*** WELCOME TO INFI 3 ***

(OLD PAGE - SPRING SEMESTER 2000/01)


I wish you a very pleasant, interesting and successful semester.

To go to the official website for this course click here.
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Office hours during the semester (Shaot Kabala):

Michael Cwikel: Thursdays 9:30-10:30 (Amado, room 730). Contact me by telephone (8294179) or email to make an appointment for other times.
Igor Zelenko: Mondays 11:30-12:30 (Amado 915).
Daphne Zelig: Tuesdays 15:00-16:00 (Amado, room 609) (Note that this time overlaps with two usual lecture times.)
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10.10.01 Shalom! The results in Infi 3 for Moed bet have been officially reported. I am very sad to say that the results are in general very bad. All students are invited to come and look at their makhberot and receive further explanations.
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16.9.01 Shana Tova! Here is the Moed bet examination which was given yesterday.
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16.7.01 Your marks (=grades) for this semester are here. Congratulations to those who did well! I hope those who did not will make rapid and good progress before Moed Bet. You are all invited to come and look at your makhberet. There are often things to be learned from the comments which we wrote in it.
Here is the solution of the examination of 3.7.01. Here is the exam itself (including some small corrections to Question 5 which were announced at the time of the actual exam).
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1.7.01: TWO THINGS: (A) Homework No. 5 has been corrected. It can be picked up from the envelope outside the door of my office. Comments have been written on your assignments, and hopefully you can learn from them.
(B) Some students asked me about an old examination from 1989. There is also a solution available (but handwritten and in English). All this material is available here. I have not carefully looked at this examination. Some of the questions may perhaps perhaps be about topics that we did not cover this semester.
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30.6.01 Many of you apparently had difficulty with question 2b of Homework Exercise No. 5. (Changing the order of integration in a triple integral). So there is now a detailed solution including some general comments here and also a graphics file showing some relevant pictures here.
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28.6.01 (SECOND MESSAGE TODAY.) One of you asked me to write a solution for problem no. 10 of Homework Exercise No. 4. It is here. If you have other requests I will try to respond to them, but cannot always promise that I will have time to do so.
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28.6.01 I will be in my office for quite a lot of the time today. If you do not find me, leave a phone or email message and I will contact you. On Sunday, either Daphne or I will be available to answer questions, also, if you wish, in the framework of a tirgul hazara,
IMPORTANT: We are now correcting your Homework No. 5. Many of you do not know the correct form of the result for describing critical points of a function (determining whether they are local maxima, local minima or saddle points) in terms of the second order derivatives, and the matrix (the "Hessian") obtained from these derivatives. Please note! It is NOT enough to simply look at the sign of the determinant of this matrix. Please look again at your lecture notes, or the notes that I already posted on this website on May 10. To avoid any misunderstanding you can also look at the solutions of some parts of Homework No. 5.
PLEASE COME AND PICK UP THE CORRECTED HOMEWORK (NO.4) FROM NEXT TO MY OFFICE. WE MADE AN EFFORT TO WRITE COMMENTS ABOUT YOUR MISTAKES SO YOU CAN LEARN FROM THEM!!
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26.6.01 If you have not yet done question 14 in Homework Exercises No. 4 then here are some hints to help you. (This is a letter which I sent to a student who asked me about it.) More details are available if needed.
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25.6.01 All the homework no. 4 exercises have been corrected. You can collect your corrected homework no. 4 from the envelope next to my door (Room 730 Amado). Homework No. 5 should be available corrected, early next week.
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24.6.01 Here are some comments about your solutions to Homework No. 4.
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21.6.01 Homework Exercise Number 6 is now ready. You do not have to submit it but it deals with topics which can appear on the examination. The main part of the exercise is available as a Microsoft Word file here, or alternatively as a postscript file here. (There are 3 or 4 places in these files where the arrows above vectors appear instead, incorrectly, as the letter "P"). There is also an additional page (postscript) with some explanations about the preceding page and one more question here.
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7.6.01 Here is the sentence that was corrected in question 14 of Homework Exercises Number 4. (This correction has already been made also in the full and "compact" versions of the homework exercises posted on this website.)
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5.6.01 Targil Bayit 5, is now available from the official Infi3 website. It is due to be submitted on 18.6.01
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27.5.01 Hag Sameakh. Greetings from the city where Bernard Bolzano lived and worked. I hope you did well on the bachan on Friday. Here is a solution, hopefully a correct one. Here is the bachan itself.
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23.5.01 The bachan on this Friday, 25.5.01, will be held in Rooms 210 and 211, Ulmann Building at 8:00. Tatzlikhu!
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21.5.01 Part of today's tirgul will deal with change of variables in repeated integrals. Here is the relevant formula. Later we will also discuss the corresponding formula for triple integrals.
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18.5.01 Here are the questions from the bachan which was held on 11.5.01.
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17.5.01 Here is a long document (Hebrew, 8 pages) including 22 exercises, mostly on maximum, minimum and Lagrange multipliers. For targil bayit number 4 you are requested to submit SEVEN of these exercises. (These particular exercises are specified in the document.) The date for submission is May 29, but you should also consider these exercises as part of the preparation for the bachan on May 25. You may find it convenient to also print the shorter (two page) document here which contains only the seven targiley khova. But there is a lot of important material appearing only on the longer version, including an exercise/explanation (see exercise 22) about tangent lines/planes/hyperplanes and gradient vectors.
A picture relevant to exercise 3 is here.
A picture relevant to exercise 4 is here.
A picture relevant to exercise 22 is here, and a few words of explanation about the picture are here.

