### Recent Posts

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41
##### Test 1 / Re: Test 1 coverage
« Last post by Victor Ivrii on March 03, 2022, 12:11:32 PM »
Look at samples posted
42
##### Test 1 / Test 1 coverage
« Last post by yingxuanwang on March 02, 2022, 07:50:06 PM »
Hi Prof. Ivrii!

I have seen that the announcement on Quercus test 1 page said we would have four question in the test, for main sitting, 1 for first order, 2 for wave, 3&4 for heat(one whole, one half). But the practice past test that you posted is not the same coverage as the announcement, the practice contains:1 for first order, 2 for whole wave, 3 for half wave, and 4 for whole heat. I am so confused and I have checked with Prof. Kennedy, he said the test format he received is the same as the practice, and I make sure with him I am asking about the main sitting. Since I mentioned the difference coverage between practice and announcement, he took a look at something, I think that was internal announcement for instructor maybe, and he told me the format is the same as practice.

So I just want to make sure that tomorrow main sitting, we will have Q1 for first order, Q2 for whole wave, Q3 for half wave and Q4 for whole heat, right?
43
##### Test 1 / Re: Test 1 Wave equation and Heat equation questions
« Last post by Victor Ivrii on March 01, 2022, 11:21:39 AM »
Yes, you need to perform calculations
44
##### Test 1 / Test 1 Wave equation and Heat equation questions
« Last post by yingxuanwang on March 01, 2022, 07:36:06 AM »
Hi Prof. Ivrii!

I wonder if we need to compute all the integral out for the heat and wave equation during the test?

Like for heat equation question, during the quiz, I found the final graded point is for simplifying the heat fomula, so I wonder if we can get full marks during test if we just simplify the fomula and leave the inside integral calculations? (I know I have had a quiz that the question cannot be integrated by it is an error function, maybe this is why we only need to simplify the fomula and leave it there)

The same question to the wave equation questions, do we need to do all detail calculations or just plug in (maybe simplify) the fomula and annotate the interval clear?

Thx!
45
##### Quiz 1 / Quiz 1 D
« Last post by ZiqiWang on February 28, 2022, 01:09:11 AM »
Here's my answer for quiz 1d.
46
##### Chapter 3 / Re: Chapter 3.1 Theorem 4
« Last post by Victor Ivrii on February 27, 2022, 07:52:52 PM »
Indeed, to be corrected. Thanks
47
##### Chapter 3 / Chapter 3.1 Theorem 4
« Last post by Zicheng Ding on February 26, 2022, 07:43:05 PM »
In the online text book, chapter 3.1 theorem 4, we have the formula for inhomogeneous heat equations. For the second integral in the formula, since it represents the homogeneous part of the heat equation and the heat equation is linear, should the range be from $-\infty$ to $\infty$ instead of $0$ to $\infty$? The equation we are solving have the range of $-\infty < x < \infty$ and $t > 0$ as usual.
48
##### Test 1 / 2020 Test 1 Q2
« Last post by kevin on February 23, 2022, 08:45:59 PM »
how did we derive 2 from 1 and 4 from 3
49
##### Chapter 2 / Textbook Chapter 2.5 Example 2
« Last post by Yifei Hu on February 21, 2022, 11:29:41 AM »
Hi Professor,

I think one coefficient is wrong in the solution.

In this problem the solution to the inhomogeneous equation with homogeneous initial condition should start with coefficient $\frac{1}{2c} = \frac{1}{6}$. After cancelling the 36 in the $f(x,t)$, we should arrive at $6\int_0^t \int_{x-3(t-t')}^{x+3(t-t')}\frac{1}{t^2+1}dx'dt'$ instead of $3\int_0^t \int_{x-3(t-t')}^{x+3(t-t')}\frac{1}{t^2+1}dx'dt'$.

Can you help me confirm if I missed something or the textbook has a typo?
50
##### Chapter 2 / Re: Derivation of D' Alembert formula under Characteristic Coordinate
« Last post by Victor Ivrii on February 21, 2022, 04:34:15 AM »
Quote
But how does this qualify us to replace the indefinite integral with the definite one?

Did you take Calculus I? Then you must know that if the preimitive (indefinite integral) is a set of definite integrals which differ by an arbitrary constant.
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