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Messages - Victor Ivrii

Pages: 1 ... 143 144 [145] 146 147 ... 163
2161
Misc Math / Re: Last Year HW:5.4.12
« on: November 12, 2012, 01:59:45 PM »


Yes, except $\int_0^l |sin(nπx/l)|^2\,dx =l/2$, so you don't need this integral. Ditto for 5.4.13, 5.4.15.



And who is P.T.?

"Paul Tan" Last year student.
[/quote]

Shame on me--I forgot--he was the best online help!

2162
Misc Math / Re: Lecture Note 22
« on: November 12, 2012, 01:58:39 PM »
Correct. Fixed.

Don't hijack topics--I renamed your post and split topic.

2163
Home Assignment Y / Re: HAY--as preparation for TT2
« on: November 12, 2012, 01:49:49 PM »
It is discussed in lecture 13. If you have the Strauss textbook, it is discussed in quite a bit of detail in chapter 4.3

See  Appendix C and Appendix B.

You linked to appendix C twice.  :)

Yes, right. Fixed.

2164
Home Assignment Y / Re: Problem 2
« on: November 12, 2012, 01:48:50 PM »
Nice! BTW, note where approximation is worse. Why here, what do you think?

2165
Home Assignment 7 / Re: Problem 2
« on: November 12, 2012, 01:46:02 PM »
Hey,

I get an ODE for problem 2, but it is not of the Euler type and I don't know how to solve it. Could anyone give me a hint?

Thanks!

I am asking you to find solutions, but to try to find them? The crucial question is What ODE should satisfy $u(r)$?

2166
Misc Math / Re: Last Year HW:5.4.12
« on: November 12, 2012, 04:58:43 AM »
Aida, please next time provide a link, like this one
http://weyl.math.toronto.edu:8888/APM346-2011F-wiki/index.php/Home_Assignment_8#5.4.12.

I am just wondering in this question when P.T. wrote Parseval's equality, it shouldn't contain "integral |sin(nπx/l)|^2"; Right?


Yes, except $\int_0^l |sin(nπx/l)|^2\,dx =l/2$, so you don't need this integral. Ditto for 5.4.13, 5.4.15.



And who is P.T.?

2167
Home Assignment Y / Re: HAY--as preparation for TT2
« on: November 12, 2012, 04:06:52 AM »
It is discussed in lecture 13. If you have the Strauss textbook, it is discussed in quite a bit of detail in chapter 4.3

See  Appendix C and Appendix B.

2168
Home Assignment Y / Re: Problem 1
« on: November 12, 2012, 03:17:14 AM »
In the last line, shouldn't the power to the second exponential be ikx instead of iky?

No--it is Fourier integral for $k\mapsto y$ (remember FT was by $y$). Calvin, WTH, why are you not defending your solution?

2169
APM346 Misc / Re: HA4
« on: November 11, 2012, 05:20:45 PM »
Well I got my mark but it would have been nice to have our assignments returned to us sooner so that we could utilize them as an aid in preparation for the upcoming test.

TAs promised to do it soon--so I guess Wednesday as Monday and Tuesday we have a break.

OK, it looks like 2/3 of the marks for HA4 (44) have been posted. No changes with HA5 so far (Mon 12 Nov 2012 09:48:00 EST)

2170
Misc Math / Re: Lecture 20 Notes
« on: November 11, 2012, 05:18:44 PM »
Hi, I was just wondering what the symbol O stands for in the notes of lecture 20, for example in formula (10). Thanks!

Too bad that in Calculus I you were not given the very standard math notations:

$f=O(g)$ means that $\frac{f}{g}$ is bounded;

$f=o(g)$ means that $\frac{f}{g}$ tends to $0$;

$f\sim g$ means that $\frac{f}{g}$ tends to $1$

and a bit less traditional

$f \asymp g$ means that $c^{-1}\le |\frac{f}{g}|\le c$ (or equivalently $f=O(g)$ and $g=O(f)$).

2171
Term Test 2 / Re: Scope of Term Test 2
« on: November 10, 2012, 06:10:01 PM »
Since I can't reply in the announcement thread: http://forum.math.toronto.edu/index.php?topic=83.0

I have a class at 18:00, so I need to go to the early sitting. To be clear; I can just show up to HU1018 at 16:00, and I don't need to sign up for anything in order to attend this sitting- correct?
YES

2172
Misc Math / Re: Lecture Note 23
« on: November 10, 2012, 05:44:49 PM »
Right

2173
Misc Math / Re: Lec 23 Possion formula clarification
« on: November 10, 2012, 05:43:06 PM »
Good catch

2175
Home Assignment 5 / Re: About HA5
« on: November 10, 2012, 05:25:45 PM »
If we are decomposing into full F.S. $f(x)=x$ on interval $[-l, l]$ then it is the same as to decompose into sin-F.S. $f(x)=x$ on interval $[0, l]$.

But if we decompose into full F.S.  $f(x)=x$ on interval $[0, l]$ then we have different picture: function is $l$-periodic and exactly this is on the picture (note that bolder line shows graph on the original interval)

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