User talk:Ben pcc

PDE
I finish my Finals this week, and would be interested working with you on the PDE book between December 15-January 8.

I'd suggest tapering it off into different modules, for one, rather than making it one large articles. Maybe something like:


 * Intro
 * Fourier series/integral intro
 * Separation of Variables
 * Heat Equation
 * Wave Equation
 * D'Alembert Solution
 * Potential Equation
 * Transformation for General Second-Order PDEs
 * Higher Dimensions

And then the electrical examples you've given can be slipped inbetween? What do you think? Fephisto 20:28, 10 December 2006 (UTC)

Hello,

It sounds good. But please do not have Fourier business in the very beginning. I personally self taught this whole PDE thing, and having to learn many new things all at once really made it hard for me. The thing is: there really doesn't exist a good book for self learners; you can only learn either by spending much effort or taking a class. As of now, toward the end of the article it hints that Fourier series are about to be introduced, so that's what the next chapter is intended to be. The text so far is very carefully interconnected, there's more under it then you'd see at first glance.

Oh, and could you please also maintain a printable version?

Thanks for helping,

Ben pcc 20:03, 13 December 2006 (UTC)

"The text so far is very carefully interconnected"

So, what is your plan? So I can try to add stuff without 'stepping over your toes' so-to-speak? Fephisto 16:13, 14 December 2006 (UTC)

My only plan is to start at the beginning and end at the end. There's nothing to keep you from adding stuff since this is Wikibooks. Right now I'm working on Fourier series. It should be more or less assembled today and airbrushed tommorow. I'm thinking of going deeper into the equation being used so far, introducing heat conduction in a rof, eventually go into eigenfunction expansions, then into polar coordinates. Then start a new unit on Laplace transforms. What electrical examples, by the way?

Ben pcc 19:56, 14 December 2006 (UTC)

I just looked over your contributions. You seem to know alot more math than I do (I'm an ME).

I'm willing to put what I know into this book. With that in mind, it might be a better use of your time to work on something you know that I (and most people) don't, such as the residues book (it looks really nice. I wish I knew complex analysis). I say that with great humbleness. If you feel you should contribute to this book please do so.

Ben pcc 22:44, 14 December 2006 (UTC)

"What electrical examples, by the way?"

None, I don't know why that came out of my fingers o_O. Anyways, I moved most discussions to the PDE discussion pages. Nice cover btw. Fephisto 20:41, 18 December 2006 (UTC)

Perhaps it would be a good idea to make an outline for where you're going with the whole book? I'd like to contribute more, but your train of thought is a lot easier for people to understand in my opinion. There's still quite a few more topics to hit. Fephisto 03:40, 14 January 2007 (UTC)

Hmmnn....

I'll probably go into eigenfunction expansions sooner or later into the Separation of Variables chapter. Also, Laplace's equation on a square with one side 1 and the rest zero, that's a nice but uncommon separation problem and it involves the Euler Differential equation. I think that'd be nice since solving PDEs often turns into solving unusual ODEs, and Euler's ODE would be a very gentle introduction into this.

I'm thinking of make the next chapter (not sub chapter) about transforms, both integral and discrete, but not beat it as hard as most do.

I want to go in depth on Green's function method and the conformal mappings that go with it, but that's much later on.

I really want to introduce some more complicated problems, such as pressure driven flow (that's nonhomogenous) in a circular pipe (that'll introduce Bessel Functions). Not sure when or where it'd be appropriate.

Ben pcc 19:26, 16 January 2007 (UTC)

Man, wherever you learned this went into a lot more depth than my PDE class, however, there should be a mention of Sturm-Louiville Problems somewhere, this turns into an eigenfunction problem, but it could probably be introduced inbetween change of variables and The Laplace Equation. Although, a full Sturm-Louiville treatment would be nice with abstract linear algebra; but I don't think it's necessary. Although, it's kind of a grand generalization of what you've been doing so far, so I might stick a link to it after the Laplacian article later. Fephisto 21:10, 1 February 2007 (UTC)

Heh... self taught :->. It started with a crappy book called Partial Differential Equations for Scientists and Engineers. Now I get most of what I know via the internet, I'm basically documenting what I'm learning. Really helps it sink in. I tried learning abstract algebra but that didn't work; there's too much engineer's mentality in my head and that crosses the line.

