Line integrals

A basic introduction on how to integrate over curves (line integrals). Several examples are discussed involving scalar functions and vector fields. Such ideas find important applications in engineering and physics.

[rugeen]

شكرا جزيلا بروفسور
Thank you so much, prof.
Nasser from Saudi Arabia

[sanjaykrish]

Awesome Chris.. I wish India had teachers like you

[DrChrisTisdell]

@sekwah09 Yes, some pictures can help a lot with the visualization. I have used them in live lectures, but am yet to upload that particular video. I always enjoy your comments.

[muntasirsiam]

SIR .u are really awsome. and ur lecture helps a great deal.building conceptual approach towards the problem.i am from Bangladesh..and hopefully i am coming to sydney macquarie university to study mathematics .i am very much interested in applied and computational mathematics..and I completed all 18 modules of maths course..on my A LEVELS..UK.

[Kudravets-Diana]

Can someone help me with that:
C is given by
x=t^2
y=t^3
z=t^2
Evaluate the integral under the region c .
The integral is:
Zdx+xdy+ydz.
I have no idea what to do..
How to solve it :/

[ezbaby]

Please teach complex analysis Dr Chris!

[DrChrisTisdell]

You are very welcome. Best wishes to all in Saudi Arabia.

[MrGoatflakes]

Thanks for these videos. They are really helpful and to my utter amazement I have been able to follow them so far.

But unfortunately you have lost me here on what you are actually doing. Is a line integral evaluating one function along the points of the curve and integrating them all together? Like say if you have 10 tons you want to get into orbit, you would integrate maybe force with respect to distance on the curve of the rocket's trajectory?

Where do the r, the s and the t come from, and what are you actually doing when you parametise this way, and in general how do you go about this sort of problem and choosing how to parametise?

If I had a constructive criticism it would be maybe to do something a bit more physical to understand the what of it rather than the how of it. Without getting too overly complicated of course.

Finally I apologies for commenting on such an old video. But definitely the video series is still relevant so please excuse the necro :p

[Gefey]

That helped quite a bit, thanks a bunch!

[SoumyataPanja]

I thank you Sir for this wonderful video!!