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Messages - Victor Ivrii

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1
Final Exam / Re: Alternative solution to the optimization in Problem 2 on the practice final
« on: April 25, 2022, 07:51:30 AM »
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
  • $g_1=0$ (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
It will be, however, more cumbersome. Note that (1) corresponds to two rays and one arc, (2) to two corners.

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

2
Test 2 / Misprints are possible
« on: March 30, 2022, 07:17:41 PM »
Misprints are possible

3
Test 2 / Re: Sturm Liouville eigenfunctions
« on: March 30, 2022, 07:15:38 PM »
they defined up to a constant

4
Quiz 5 / Re: Quiz 5
« on: March 27, 2022, 11:44:46 AM »
Quote from: Kexin Wang on March 27, 2022, 10:06:51 AM
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 [$-\pi$, $\pi$]?
No
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 $[\alpha,\beta]$.

5
Chapter 5 / Re: Theorem 3 in chapter 5 question
« on: March 18, 2022, 08:17:41 AM »
It is the derivative of Fourier transform; otherwise it would be $\widehat{f'}(k)$ and covered by another property

6
Chapter 5 / Re: Chapter 5.3 Problem 1.1
« on: March 13, 2022, 04:19:38 PM »
You are right, it was a misprint

7
Test 1 / Re: Test 1 coverage
« on: March 03, 2022, 12:11:32 PM »
Look at samples posted

8
Test 1 / Re: Test 1 Wave equation and Heat equation questions
« on: March 01, 2022, 11:21:39 AM »
Yes, you need to perform calculations

9
Chapter 3 / Re: Chapter 3.1 Theorem 4
« on: February 27, 2022, 07:52:52 PM »
Indeed, to be corrected. Thanks

10
Chapter 2 / Re: Derivation of D' Alembert formula under Characteristic Coordinate
« 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.

11
Chapter 2 / Re: Text Book 2.4 Example 2.1
« on: February 20, 2022, 10:04:48 AM »
We integrate from $t=0$ because for $t=0$ initial conditions are done. $-1<t $ is a domain where $f(x,t)$ is defined

12
Chapter 2 / Re: Derivation of D' Alembert formula under Characteristic Coordinate
« on: February 20, 2022, 10:01:28 AM »
Reproduce formula correctly (there are several errors) and think about explanation why $\phi'(\xi)=0$.

13
Quiz 3 / Re: LEC0101 Quiz3-1c
« on: February 15, 2022, 12:46:54 PM »
It is the same answer for $x>ct$ and $x-ct$. Explain why

14
Chapter 4 / Re: Chapter 4.2, Example 6
« on: February 14, 2022, 07:12:14 AM »
Indeed, fixed. For consistency added index $_n$ to similar places of Example 4.2.7


Please post in the appropriate subforum

15
Chapter 3 / MOVED: Chapter 4.2, Example 6
« on: February 14, 2022, 07:10:42 AM »
This topic has been moved to Chapter 4.

http://forum.math.toronto.edu/index.php?topic=2654.0

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