Indeed, eigenfunction expansion and Sturm Louiville theory go hand in hand. Right now I'm going in for a bit of an intermission into a slightly unrelated topic: scale analysis. I can't find ANY good document on it online, and good books on it are hard to come by too; it's mostly taught by word of mouth which horrifies me since it's rather important. It's more of an engineering thing then a math thing, though.

I was thinking of proceeding after that unit into either eigenfunction expansion, Green's functions, or transforms (integral and discrete). I also had better mention the wave equation somewhere along the way. Not sure where I'll stick that in, though. Maybe I should continue the separation of varialbes unit with it, and go in depth later.

This really nice document that taught me the relation between eigenfunction expansions and Sturm Louiville theory. That stupid book (PDEs for scientists and Engineers) made no mention that they were related.

It may be good to go into eigenfunction expansions next as I really don't have green's functions down, and I don't like most of the transforms since they're somewhat inflexible. I inted to make it a self contained unit (ie, not under separation of variables).

Thank you,

Ben pcc 03:22, 2 February 2007 (UTC)

Formatting
I like what you've been adding to the PDE book, may I make a few suggestions?
 * 1) That page is getting pretty big, and I think the time is coming when we are going to want to break it up into sub-pages with a proper table of contents and navigational templates. I can take care of that if you want, or I can help you do it. We can leave it like it is for now if you think that's the way to go for right now.
 * 2) If you want to lable an equation, we have a handy template for use, the eqn template. This template lables an equation. For instance, we can turn this:

$$\frac{\partial u}{\partial t} = \nu \frac{\partial^2 u}{\partial y^2} \qquad \mbox{(PDE)} \,$$

Into this:

$$\frac{\partial u}{\partial t} = \nu \frac{\partial^2 u}{\partial y^2} $$

Also, in some of the places where you are using the "down arrows" to show the progression of an equation, you could try centering it:

$$0 = \frac{P_x}{\nu \rho} \cdot 1^2 + C_1 \cdot 1 \Rightarrow C_1 = -\frac{P_x}{\rho}\,$$

$$\Big\Downarrow$$

$$u = \frac{P_x}{\nu \rho}(y^2 - y)\,$$

I think it looks nicer like that. Anyway, those are my two cents, feel free to take them as you like. Let me know if you need anything. --Whiteknight (talk) (projects) 23:09, 13 December 2006 (UTC)


 * That template is justified at the far right of the page, I made it that way to mimic equation numbering schemes that i've seen in other textbooks. We could possibly move it away from the boarder by a little bit, but I think if you want to have a lable closer to the equations, I could make another template to do just that. I'll get to work, and let you know what I come up with. --Whiteknight (talk) (projects) 00:30, 14 December 2006 (UTC)

Regarding your image uploads
Ben, as I was browsing through the untagged images hosted here on the English-language Wikibooks, I came across one of yours (Image:PDEBook0015.png). Would you please tag it with whatever license you would like? Also, please consider looking through your image gallery and nominating any orphan-duplicate images therein. I noticed that there are a few of them. And just for future reference, remember that you can upload an image over another image, so if you make slight modifications, you can just upload directly over your first image! I hope this helps. If you have any questions, please contact me here; I will be watching your user talk page. Cheers, Iamunknown 03:17, 13 February 2007 (UTC)

Hello unknown guy,

Thanks for the heads up. I keep in a text file a list of orphans and tag them all at once once in a while. Not recently though. I didn't know you could upload over an existing file, I tried this some time ago and I couldn't get it too work. I'll try again next time I need it.

Ben pcc 04:45, 13 February 2007 (UTC)


 * Hey Ben, make sure to tag Image:PDEBook0017.png. Since you made it yourself, you have a couple options: GFDL, public domain, CC. The default image license for GFDL textbooks is probably ... GFDL. To do that, just type  without any of the spaces. Hope this helps. --Iamunknown 05:22, 12 March 2007 (UTC)

Welcome back!
Just like to say I enjoy the PDE book so far, keep up the good work! Mattb112885 (talk to me) 23:05, 8 August 2007 (UTC)

Thank you very much! Not likely that I'll contribute as often as I did in early 2007, but I haven't forgotten about this thing. I believe that teaching is learning, so when I want to learn something... I document it. You can get a pretty good guess of what I'm working on by looking at what I just added.

But thanks again. I like knowing that it's useful. -Ben pcc 01:18, 9 August 2007 (UTC)