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Summer 2004 - Yossi Farjoun's Homepage

Summer 2004

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Math 128a Wiki

(This wiki page is stale...there's little point in editing it)

This Wiki is intended for Math 128a students to discuss the various issues encountered while taking studying in the summer session of 2004. Please feel free to add questions, answers, topics, corrections etc.

If this is used and becomes useful, I'll break it up a little...

You can now edit your preferences and add an email so that you'll get notification if there has been any change.

Is anybody reading this at all? Is there any point to this? I find it hard to believe that nobody has any questions. If someone has no idea how to change the text in this page or would like a place where they can experiment without risking being flamed (not that it will happen here...) you can visit the SandBox

If I don't see that someone is reading this...I'll just stop updating and checking it. so even if you just want to say that it has been useful, write me an email, or comment in the wiki. --Yossi

You can now upload files to the wiki by clicking upload and selecting the file on your compouter. you will then be given a link to the file. to add a link to the file on the wiki simply edit the wiki and add the link in the text, like this: upload:sample.m . Now you can download the file and thus exchange ideas.

To add a new page, simply add a link to it and then save, then click on the page and edit it. for example, Here is a page on the midterm: [MidTerm2] now you can click on it and go to the page that will discuss the! (BTW, at first, when the page doesn't yet exist, a little question mark will appear next to the link...then when the page is acually defined, it will become a proper link....)

When you edit the wiki, don't forget to click 'Save' so that the changes you made will actually be saved....

Course Material

Written Homework

  • Typos:
    • Calculus review problem 8: The last exponent of x should be n+1 not n+2.
    • Calculus review problem 9: The exponent of -1 should be n+1 not n+2.
    • Calculus review problem 13: subscript N should be n. Also add the word "using" between pi and cA_8+c'A_16.
    • Fixed Point Iteration there's a square-root sign missing in 2 b). The version online has been updated.
    • \Orthogonal projection the inner product should be defined as the integral from -1 to 1!!! not from 0 to 1!!
  • Questions:
    • I have a question about the first problem on HW 5 on "Problems on Interpolation". It isn't clear to me how I should apply the MVT to this problem. I have thought a lot about how the MVT works and possible applications to this problem, but none seem to work out. What you have to prove in this question is that p(x) has at most n roots. Therefore, assume that p(x) has n+1 roots, and use MVT to say something about the number of roots that p'(x) has. Continue like this until you reach a contradiction. Remember that a non-zero constant has zero roots and since p(x) is assumed to be of order n that means that a_n (the coefficient of x^n) is non-zero.

Computer Assignment


  • There was a typo in the location of the x_m in the second part of the interpolation computer assignment. The correct version is now online.
  • There was a typo in the Interpolation homwork. In the definition of the divided differences, the three dots between the f[] should be a minus sign. The online version has been updated.

Questions (can someone please answer these?)

How to make a function?

How to set the axis on a graph?


Apperently X(2:end) doesn't work in (older versions of) Octave. so you'll need to use the function size. This function returns the dimensions of it's argument. For example:

octave:12> X=1:10;
octave:13> size(X)
ans =

1 10

Adding a number as the second argument returns the size of that dimension:

octave:14> size(X,2)
ans = 10

so what whould have been X(2:end) in matlab is now X(2:size(X,2)) in Octave.

Opening new figures Here's what I found out: in Matlab simply writing 'figure' opens a new window for a plot. In Octave you must call figure with a number. Say 'figure(2)' to direct the next 'plot' command. In the example, the next plot will go to the second figure (the default is 1) so if you want to have to figures you have to write:

plot(...) %your first plot
figure(2) % change the output to the second figure
plot(...) %your second plot.

and further output will be directed to the second plot, unless you call figure again.


on windows

Octave: Right mouse button click on the icon of the graph window. Under "options" you should have a "print" option. Easy!

on UNIX Octave: I found the following weird solution:

figure(...) %make sure figure is pointing to the figure that you want. this line may be unnecessary.
gset output "" % set the output to be a postscript file
gset terminal postscript % set the output format to be postscript
replot% tell octave to replot using the new settings.
gset output %the output is being set back to the file
gset terminal x11 % the format of the output is being changed back to x11, the default format (?)

Now you will have a postscript file in your directory, print it out somehow.

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