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Messages - Ian Kivlichan

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31
Home Assignment 6 / Re: Problem 4
« on: November 07, 2012, 04:32:43 PM »
Is there a way to go from $\int_{-\infty}^{\infty}{\frac{\sin^2(x)}{x^2}dx}$ to $\int_{-\infty}^{\infty}{\frac{\sin(x)}{x}dx}$?

32
APM346 Misc / Re: Should be the night class offered at Fall or at Spring?
« on: November 03, 2012, 04:51:21 AM »
As is, students can only take this course in Fall semester -- for that reason alone it would be better to offer a section in Spring semester.

But yes, constant holidays on Mondays in Fall mean that Monday night lectures shouldn't really be offered... the Faculty Registrar probably doesn't care though...

33
APM346 Misc / Re: Are the grades going to be bellcurved?
« on: November 03, 2012, 04:44:13 AM »
So, the average is pretty low. The question is: Are the grades going to be bellcurved?

Levon: Bell curving is absolutely forbidden by the ArtSci Faculty (http://www.artsci.utoronto.ca/faculty-staff/teacher-info/academic-handbook-for-instructors/sections-4-5#calibrating):
Quote
Calibration of test scores should be done fairly and equitably, and bear a justifiable relation to academic performance. Policy explicitly forbids manipulating marks to fit into a “normal curve” or any other prior expectation – in the language of the Policy: “academic assessment must not be predetermined by any system of quotas that specifies the number or percentage of grades allowable at any grade level. ”

As far as I know, linear adjustments are most commonly used to change course averages (via new_mark = old_mark * multiplier + shift), but this depends entirely on whether Prof. Ivrii thinks the marks are fair.

Usually, course coordinators are pressured to maintain a C or C+ average (the lowest course average on my transcript is C, and the lowest I've heard of is a C-), so since the TT1 average is 57.5% (D+) it's likely that the final average will be higher.

34
Home Assignment 5 / Re: Problem 4
« on: October 31, 2012, 09:53:35 PM »
Hopeful solution for 4.b) attached!

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Home Assignment 5 / Re: Problem 4
« on: October 31, 2012, 09:44:27 PM »
Additional solution for 4.a) (essentially the same as Aida's post here http://forum.math.toronto.edu/index.php?topic=108.msg552#msg552 , but showing more of the sketch, as well as with details on the odd continuation used for sin Fourier series).


36
Home Assignment 5 / Re: Problem 6
« on: October 31, 2012, 09:38:35 PM »
Hopeful solution to 6.e) attached!

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Home Assignment 5 / Re: Problem 5
« on: October 31, 2012, 09:32:43 PM »
Hopeful solution for 5.a)!

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Home Assignment 5 / Problem 4
« on: October 31, 2012, 09:32:02 PM »
Hopeful solutions for 4.c)! :)

edit: Note that sketch is for m=1.

39
Home Assignment 5 / Re: Problem 1
« on: October 31, 2012, 02:27:03 AM »
Jinchao: you can integrate (e^x)sin(x) by parts. Set u = e^x, dv = sinx dx, and go through. You'll have to integrate by parts a second time, but you'll end up with (e^x)sinx integrals on both sides. Hope that helps! :)

40
APM346 Misc / Dropping two worst assignments
« on: October 24, 2012, 03:40:08 PM »
Hi all,

I noticed on http://www.math.toronto.edu/courses/apm346h1/20129/about_home_assignments.html that it says

Quote
  • Two worst assignments (included those you did not submit and got 0) will be dropped;
  • So, if there will be 10 assignments, only 8 will be counted and each would contribute 2.5 to the Term Mark;

To be clear, does this mean that no matter how many assignments there are, 2 will be dropped? (Ex. if we had 8 assignments, only 6 would be counted, and each would contribute 3.3% to the Term Mark.)

41
Misc Math / Lecture 12 Eqn 9 Question
« on: October 24, 2012, 01:59:26 AM »
Hi all,

Just to clarify - should equation 9 in the notes for lecture 12 (http://www.math.toronto.edu/courses/apm346h1/20129/L12.html#mjx-eqn-eq-9) read

$\lambda_n = - n^2 \pi^2 / l^2$ ?

Cheers,

Ian

42
Term Test 1 / Re: TT1 = Problem 3
« on: October 17, 2012, 01:11:39 AM »
PS. Ian, your posts are virtually useless for a class: too poor handwriting makes it almost impossible to read for anyone who does not know solution. Could you repost?

Sorry!!  :(

I have tried my best to re-write it nicely (edited original post).

43
Term Test 1 / Re: TT1 = Problem 2
« on: October 16, 2012, 09:53:02 PM »
Ian, while explanation is basically correct I would like to see more convincing arguments. In particular: where solution will be defined uniquely?
With the given conditions, the I think solution is defined for -inf < x < -t, . The given conditions on u and u_t restrict it there, as any wave starting early in time would have to pass through (x,t)=(x,0). 0 < x < -t, however, does not have the required conditions for uniqueness.

44
Term Test 1 / Re: TT1 = Problem 1
« on: October 16, 2012, 09:24:06 PM »
Subqueston (d):

$ \frac{dt}{1} = \frac{dx}{x^2} $
$ t = -x^{-1}+c $
so the general solution is $ u(t,x)=f(t+x^{-1})$.
$u(0,x)=f(x^{-1})=g(x)$
$f(y)=g(y^{-1})$
Since $y=x^{-1}$, so when $x>0$ we have $y>0$ as well.
$u(t,x)=f(t+x^{-1})$
We need $t+x^{-1}>0$
Since $x>0$,
therefore $tx+1>0$
so the domain be defined is $\{(t,x) | tx>-1 \}.
I think Jinchao has the most correct solution.

Qitan, is it possible to only have the one discontinuity in your solution - won't your characteristic curves be "blocked" by the discontinuity at tx=-1, and not able to go any further?

45
Term Test 1 / Re: TT1 = Problem 5
« on: October 16, 2012, 08:25:25 PM »
Solution is attached,

Aida, I think your solution is not correct - the integral from -1 to 0 will only be 0 if x < y in H(x-y), i.e. x < -1.

Also, consider extreme cases - for C(-100), H(-100-y) can never be greater than 0, so a solution with C(x) = 1 cannot be right (unless I've totally misunderstood something).

I believe your solution is not correct; H(x) and H(x-y) has the same value for these two different domain because it is a constant function.

Shouldn't they be different though? For H(x), it's 1 for x>0 and 0 for x<=0, but H(x-y) is 1 for x-y>0, or x>y, and 0 for x<=y.

In any case, how can C(-100) be nonzero? x-y=-100-y>0 is impossible for -1<=y<=1, which is the only area where Q(y) is nonzero.

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