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Messages - JUNJING FAN

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APM346--Misc / Scope of TT2?
« on: March 11, 2019, 05:17:23 PM »
As titled, what chapters will be on TT2?

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Home Assignment 3 / Re: S2.3 Problem 8
« on: February 05, 2019, 07:57:09 PM »
Find the general solution and then plug to initial conditions
Hello professor, could u give me a hint as to why we have to impose the restriction for absolute value of x to be smaller or equal to 1?

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Home Assignment 2 / Re: problem 5 (23)
« on: January 27, 2019, 07:47:30 PM »
There is NO root. You need to parametrize before integration

but, when we parametrize Y in terms of X, don't we have to use $$y^2+x^2=C$$
and thus $$y= +/- \sqrt{C-x^2}$$?

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Home Assignment 2 / Need help with S2.2 P1 #4
« on: January 27, 2019, 03:13:52 PM »
I have attached my attempt. However I'm having trouble solving the problem fully with the initial condition provided. Anyone knows how to do it? Or did I make any mistakes along the way?
Thanks.

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Home Assignment 2 / Re: problem 5 (23)
« on: January 27, 2019, 12:11:13 PM »
Heller professor
By parametrizing Y in terms of X, do we need to put a plus/minus sign in front of the root? If yes, does that mean when we put down the final solution, we need to include plus and minus as well?

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Home Assignment 1 / Re: Home Assignment 1
« on: January 16, 2019, 05:07:33 PM »
Junjing, you are right but I am not sure if anyone but me would be able to read your solution
Okay. Next time I will make it 'skinnier'. Sorry.

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Home Assignment 1 / Re: Home Assignment 1
« on: January 16, 2019, 04:36:55 PM »
Not sure if this will work

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MAT334--Lectures & Home Assignments / Re: Residue for FE P3
« on: December 12, 2018, 07:02:59 PM »
I don't think that is correct because if let $\sin^2(z) = (z-n\pi)^2h(z)$ where $h(n\pi) \neq 0$, then $\frac{1}{h(z)}$ is analytic at neighbourhood of $n\pi$.
Thus $Res(\frac{\cos(\frac{z}{6})}{\sin^2(z)}, n\pi) = Res(\frac{\cos(\frac{z}{6})}{(z-n\pi)^2h(z)}, n\pi) = $ coefficient of $(z-n\pi)^{1}$ for function $ \frac{\cos(\frac{z}{6})}{h(z)}$
while $cos(\frac{z}{6}) =a_0 + a_1(z-n\pi)^{1} + O((z-n\pi)^2) $ and $\frac{1}{h(z)} = b_0 + b_1(z-n\pi)^{1} + O((z-n\pi)^2) $
thus the coefficient for the fraction at $(z-n\pi)^{1}$ is $a_0b_1 + a_1b_0$, which I get is $ 0 + (- \frac{1}{6} sin(\frac{n\pi}{6})\frac{1}{\cos^2(n\pi)})$

Just asking for a check of this idea.
what i do is since it is a double-pole, i find the coefficient for the degree 2 term of the sine squared function, then i find the coefficient of the degree 1 term for the cosine function, then divide it out.

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MAT334--Lectures & Home Assignments / Re: Final Exam Scope?
« on: December 12, 2018, 07:00:40 PM »
So we need to know how to do TT1 + TT2 + Q7 ***AND*** the Sample Final correct?

Also, the Sample Final contains questions about the stretch and rotation angle of a mobius transformation. Isn't that part of Chapter 3.4? I don't see anything in 3.3 that discusses rotation and stretch.
same question here
but i guess it never hurts to know how to do it.

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MAT334--Lectures & Home Assignments / Re: What's the answer of FE q2 d.e.f?
« on: December 11, 2018, 08:39:41 PM »
Can you explain how you figured it out?
so refer to textbook page 50, the book provides a method. For x just follow the book, for y follow it until the end to prove that y1+y2=0, however the range of y is not limited to be positive in this question. In this case, we will have to expand:

cos(x+iy) = cosx coshy - i sinx sinhy

and realize that sinx is never 0, meaning sinhy will always be there, and sinhy is injective for a positive or negative y of same magnitude.

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MAT334--Lectures & Home Assignments / Re: What's the answer of FE q2 d.e.f?
« on: December 11, 2018, 08:28:39 PM »
There are only answers of part a and part b and it seems that we cannot reply to the question anymore.
Can somebody please post the answer of part d e f?
Thanks
never mind, it is one-to-one. I figured it out.

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MAT334--Lectures & Home Assignments / Re: What's the answer of FE q2 d.e.f?
« on: December 11, 2018, 08:17:28 PM »
There are only answers of part a and part b and it seems that we cannot reply to the question anymore.
Can somebody please post the answer of part d e f?
Thanks
also, for the graphing of the domains, textbook section 1.5 question 26 refers to figure 1.26 on page 53 as the domain of the mapping function. In the question it states that the mapping is one-to-one, but from what I can see it is not one-to-one.

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MAT334--Lectures & Home Assignments / Re: What's the answer of FE q2 d.e.f?
« on: December 11, 2018, 08:12:08 PM »
There are only answers of part a and part b and it seems that we cannot reply to the question anymore.
Can somebody please post the answer of part d e f?
Thanks
same, I am stuck at proving the function to be 1 to 1.

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