*** WELCOME TO FOURIER SERIES & INTEGRAL TRANSFORMS ***
We wish you a very pleasant, interesting and successful semester.
*** ( F. S. I. T. ) ***
(THIS IS THE OLD WEBSITE, 2003 AND EARLIER.)
15.3.03 The exam of 12.3.03.
and its solution.
26.2.03 Most, but not all details about your examination scores
on 11.2.03 are available from the "grades" site. But to obtain a few
more details first read this and
then look at this table.
... and its solution
CORRECTED Partial solution for Homework no. 2
CORRECTED Partial solution for Homework no.
9.2.03 CORRECTED Partial solution
for Homework no. 4 (There is only one small correction. The factor (s^2+1) in
the denominator of the answer to 1 alef should be deleted. Thanks Shay for
Comments and a list of topics
for the final examination(s) are now available here.
17.01.03 Homework Exercises No. 4 (Laplace
Transforms) is now available here.
I plan to give a targil hazara to answer questions etc. for my lecture group on
February 9, starting at 12:00. The room will be announced later. There will
probably be room for students from other groups too if they are interested.
3.01.03 Homework Exercises No. 3 (Fourier
Transforms) is now available here. (The version posted on 21.12.02 has
been corrected. There is only one change: "sin t/3" has been replaced by
"cos t/3" in part B of the first question.)
15.12.02 HOW TO SEE YOUR BAKHAN, and eventually lodge an "irur".
(A). Please be familiar with the
and also their solutions
BEFORE you come to see your bakhan. This will save a lot of time for
you and for the person who has to answer your questions. It is also good
preparation for the final exam.
You can go to see your bakhan some time during the next FIVE weeks.
Please view the following
list to see which lecturer has your
bakhan and when are the weekly shaot kabala for going to see
her/him. It will save time if you can tell the
lecturer what room you sat in (appears as "r=???" in the list), and your "serial
number" (appears as "[???]" in the list.)
9.12.02 Updated version of notes about Term-by-term differentiation and
integration of Fourier series, and Fourier series on other intervals.
(This has been updated yet again, only small changes, on 13/1/03)
This is now available below (or also
30.11.02 Solution of the
midterm test (27/11/02).
In some exercises in this course you are asked to determine whether
Fourier series converge UNIFORMLY (b'mida-shava) on some set. Uniform
convergence is a topic which you are supposed to remember
from Hedva 1 or Hedva 2. Although in general it is very important, it
plays a limited role in this particular course.
quick summary, a "Uniform Convergence Survival Kit" containing the main
things you need to know about Unif.Cgce. for this course.
Here are notes about two topics:
Differentiation and integration of Fourier series, term by term, and
Fourier series on other intervals instead of [-pi,pi].
Here are some comments about
Dirichlet's theorem. In lectures we gave you a proof of it:
(1) using the Dirichlet kernel, as presented in
Chapter 2 of the book by Pinkus and
But if you are interested, you can also
(2) read (3 pages, English)
This is a short different proof of Dirichlet's theorem in a special case
the function f is "nice". There is a fourth page with some further
comments and questions.
(3) For a version of the FULL proof which is different from the usual
version in (1) you can read 7 pages (English)
(Part of pages 2 and 3 of this document, is the calculation of the
Fourier series of a particular function, which is a typical technical
exercise that you
should be able to do.)
29.11.02 Khag Khanuka Sameakh. I have now made a very very small change
to the version of the midterm test which I posted here yesterday.
28.11.02 Here is one version of yesterday's
midterm test. You can also get hard copies of the same
test from the envelope
outside my door (Amado 730).
24.11.02 Homework Exercises, Set 2, Fourier Series.
This is the final version (almost exactly the same as the preliminary version).
Here are some hints for SOME of the first
set of homework
Here is the FINAL version of the
first set of homework
exercises, on inner product spaces.
We added three more questions to the preliminary version.
If you already downloaded a copy of the preliminary version, you do
not need to access the above file. You only need
this last page and you will have
the complete final
23.10.02 If you want more notes about orthogonal projections you can find
them (in English) here. The same
notes also discuss Bessel's inequality and the Riemann-Lebesgue lemma.
(An apology: In my lecture today I made a small mistake when I formulated
projection theorem. The corrected version (in Hebrew) is
14.10.02 We, the teachers of the course, wish you a very pleasant,
and successful semester. Most of the topics in this course are extremely
important tools in many branches of science and engineering, so we
recommend taking this course seriously.
If you have questions, please try first to look at the text book and
other documents on this website, but if you do not find the answers there
reasonably quickly please do not hesitate to ask us.
I will usually put new information for the course here on my "private"
PLEASE BE SURE TO READ the VERY IMPORTANT document
instructions and information about (1) the format
tests/exams, (2) homework exercises, (3) the calculation of your tsiyun
sofi, (4) miluim during the semester or test or exam, (5) students with
learning disabilities or other problems.
Not reading the document could seriously effect your final grade.
A detailed syllabus is available
To go to the OFFICIAL website for this course click
That site also contains ESSENTIAL information, exercises, text book,
previous examinations, etc.
To go directly to download or read the text book for this course, written
by Allan Pinkus and Samy Zafrany, click here,
Information about your lecturers and teaching assistants, and how to contact them is
22.2.02 Here is a 6 page Hebrew document
which summarizes some of the basic
This document was prepared last year. As written in the document,
some of the material it contains was not included in the exam last year,
because of the strike. But that material IS REQUIRED this semester.)
WARNING: A quick summary can be useful, but it is NOT a substitute for
really understanding the material and doing plenty of exercises.
Thanks to Yoram Yihiye for
helping prepare this document.
This document is NOT a list of formulae to be used during the
The questionnaire of the examinations for Moed Alef and Moed Bet
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 will be printed on TWO sides of a single page. WE will provide it, please do
NOT bring your copy. (You will not be allowed to use your copy.)
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. (There are
also solutions for many of them.) Many old examinations 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. (You can also find links to several
examinations and bakhanim from my page of last semester.)
The page for Fourier Series..... which I used a year ago is here. It contains several lists of problems and extra
explanations about material from the lectures, and some examinations and
solutions to some of them. Most of these things can also be useful this semester.
As the semester proceeds I plan to also put more explicit links here to some of