Thread Closed

stock's theorem?

 
Share Thread Thread Tools
Sep16-04, 01:14 PM   #1
ori
 

stock's theorem?


c is a curve of the cutting of the to surfaces:
x^2+y^2=1
z=xy
at the point (1,0,0) the tangent to C is toward j^
so what is
S(xz^2-y)dx+(3x-yz^2)dy+(zx^2-zy^2)dz
C
?

hmm..
i calculated this vectorian field rotor: it's (0,0,4)
i know i should use stocks and make it
SS(0,0,4)*n^ ds
but how can i build a surface (so i could know the integration borders and what is the normal)?

thanks
PhysOrg.com
PhysOrg
science news on PhysOrg.com

>> Bird's playlist could signal mental strengths and weaknesses
>> Minus environment, patterns still emerge: Computational study tracks E. coli cells' regulatory mechanisms
>> Bacterium uses natural 'thermometer' to trigger diarrheal disease, scientists find
Sep16-04, 10:56 PM   #2
 
Recognitions:
Homework Helper Homework Help
Science Advisor Science Advisor
come again?
Sep17-04, 08:11 AM   #3
 
Recognitions:
Gold Membership Gold Member
Science Advisor Science Advisor
Retired Staff Staff Emeritus
(Ori, I hope you are not offended by our confusion. I assume that English is not your native language and I assure you that your English is far better than my command of whatever language is your native language!)

I'm not at all sure what "stocks" are here and I THINK that "vector rotor" is the curl. I'm pretty sure this person is using "S" to indicate integral and the problem is to integrate the vector function (xz^2-y)dx+(3x-yz^2)dy+(zx^2-zy^2)dz
around the intersection of the surfaces given by x^2+y^2=1 and z=xy.

Aha! Stoke's theorem! x2+ y2= 1 is the cylinder along the z-axis. We can write that in parametric equations as x= cos(θ), y= sin(θ), z= z (with θ and z as parameters) and the intersection of that with z= xy is x= cos(θ), y= sin(θ), z= sin(θ)cos(θ).
Integrating the vector function around that curve would be tricky but doable. To use Stoke's theorem you need to find the curl of the given vector function.

You don't really need to find an expression for a surface inside that boundary. The nice thing about Stoke's theorem is that it applies to ANY surface having that boundary.

Take as your surface the surface z= xy itself. Here is how I would do it:
f(x,y,z)= xy- z= 0 has z= xy as a "level surface": div f= yi+ xj- zk is perpendicular to that surface and we can "normalize" to the projection onto the xy-plane by dividing by the k component: Integrate the dot product
((xz^2-y)i+(3x-yz^2)j+(zx^2-zy^2)k).(-y/z, -x/z,1)dx dy.

You will, of course, need to use z= xy to reduce the integral to x,y only. The integration is over the unit disk so you may want to convert to polar coordinates.
Sep17-04, 09:54 AM   #4
ori
 

stock's theorem?


10x
my native lang is hebrew
Sep17-04, 04:59 PM   #5
 
Recognitions:
Gold Membership Gold Member
Science Advisor Science Advisor
Retired Staff Staff Emeritus
Your English is fine. It is "Stoke's theorem", not "Stock's" and "vector rotor" for "curl" makes sense to me! I've also noticed that in another thread you referred to Green's "sentence". The English word is "formula" (if not "theorem").
Sep17-04, 05:26 PM   #6
 
Oh right Stokes' Theorem--- I was wondering for a second hehe.
Sep18-04, 02:03 AM   #7
ori
 
look guys
if i was writing stoke's theorem it was borring
if im writing stocks theorem, it's attracts ppl to read - maybe there's a new mathmatical theorem about stocks etc.. plus it sound like stoke's..
(kiddin , it just a spelling mistake)
Sep18-04, 10:24 AM   #8
 
Recognitions:
Homework Helper Homework Help
Science Advisor Science Advisor
by the way, the original term for curl, in maxwell's book, was "rotation". and "stokes" theorem is apparently due originally to lord kelvin.
Thread Closed
Thread Tools


Similar Threads for: stock's theorem?
Thread Forum Replies
greens theorem and cauchy theorem help Calculus & Beyond Homework 4
Gauss' Theorem/Stokes' theorem Advanced Physics Homework 2
Mean Value Theorem Calculus 8
CPT theorem General Physics 6
Gauss's Divergance Theorem and Stokes's Theorem Classical Physics 1