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Line integrals: path dependence | MIT 18.02SC Multivariable Calculus, Fall 2010
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- เผยแพร่เมื่อ 2 ม.ค. 2011
- Line integrals: path dependence
Instructor: Joel Lewis
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
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On a) I found it easier to parameterize as follows:
x = 1 + t
y = 1 + 3t
with t from 0 to 1
I did the same, using the method we learned to parameterize lines
i am from argentina and i can undertand this guy better than my college teacher
I'm in USA and this is WAY better than my graduate teacher.
Great explanation, clear examples and good teacher!!
Thank you MIT for this video! Very clear and easy to follow. Calculus would be a lot more enjoyable if my professor was as clear as this. I should submit an application!
-Dylan Miller
It shows the sad state of American education that this only has 3,373 views.
Thanks Joel Lewis for being an excellent lecturer.
but the whole world has access to youtube.... not just america
The vector field Joel is defining is not conservative (it is not the gradient of a scalar function). I chose the parameterization as x=2t and y=4t^2 with 0.5
Oh duuh :) I noticed the title is "Path dependence of line integrals", then of course different parameterizations or paths will yield different answers. Hence he chose the vector field as non-conservative...
Is it wrong to choose the parametrization: x = 1+t and y = 1+3t with t varying from 0 to 1 for the first curve, in part a?
no it is absolutely correct any parametrization will work just avoid non defined functions for example if x takes the value 0 do not take the parameter t such that x = 1/t.
Your parametrization makes the calculation easier than that of the teacher does.
I did the same and I got the same result as the instructor, so I'm guessing that it isn't wrong.
I thought work done is independent of the path taken.. so why is the line intergral path dependent?
This was so helpful!
Thank you very much! It helped me greatly.. Now I am understand it. :D
This is very clear. Thank you.
thank You ..MIT ..great video
I don't see the point of introducing a new variable t, that just seems to be more work to do. Is there any particular reason for that or is it just a fancy approach ?
This helped so much
this was helpful but you jumped some steps and it made it a bit challenging to understand
how to do for 3 variables
just parametarize a given curve using one parameter, t, as he did.
For 3 variables you need to parametarize using 2 parameters. For example in case of sphere of radius a you need to use phi and theta.
i like your smile before you talk anything XD
+lim linkua Xd