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Topics - Bruce Wu

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Textbook errors / Section 5.2 Theorem 3.c)
« on: November 18, 2015, 02:06:20 PM »
In the proof it says $$\int\left(e^{-ikx}\right)'f(x)dx=ik\hat{f}(k)$$
However, $\left(e^{-ikx}\right)'=-ike^{-ikx}$, so shouldn't it be $-ik\hat{f}(k)$? So is it the rule that is wrong or is it the proof that is wrong? Recall that the rule is $$g(x)=f'(x)\Rightarrow \hat{g}(k)=ik\hat{f}(k)$$
Should it be instead $$\hat{g}(k)=-ik\hat{f}(k)$$
Which makes sense since in quantum mechanics $\hat{p}=-i\hbar\frac{d}{dx}$

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APM346--Lectures / 8.1 in TT2?
« on: November 15, 2015, 03:33:25 PM »
On the lecture notes page it says that TT2 will cover chapters 4-7. However, problem 6 of chapter 7 requires 8.1. I just want a clarification of whether or not section 8.1 will be included in TT2.

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Textbook errors / Section 7.2 Equation 3
« on: November 15, 2015, 02:27:36 PM »
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter7/S7.2.html#mjx-eqn-eq-7.2.3

In the line above the equation it should be $\textbf{U}=w\nabla u$

Indeed

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Website errors / Lecture notes
« on: November 14, 2015, 11:54:30 AM »
http://www.math.toronto.edu/courses/apm346h1/20159/lectures.html

At the bottom of the page I think it was meant to say HA1-11

Sure

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Textbook errors / Equation 6.5.3
« on: November 08, 2015, 01:54:56 AM »

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Textbook errors / Equation 6.4.12
« on: November 08, 2015, 12:52:15 AM »
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter6/S6.4.html#mjx-eqn-eq-6.4.12

We are already evaluating $u$ at $r=a$. So after the summation sign it should be $a^n$ instead of $r^n$

Correct

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Website errors / Section 6.5 wrong link
« on: November 07, 2015, 04:30:02 PM »

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Textbook errors / 3.2 eqn 17
« on: October 19, 2015, 01:13:00 PM »

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Textbook errors / 3.1 equation 12
« on: October 17, 2015, 08:47:21 PM »
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter3/S3.1.html#mjx-eqn-eq-3.1.12

I might be wrong, but based on the definition of the error function given, shouldn't it be equal to $$\frac{1}{4}+\frac{1}{4}erf\left(\frac{x}{\sqrt{4kt}}\right)$$?

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Textbook errors / Section 2.6 errors
« on: October 11, 2015, 03:34:15 PM »
In text: http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.6.html#mjx-eqn-eq-2.6.23
The middle of paragraph b. it should be $u_{x}|_{x=b}=q_{r}(t)$ instead of $u_{x}|_{x=a}=q_{r}(t)$

In problem 2 part a.: http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.6.P.html#problem-2.6.P.2
At the bottom it is missing some letters. The different regions should be $x>c_{1}t,0<x<c_{1}t,-c_{2}t<x<0$ and $x<-c_{2}t$

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Textbook errors / Section 2.7 problem 3
« on: October 09, 2015, 10:44:10 PM »
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.7.P.html#problem-2.7.P.3

This is bonus problem 4 of week 4. I believe that the boundary conditions are missing their defining functions.


Right. All $0$ (and there were several similar misprints). V.I.

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Textbook errors / Section 3.1 error in equation 9
« on: October 07, 2015, 07:01:08 PM »
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter3/S3.1.html#mjx-eqn-eq-3.1.9

The $kt$ in the denominator should also be under the square root. Similar error in the line below as a part of remark 2.

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MAT244 Math--Lectures / Integrable/non-integrable systems
« on: December 05, 2014, 03:23:08 PM »
What is the difference between integrable and non-integrable systems of first order ODEs?

I remember the professor talking about it in class but I cannot find it in the textbook. I know what it means, but how does this property affect its solutions?

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