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Messages - Victor Ivrii

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Chapter 1 / Re: More on inversion
« on: September 17, 2020, 01:58:27 PM »
Note that our inversion differs from geometric one $\vec{z}\to \frac{\vec{x}}{|\vec{x}|^2}$. It includes a mirror-reflection. See handout (I made a picture based on your example, corrected. Thanks a lot)

Chapter 1 / Re: Question about Inversion
« on: September 17, 2020, 01:27:45 PM »
Hi guys, we talked about inversion during the previous lecture and I am a bit confused by the last slide. So by definition, we have
 $z\to w=z^{-1}$, and then we can calculate the inversion of any point either by its inverse or its polar form. We have also proved that the inversion of a circle is a vertical straight line in the same slide. But I am a bit confused by the red highlighted part, "inversion is self-inverse". My thought is that an inversion of a circle is a straight line and correspondingly the inversion of that straight line is the original circle. And this property thus makes it self-inverse. I don't know if my understanding is correct so I am writing this post to look for some help. And one more brief question, do we have any restriction on inversion/self-inversion?

(btw slide pic is attached below)

First of all only circle, passing through origin becomes a straight line, and this straight line is vertical only if the center of this circle, passing through origin, is on $x$-axis.

Inversion is self-inverse means that the double inversion is identical (so, operation, inverse to inversion, is inversion itself). Mirror-reflections have the same property as well.

Chapter 2 / Re: Lecture 0201 question
« on: September 17, 2020, 12:34:30 PM »
We use $x$ and $y$ because we can exclude $t$ but neither $x$ nor $y$

Chapter 2 / Re: Boyce-DiPrima Section 2.1 Example 1
« on: September 17, 2020, 12:33:02 PM »
I think that the textbook just uses the product rule: [f*g]=f'*g+g'*f. Here, you can think f as 4+t^2 and g as y. Hope this helps.

Please, never use * as multiplication sign (which even is not needed here). Your formulas are correctly formatted, but if you surround each by dollar sign like

Code: [Select]
I think that the textbook just uses the product rule: $[f*g]=f'*g+g'*f$. Here, you can think $f$ as $4+t^2$ and $g$ as $y$. Hope this'll get
I think that the textbook just uses the product rule: $[f*g]=f'*g+g'*f$. Here, you can think $f$ as $4+t^2$ and $g$ as $y$. Hope this helps.

Again, * is reserved for a different operation, and it usage as multiplication sign may be considered as a mathematical error

Chapter 2 / Re: Textbook Section2.1 Example5
« on: September 17, 2020, 12:28:15 PM »
You can select any lower limit you wish, the difference goes to the constant. However, as Ella correctly observed, it makes sense to select $t=0$ since the $t_0=0$ in the initial problem

Chapter 2 / Re: Lecture 0201 question
« on: September 16, 2020, 03:47:54 AM »
You can investigate $f(x)$ as in Calculus I.

Also because $x=x(t)$ and $y=y(t)$ and $x=a,y=b$ is a constant solution (equilibrium). Look at the picture on the next slide. We excluded $t$ from our analysis but it does not mean that it had gone

Chapter 2 / Re: Lecture 0201 question
« on: September 15, 2020, 01:11:04 PM »
Indeed, there should be no $-$ on the right, unless I change $b-y$ to $y-b$ (which I intended to to but doid not). I updated handout, it is just a single place as on the next frame everything is right.

Chapter 6 / Re: Laplace Equation Section 6.4
« on: March 21, 2020, 09:55:28 AM »
It means that $\Theta $ is $2\pi$-periodic.

Chapter 3 / Re: 3.1 question 13 typo
« on: March 16, 2020, 10:08:38 AM »
Thanks. Fixed

Chapter 5 / Re: Section 5.1, 5.2 - ok to consider delta distribution?
« on: March 10, 2020, 08:35:56 AM »
Then you need to explain more or less rigorously, what is $\delta$-distribution and how Fourier transform is defined for it. Yes, online textbook covers this topic and much more than your physics class but in more advanced chapters, we do not cover

Chapter 2 / Re: 2.4
« on: March 07, 2020, 08:08:06 AM »
Either investigate the power series or to use theorem that if $f$ is analytic in some disc $D(z_0,r)$, then the expansion at its center $z_0$ converges in this disc.

Chapter 4 / Re: 4.1 typos
« on: March 07, 2020, 08:06:06 AM »
You seem to have a different texbook than posted

Chapter 2 / Re: S2.4 online textbook
« on: February 21, 2020, 05:09:16 PM »
The error was done before. Now it fixed. Thanks

Chapter 2 / Re: Section 2.6 Problem 2
« on: February 19, 2020, 01:11:02 PM »
Pst problem or provide a link to it

Chapter 3 / Re: Section3.2
« on: February 14, 2020, 12:51:46 AM »
Sometimes, for some functions there are shortcuts, but generally not

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