This is an OLD (Oct. 2001-July 2002) version of my Infi3 page

*** WELCOME TO INFI 3 ***

We wish you a very pleasant, interesting and successful semester. We realize that the strike will make this considerably harder to achieve. Within the constraints of the situation, we will do whatever we can to minimize the difficulties, and also to help you know what you need for the continuation of your studies next semester.

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To go to the official website for this course click here.
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Information about your teachers and how to contact them is here.
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Last semester's page for Infi 3 is here.
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Those of you who want to know what is happening concerning the extra vector analysis lectures are invited here.
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22.3.02 The solution of the examination of 24.2.02 is now available here.
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20.3.02 The exam results were given to mazkirut limudey hasmakha yesterday. The makhberot are now available for photocopying if you wish. Both parts of the examination of 24.2.02 are now available here.
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4.2.02 The fourth and final set of homework exercises for this semester is here.
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3.2.02 I have revised my notes about double, triple and n-fold integrals. The new version is here. It is very long (21 pages) and some of the material is quite difficult. I do not expect you to know all of it for the examination. But you should be familiar with the parts that were presented in lectures. Also there will soon be one homework exercise about this material which you should solve.
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27.1.02 The third set of homework exercises is here. It includes references to other interesting exercises and to an explanation about the connection between the gradient of a function and the perpendicular vector to the level curve or level surface of the same function.
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25.1.02 The solution for the midterm test (18.1.02) is here. I have lots of spare copies of the test itself if you want one. Otherwise you can get the test here.
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17.1.02 Here (as requested by some of you) is the solution of Question 8 of the second set of homework exercises.
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15.1.02 Here and here are (partial) solutions to homework exercises number 12 and 10 from the second set.
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8.1.02 Here are some notes about implicit functions (funktsiyot stumot) (English, 9 pages. These notes also mention Lagrange multipliers.) This is a preliminary version. I hope to have time at some stage to rewrite this material later to include some examples. Of course there are lots of examples in various previous examination papers and sets of exercises, and also in the book by Buck and other books.
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6.1.02 The material which I did not cover in today's lecture and which I left you to learn by yourselves as homework is Corollary 3 on the last page of the document about differentiability of inverse mappings which I posted here on 1.1.02. (Today I made some very small changes to that document. They are so small that it is not worth downloading it again if you already have a copy.) I am willing to explain this material to anyone who wants me to after you have looked at it yourself. It is quite short, but it uses an auxiliary result: Cramer's rule for finding inverse matrices, which you probably know from linear algebra.
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1.1.02 Here's wishing everyone a very very good 2002!
To see in advance some of the material for the next lecture (differentiability of inverse mappings etc.) click here (3 pages). Serious students who want to see more information about C1 mappings and preparation for using them to change variables in double, triple and n-fold integrals can 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. (Because of the strike this semester we may perhaps have to treat it in a limited way.) But in some ways it is easier to learn it now.)
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25.12.01 For more details about today's lecture, in particular the result that a one-to-one continuous function defined on a compact set has a continuous inverse, see here.
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25.12.01 Now we are studying the connection between the Jacobian of a transformation T and the property that T is LOCALLY one to one on certain sets. I was badly surprised by the large number of students who did not understand or did not learn this not so difficult topic last semester. To help make sure that this semester you do not have the same misunderstandings as they had, I ask you PLEASE to solve Question 3 in Part 1 of the examination (moed bet) which I gave last September. That examination is here.
(If you look at the solution which I wrote for Question 2 for the examination (moed alef) in July, you will see how frustrated I was about this. You have still not learned all the things you need to know to solve that question.)
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19.12.01 The second set of homework exercises is now here.
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11.12.01 HERE is a recently revised version of some notes about proving that C1 transformations are differentiable. (English 5 pages, revised on 11.12.01.)
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9.12.01 Here are some notes about the chain rule. (English, 3 pages.)
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29.11.01 Now, thankfully, that the strike is over, I can invite you to look at the following document here (English, 4 pages) to recall what happened before the strike and to prepare for the next topic. You may also want to download the document here (Hebrew, 2 pages) about limits, which is referred to and used in the first document.
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26.10.01 Last semester's page for Infi 3 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 these items.
Many many thanks to Prof. Mayer-Wolf for his kind and immediate offer to replace me as lecturer in this course during this time when I am on sick leave. He can be reached by email at emw@techunix.technion.ac.il. His office hours are on Mondays, from 13:30 to 15:00 in room 627 of the Amado building. (tel. 8294195)
Please click here for VERY IMPORTANT information about (1) the format of the tests/exams, (2) the calculation of your tsiyun sofi, (3) miluim during the semester or test or exam, (4) students with learning disabilities or other problems.

The first topic in my lectures, which will now be continued by Prof. Mayer-Wolf, deals with open and closed and compact sets in R^n, and includes versions for R^n of theorems of Bolzano-Weierstrass and Heine-Borel. These are quite similar to the proofs that most of you already know for the cases when n=1 and n=2. I will NOT ask you to reproduce the proofs of these two theorems in Infi 3 exams/tests this semester. But I WILL expect you to know and understand these results well enough to use them correctly in other proofs and exercises.
The following items (from last semester's Infi 3 course) may help you achieve this:
A page (in English) which recalls the proof of the Bolzano-Weierstrass theorem is here.
Some basic exercises about topology in R^n and "cubes" etc. in R^n 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) .)
The next document discusses the definition of "cluster point" (nekudat hitstabrut) (a different but obviously equivalent definition to the one which I gave this semester) and gives a proof of the Heine-Borel theorem. It is here (Hebrew 3 pages). (Last semester I used a different "official" definition of compact set. But, as this theorem shows, it is equivalent to this semester's definition.)
There are 3 more exercises about topology in R^n here. (English 1.5 pages.)
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