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**Test 2 / Re: 2022 midterm 2 solution: Possible typos?**

« **on:**March 25, 2023, 06:48:46 AM »

Thanks! Fixed

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Thanks! Fixed

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Section 4.1ODE is not enough. You need to take into account also boundary conditions. See Section 4.1

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If domain is "simple" in the appropriate coordinate system it is a good idea to try to find such solutions. For linear equations we even can construct general solutions as linear combinations of such solutions. Details in the class later.

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I will post solutions to show that all the integrals can be computed using elementary functions and $\operatorname{erf}(.)$

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Yes––as long as you post your variant solution

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yes, it is

Please write more legibly. Look how I corrected your previous post

Please write more legibly. Look how I corrected your previous post

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Part $u$ is also linear and homogeneous$. Thus the *correct and precise answer* is linear homogeneous.

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Yes, it can be solved using Lagrange multiplies. However note, if restrictions are $g_1\le 0$, $g_2\le 0$, $g_3\le 0$ you need to consider

No, you need not consider quadratic forms after you found all suspicious points. It would serve no purpose.

- $g_1=0$ (and $g_2\le 0, g_3\le 0)$); there will be
**only one**Lagrange multiplier at $g_1$. Two other cases in the similar way - $g_1=g_2=0$ (and $ g_3\le 0)$); there will be
**two**Lagrange multipliers. Two other cases in the similar way

No, you need not consider quadratic forms after you found all suspicious points. It would serve no purpose.

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they defined up to a constant

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My question for Quiz5 was to decompose a function into full Fourier Series [0, $\pi$]. I wonder is it equivalent as decompose into full Fourier Series on [$-\pi$, $\pi$]?

Quote

I understand it is equivalent when the function is even, but I'm wondering what should I do when the function is odd.What is the problem? There are formulae for interval $[\alpha,\beta]$.

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It is the derivative of Fourier transform; otherwise it would be $\widehat{f'}(k)$ and covered by another property

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You are right, it was a misprint

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Yes, you need to perform calculations