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Thanks. Currently, I only know how to solve for a volume integral dV = r dr dtheta dphi with the bounds being two constants for r, 0 —> pi for theta and 0 —> 2pi for phi.
Also, how does a surface integral work? I need to know this for one of Maxwell's Equations (Gauss' Law).
EDIT: I'm weak at geometric analysis. Most I can figure out is simple double integrals, like say, getting the area using double integrals of a region bounded by 2 curves and a line.
edited 6th Dec '09 11:21:53 PM by Mapichan (weaving)
Okay, let's take a look at the following:
Consider the area which is being integrated. 0<x<1 and 0<y<x. This can be written as 0<y<x<1, or 0<y<1 and y<x<1. Thus, we get the second integral being the same as the first. (I think I might be violating mathematical rigor in switching integrals at all, but you're an engineer so you don't need to worry about that—only crazy math majors like me have to worry about rigor.) Basically, write things in terms of a<x<b, where a and b can be based on the variables on the integrals outside of the one with that variable but not on those inside. Hopefully what I'm saying actually makes sense. edited 6th Dec '09 11:34:12 PM by WilliamWideWeb SHIKI is dead.
Wait, what about Fubini's theorem?
EDIT: Oh, Fubini's only applies to constants I think. No wonder it doesn't always hold. I'm still trying to digest this, but thanks a lot William!
edited 6th Dec '09 11:42:32 PM by Mapichan (weaving)
edited 6th Dec '09 11:42:47 PM by WilliamWideWeb SHIKI is dead.
Okay, now I understand. Thanks a lot!
Thank goodness all the triple integration I'll be doing will involve having 0 —> pi for the bounds of theta and 0 —> 2pi for the bounds of phi in spherical coordinates.
(weaving)
You're welcome. (Also, see that image up there? The first time I uploaded it, I accidentally had "x" instead of "y" as the bound in the second integral. I am the king of stupid mistakes.)
edited 6th Dec '09 11:49:37 PM by WilliamWideWeb SHIKI is dead.
I didn't notice. At least I finally understand why Fubini's doesn't always apply. ^{ anecdote}
As for surface integrals... since I don't know what a line integral is (yet), I can't figure this one out.
edited 6th Dec '09 11:55:52 PM by Mapichan (weaving)
I'll explain that part once I can drudge back the old memories from Calc III, since it's been two years and my later classes haven't done much multivariable stuff.
SHIKI is dead.
Woah, you seriously are pro at this. Thank goodness I found this thread; this might make math a bit easier alongside the physics I've got.
Take your time William; our next exam in Electromagnetics is sometime in January, after Christmas break, so only then will I truly need to know surface integrals to use Gauss' Law properly.
edited 7th Dec '09 12:01:42 AM by Mapichan (weaving)
Alright; the line integral stuff is sort of coming back to me. A line integral can sort of be seen by thinking about a curve as a set of functions; x(s), y(s), and z(s). Usually x'^{2}(s)+y'^{2}(s)+z'^{2}(s)=1 so that s is arc length, but that isn't always necessary.
And when the integral of F(x, y, z)ds over a curve C is talked about, it's basically a normal integral of F(x(s), y(s), z(s))ds where s is a variable that parameterises the curve.
Surface integrals are similar but I think parameterisation of them is a bit harder because of Gaussian curvature^{ *} and the like.
SHIKI is dead.
Oh no, I have to go back to parametrization. Yes, time to review some old notes. At least I know somewhat how a line integral works now.Thanks again; I'll return to this post once I've brushed up on parametrization.
Surface integrals are similar but I think parameterisation of them is a bit harder because of Gaussian curvature
Exactly. Because Gauss' Law is this:
So yeah, Gaussian curvature indeed. Although in class, we defined it as D = E(8.854 x 10^12 F/m) or epsilon subzero, but we retain the surface integral as dS. edited 7th Dec '09 12:17:26 AM by Mapichan I see the Awesomeness.
