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10.10.01 Shalom! The results for Moed Bet (16.9.01) have been officially reported. I am very sorry that it took so long to complete the checking of these examinations. Warm congratulations to the five students who got more than 100. Unfortunately your official marks will only be 100.

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17.9.01 Shana Tova! Here is the Moed Bet examination which was held yesterday. And here is a solution (Version 5, of April 2005, posted on 6.6.2005). The graph that you were asked to draw in question 3 of part 2 is here.
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26.7.01 Here is a detailed solution to the examination of 13.7.01. The graph which you were asked to draw in question 2 is here ("gif" file in colour). The text of the examination itself (compact version to save paper) is here. As Yoram announced, the results of the examination are also available on the web.
Congratulations to those who did well! I hope those who did not will do much better in the future.
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12.7.01 If somehow you did not yet find the solution for Homework exercise No. 2 etc. you can get it here. I am in my office now and plan to be here till approximately 19:00, maybe later.
If I leave the office, e.g. to talk with a group of students, I will put a note on my door saying where you can find us. You can also telephone here (829-4179).
In answer to some of your queries, it is possible that the examination will have both multiple-choice (="American") questions and/or usual ("open") questions. In any case, you need to know the same material and to do the same kind of thinking and calculation to answer both types of questions. So it is a waste of time to worry about these details. Just learn the material. You will need it later too, not just tomorrow!
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12.7.01 The solution to Homework Exercise No. 4 is here. BHATZLAKHA for tomorrow!!
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10.7.01 The examination will be WITHOUT ANY "HOMER EZER". This means also, that you are not allowed to use calculators. As explained below, there will be a list of formulae provided with the examination. Please DO NOT bring your own list. You will not be allowed to use it. Bhatzlakha!!
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2.7.01 The questionnaire of the examination on July 13, (and similarly for Moed bet, 16.9.01) will include the standard list of formulae that has appeared on most recent exams in this subject. The exact list that we will use is here. It is DIFFERENT from the list that appeared in the most recent minibachanim.
If you are looking for old examinations as a source of questions for revision, it should be mentioned that some of these are on the page of the metargel hakhrayi, and some on the main official page of the course. Many are on both sites, but to get absolutely all of them you currently have to visit both of these sites. I will request that both of these sites be updated, to include all examinations, but I do not know when this will be done.
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25.6.01 Here is the fourth set of homework exercises, on Laplace transforms (1 page). It is NOT compulsory to submit these exercises. But they are intended to help you prepare for the examination. The tsiyun magen based on minibachanim/homework will be calculated on the basis of the three earlier minibachanim. For more details about that see the earlier email messages sent to all students on June 8. We will publish a solution of these new set of exercises on 12.7.01. For this reason, if you want to qualify for the (small optional extra 4 point) tsiyun magen, you will have to submit these new exercises before midnight on 11.7.01. They must be put in the special "mailboxes" for this course near the elevators at level 0 of the Amado Building. Please use the box corresponding to the tirgul in which you are registered. (Most of these are in the fourteenth or fifteenth column of boxes.) Please note, this submission date is ONE DAY EARLIER than announced in the message on June 8.
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23.6.01 Here are graphs of three functions mentioned in set no. 3 of homework exercises.
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22.6.01 Here is a detailed solution (12 pages) for set no. 3 of homework exercises.
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21.6.01 Here are the solutions of the three minibachanim which were held this week. Here are the questions that were on those minibachanim.
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15.6.01 In the minibachanim next week we will include a list of formulae for Fourier transforms. You can see that list here. But please DO NOT bring it to the tests. We will provide EXACTLY the same page as part of your question sheets.
Bhatzlakha!!
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8.6.01. Homework assignment number 3 is available from the official Fourier website (the page of the metargel akhrayi) and also from here. The minibachanim based on this assignment will be held during the last week of the semester (June 17-21) Because we are late with the minibachanim, we will give you a larger tsiyun magen (6.6 each) for each of the first three, so the total will still be twenty points. There will also be a fourth homework assignment on Laplace transforms. We recommend doing it, also as preparation for the final exam. You can submit it as a regular homework assignment any time up to the date of the final exam, and obtain an additional 4 points of magen (if it is done well).
