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I "greatly dislike my inability to understand" Stokes and his stupid theorem, help please(calc)

T

Turin39789

Lifer
I cannot get the hang of this, I was going to go to the proffesors office today, but no I had to take my car in for service and work, so i didnt have time to catch a bus downtown.

Anyway

F(x,y,z) = e^(-x)i + e^xj + e^zk
C is the boundary part of the plane 2x+y+2z=2 in the first octant

So I have Stokes Theorem that intF dot dr = curlF dot dS

I have found the curl to be e^xk
I dont know where to go from here, how to work dS or set my intervals
Every example in the book deals with a frikken cricle or such, and they always go through like 4 trig substitutions and convert to polar coordinates which make their integrals pretty and give them boundaries. I dont know how to deal with the triangle or even what exactly dS is. Ive been working for hours and am becoming numb reading the same pages over and over.

Please Help guys
 
Originally posted by: Turin39789
Thanks for the help, but any chance you could walk me through it? Im not sure how to set it up, I learn better by example.
Click to expand...

hahaha@title change



sorry dude, i havent done this stuff in like 4 years, you dont want my help. i barely remeber it.
 
thats alright, thanks for ducking in and keeping me at the top, I'm scouring the internet now trying to find a better resource than my book
 
I'll give you a quick and dirty explanation:
- you can use an oriented surface and do a double integral of the curl over that surface

OR

- you can parametrize your boundaries into a curve r(t) (in this case you will get a piecewise function) now use int( F(r(t)). r'(t), t)
I won't bore you with the details, but either way works. Meanwhile I've got to be in class for a final in less than 8 hours so I think I'll get some shut-eye now


PS: dS is an oriented surface

Good luck on your final/assignment/whatever-the-hell-you're-trying-to-finish
 
guess thats the crux, hadnt considered having to do it piecewise. My boundary curve is essentially a triangle. Ill try that in the morning, going to crash now. Was confused when i ended up with 3 variable in a double integral and needed an exact answer.
 
Originally posted by: Turin39789

F(x,y,z) = e^(-x)i + e^xj + e^zk
C is the boundary part of the plane 2x+y+2z=2 in the first octant

So I have Stokes Theorem that intF dot dr = curlF dot dS
Click to expand...

I get a headache just looking at that...

Grasshopper
 
don't feel bad...I learned all this and went on to do well in Linear Algebra and Differential Equations and six years later i remember hardly anything...I remember studying the Stokes theorem but thats it..

i guess my point is, look at this as more of a lesson on learning to learn more than learning stokes theorem, cuz if you're like me, thats what you'll take from this six years from now...learning to find/learn solutions.


...or should i have just put "bump"?
 
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