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anonymous
 one year ago
"Since integral curves can’t cross an integral curve itself is both an upper and a lower fence"
Can anyone explain this for me a little more. I'm not sure if i'm getting it right.
I kind of understand this
"An integral curve is also a fence of both types"
The quote is a Remark in this
http://ocw.mit.edu/courses/mathematics/1803scdifferentialequationsfall2011/unitifirstorderdifferentialequations/geometricmethods/MIT18_03SCF11_s2_5text.pdf
anonymous
 one year ago
"Since integral curves can’t cross an integral curve itself is both an upper and a lower fence" Can anyone explain this for me a little more. I'm not sure if i'm getting it right. I kind of understand this "An integral curve is also a fence of both types" The quote is a Remark in this http://ocw.mit.edu/courses/mathematics/1803scdifferentialequationsfall2011/unitifirstorderdifferentialequations/geometricmethods/MIT18_03SCF11_s2_5text.pdf

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437290124325:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Because to go outside the fence requires to cross the fence; at the point of crossing, there will be two different slopes. But the direction field allows you to have only one slope at a point.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for answering, i knew that. I just got confused by that specific remark, like how an integral curve itself could be both an upper and a lower fence, arent the integral curve suppose to be between them (if conditions says so)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so the solution curves inside the fence stay inside forever the solution curves outside the fence stay outside forever dw:1437290828331:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh. I think i get it now. So the red integral curve is algo being a lower fence for the purple integral curve.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Btw, i know that if an integral curve is inside a fence it never gets out, i'm just wondering about that specif remark saying an integral curve is also a fence

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yes that follows from the fact that the integral curves cannot touch each other

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks, i think i understood

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1the fence shown in the diagram is indeed an integral curve

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1don't get tricked by the word "fence"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437291167999:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry you lost me again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i meant i'm lost again xD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0straight black lines are also integral curves, why?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, they are integral curves, it is given.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it? it just says those lines are fences and that any integral curve between them will remaing there forever. How comes those fences are now integral curves.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1If they are not integral curves, then there is nothing stopping to have a solution curve like this : dw:1437291488143:dw