I am willing to give one or two targiley hazara before the final examination. (13/7/01) The problem is to find a time which suits most people. My tentative suggestion is Monday 9/7/01 from 15:30-17:30. I will also send you an email form where you can suggest other times.
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7.6.01 As promised, the replacement bachan for students who missed the bachan of 29.4.01 because of miluim, will be held tomorrow, Friday 8.6.01, at 8:00.
Please come to room 305 in the Ulmann Building.
Please bring your ISHUR that you were on miluim on 29.04.01 to the bachan tomorrow.
Tomorrow's bachan will (of course) be on the same topics as were announced for the original bachan.
Bhatzlakha!
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23.5.01 Here is a rather specialized discussion about the following question. If f and g are both functions in G(R) is their convolution f*g also a function in G(R)? This is not compulsory material for the course but perhaps some of you might find it interesting.
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2.5.01 I have written a summary of two topics: Differentiation and integration of Fourier series, term by term, and Fourier series on other intervals instead of [-pi,pi].
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30.04.01 The solution (and questions) from yesterday's bachan is here (postscript file) and the graphs you were asked to draw are here(jpeg file.)
THE SECOND MINIBACHAN IS NOW SCHEDULED FOR TWO WEEKS FROM NOW.
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27.04.01 Some details about the topics for the bachan on Sunday are here. BHATZLAKHA!
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20.4.01 The second homework exercise is here. (A small misprint in Question 1 part vav has now been corrected.) The same exercise is also available from the official course website. The second minibachan, including questions from this exercise and from similar topics in the class exercises, will be held soon, but not before the midterm test.
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5.4.01 Khag Sameakh and a pleasant vacation. To see the solutions of the three minibachanim held this week click here.
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27.3.01 Even though we have not yet proved that the standard trigonometric orthonormal systems are closed in E[-pi,pi] you can assume this already in homework exercises etc. Some new notes are here. (English, 4 pages). They give the easy proof of the equivalence of Parseval's identity to closedness of an orthonormal system, and describe the Gram-Schmidt procedure. The last two pages are a discussion of some more exotic questions, about the connection between closed orthonormal systems and complete orthonormal systems.
(Added in August 2002:) For other versions of exotic counterexamples showing that an orthonormal sequence may sometimes be complete but not closed, see some notes prepared in Hebrew by Dr. Alla Shmukler and also my notes here.
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24.3.01 We will soon be studying the convergence of Fourier series. The main result is Dirichlet's theorem. Here are some notes which explain and prove Dirichlet's theorem in a different way than is done in most books and lectures. (English, 7 pages.) Maybe it is a simpler way.
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20.3.01 Some notes about the projection theorem, Bessel's inequality and the Riemann-Lebesgue lemma are here.(English, 3 pages)
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19.3.01 The first "targil bayit" is available now from the official website of the course and also from here.(Hebrew, 1 page) I suggest that you also look at a few small additional explanations about the questions of the targil. They are here.(Hebrew, 1 page)
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14.3.01 In the lecture two days ago we talked about trying to make the "standard" inner product (u,v) on C[a,b] also be an inner product on the space E[a,b]. We saw that, for u in E[a,b], it does not quite have the property:
(u,u)=0 implies u=0.
I explained how to overcome this problem. I promised to give you some more details. To get them click here. (2 pages in English.)
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5/3/01 The items below the next line are from the old version of the page from the last time I taught the course in 1997. I will add some new things soon. But some of the old material can also be quite useful. (Probably most or all of it is now also on the official website of this course.)
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OLD MATERIAL FROM 1977 AND BEFORE The new examination results from MOED BET 6.3.97 are NOW available on this site.
Results from 6.3.97

The old examination results from 7.2.97 are still available on this site.
Results from 7.2.97
If you use netscape: Load the files below by pressing the right mouse button and then selecting
``Save link as ..''.
If you use lynx just press d (i.e. download the file.)
Once you have the file you may print it by:
lpr -P(printer_name) (filename.extension)

A postscript file of the solution of the examination in Fourier Series and Integral Transforms held on 6.3.97 (Moed bet) is now available here.
- This is a postscript file of the questions and detailed solutions of the midterm test (``bakhan") in Fourier Series and Integral Transforms which took place on 26.11.96. - This is a postscript file containg the following three items which most of you have probably already seen:
1. A table of Laplace transforms which appeared in the examinations on 7.2.97 and 6.3.97. (Similar to page 139 of the text book.)
2. A brief policy statement about theoretical questions in these examinations.
3. Corrections of some small misprints in the text book of the course.

A postscript file of the solution of the examination in Fourier Series and Integral Transforms held on 7.2.97 is available here.