Riiiiight, I'll leave the math to WWW since he's better at this than I am.
(weaving)
Surface integrals over spheres and the like? I'm pretty sure I always used this to actually calculate those.
SHIKI is dead.
Defining flux as the action of a vector field inside a Gaussian surface... That's exactly what Gauss' Law is in electromagnetics, as in conceptual terms, Gauss' Law says that electric flux through a Gaussian surface is equal to the charge enclosed.
I think I just received an epic case of Fridge Logic. O__o
(weaving)
Notice how the Gauss' law page has a differential and an integral version?
The integral and differential forms are related by the divergence theorem, also called Gauss's theorem. Each of these forms can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge, or in terms of the electric displacement field D and the free electric charge.
SHIKI is dead.
We use the second, using D. This... this is awesome, yeah that's what it is. Heh.
I'm such a nerd, aren't I?
(weaving)
You're talking to the person who proves theorems for fun.
SHIKI is dead.
^{ 143} Hydrall, Mon, 7th Dec '09 12:41:20 PM from The Bodhi System
Relationship Status: Above such petty unnecessities The Republic Lives
Can you guys help me with my english homework?
I have to write a compare/contrast essay for The Weary Blues, by Langston Hughes, and The Bells, by Edgar Allan Poe. So my topics have to be sound and rhythm. Pretty simple, got plenty of things to say, but I just can't come up with a thesis!
I have no idea what to do.
edit: ...Seriously? Either my teacher misspelled both of their names, or we lack a page on Poe.
editedit: Allan?
edited 7th Dec '09 12:42:17 PM by Hydrall ^{ 145} Fawriel, Tue, 8th Dec '09 9:12:01 AM from the bottom of my heart
Relationship Status: If it's you, it's okay THE MEEK
Ah uhm yes! I'm sorry, I really should've replied earlier. I wanna say thanks for the help I got for my earlier question, but... since I'm just supposed to make a simple presentation that won't even be graded, buying books for that seems a little overkill. Of course, now I actually have some points planned out*, so I'm gonna go ask for suggestions right at the source in the Anime&Manga subforum.
* No, Fawriel, asking people for help with some poorly defined problem will not magically tell you what to do. Geez.
edited 8th Dec '09 9:12:20 AM by Fawriel SHALL INHERIT THE EARTH
Does anyone know what the current situation in Copenhagen is?
You can't even write racist abuse in excrement on somebody's car without the politically correct brigade jumping down your throat!
http://www.copenhagendiagnosis.org/
Might help.
Oh, and I think this is their official site:
http://en.cop15.dk/
edited 8th Dec '09 4:15:32 PM by Penguin 4 Senate I see the Awesomeness.
Can someone give me a quick review on how conduction and convection work, I'm good on radiation but I had a shitty fluids professor?
edited 8th Dec '09 5:31:14 PM by Deboss Maid of Win
Hydrall, I work at an English writing help centre, so I'll try to help you out as best I can with your thesis statement.
Firstly, consider what exactly it is you want to write about. "Sound and rhythm" are the what; but what about them? Why are they important to the story? What is their effect on it? How are they used? Consider these, and then consider if any of the answers to those questions strike your fancy enough to want to write 1500 words about it.
Once you've got your basic idea in mind, get to writing a simple sentence outlining your idea. A device I use to get the idea into a single sentence is "I want to tell you about how in (the stories here), [...]". Take that phrase, then fill in the ellipses with a nice sentence that follows from that exact phrase. Once you've got something, cut everything before "in", and you'll have a basic thesis statement. For example, "edited 8th Dec '09 5:56:29 PM by Ronka87 Thanks for the all fish!
Our philosophy prof has given us his blessing to be "creative" for our paper about "an intellectual throwdown" between Descartes and Hume. I'm thinking more of a smackdown. A rap battle or something. Free verse. Limericks.
Suggestions?
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