The material for the bachan on May 25 will include all topics from the beginning of the semester, up to and including maxima and minima on sets and Lagrange multipliers. The topic of classification of critical points using second derivatives and everything after that topic will NOT be included. The detailed explanation (exercise 22) about tangent lines/planes/hyperplanes and gradient vectors, is also not included in the material for the bachan, but there are other related facts about the gradient vector and directional derivatives which ARE included.
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15.5.01 I have written some notes (18 pages in English) describing the theory behind Riemann integrals, including double and triple integrals. They are available here.
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10.5.01 Here are three pages about classification of critical points using second derivatives.
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22.04.01 The third homework exercise (due on May 7) has been posted on the official Infi3 website and is also here.
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17.4.01 Here are some notes about implicit functions (funktsiyot stumot) (English, 9 pages. Also mentions Lagrange multipliers.) This is a preliminary version. If I have time I will rewrite it later to include some examples.
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13.4.01 Khag Sameakh. I hope you are having a pleasant vacation. Next Monday there will be a LECTURE instead of a tirgul. It will be in Ulmann Room 504. (There will be extra tirgulim in place of lectures later in the semester.) To see in advance some of the material for the next lecture (differentiability of inverse mappings etc.) click here (3 pages). For more information about C1 mappings and preparation for using them to change variables in double, triple and n-fold integrals click here (8 pages). (This material comes at a later stage of the course and we will not talk about it very much in lectures now. But in some ways it is easier to learn it now.)
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2.4.01 The second set of homework exercises, which is due to be submitted on 19 April is now available from the official Infi 3 website or from here.
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31.3.01 From now on, the lectures on Tuesdays at 17:30-19:30 will be held in room 231 of the AMADO building.
Unfortunately I could not find a more convenient time which suits everybody. For details of my/our attempt to do so you can look here.
Our "bachan" is now scheduled for Friday, May 25, 2001. To see how I reached that conclusion you can look here.

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27.3.01 Here are some notes about proving that C1 transformations are differentiable. (English 5 pages.)
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24.3.01 Here are some notes about the chain rule. (English, 3 pages.)
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15.3.01 Next Monday there will be a tirgul from 13:30-15:30 in the same rooms as last week. (See below.)
I wrote a short note about limits with respect to a set. It was for the (easier) course Hedva 2m and there the functions f:D --> R , are scalar functions, i.e. they do not map into R^n, for n>1. But the note might still be helpful. It is here.(Hebrew 2 pages.)
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11.3.2001 Tomorrow (Monday 12.3.2001) the lecture from 13:30-15:30 will be replaced by tirgulim. Here are the rooms:
Tirgul 11 (metargel: Igor Zelenko) in room 505.
Tirgul 12 (metargelet: Daphna Zelig) in room 504.
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10.3.2001. I have posted 3 more exercises about topology in Rn here. (English 1.5 pages.)
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9.3.2001. New document posted.
I apologize. I would like after all to change the definition of the term "cluster point" (nekudat hitstabrut) from the one I gave in class today. Different books use it in different ways and I think I should adopt the same usage as in the book by Buck. I have now posted a new document here (Hebrew 3 pages) which gives more details of this and a recapitulation of the proof of the Heine-Borel theorem. There I will also write condition (2) of the theorem slightly differently. (I hope this will be later today.)
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8.3.2001 If you did not yet receive an email from me asking you to tell me what dates are possible for you for the bachan then you are not subscribed to the mailing list for Infi3 and perhaps you are not registered for the course, or your email is not working.
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7.3.2001 Some basic exercises about topology in Rn and "cubes" etc. in Rn are here. (English, 2 pages. The second page, for anyone who is interested, is a reminder about the Cauchy-Schwartz inequality and how it leads to the triangle inequality for d(x,y) .)
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6.3.2001 A page (in English) which recalls the proof of the Bolzano-Weierstrass theorem that we did today is here.
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I have chosen the date Friday 11 May, 2001 for the mid-term test (bachan). If this date is problematic I am happy to change it provided that ALL STUDENTS can agree on a different date. Meanwhile I see that this is not a very good date for many people. I will soon email a form to all of you, so you can tell me, by email, what are possible dates for you.
You can also write to me about this if necessary (and of course about other things too). Please give your message the subject INFI3.
My address is mcwikel@math.technion.ac.il .
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The mid-term test will be "magen", and will have a weight of 25% in your final mark. There will also be a 10% mark for homework. This will be "takeff". We will soon inform you of the exact procedure. Possibly there will be some "mini-tests" on homework exercises which you have already seen, or exercises very similar to them.
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The teaching assistants (metargelim) this semester are Igor Zelenko zigor@techunix.technion.ac.il and Daphna Zelig zeligd@techunix.technion.ac.il
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Please note that this week and also from time to time in the future, it will happen that the "tirgul" on Tuesdays will become a lecture, and/or the lecture on Monday will become a "tirgul". The total numbers of lectures and of "tirgulim" for the whole semester will not be changed.
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I have prepared three exercises on the topic of level curves ("kavey gova") and level surfaces ("mishtakhey rama"). They are here. (Hebrew, postscript file, 1 page).
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If you are curious to see how to construct the amazing Peano curve (this is a one and a quarter pages, and is NOT officially part of the course) you are invited to click here. (Hebrew, postscript file, 2 pages).