Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus

When a vector field is a velocity field, a natural phenomenon we can measure is the Flow. This accumulates the tendency of the vector field to be tangential to the curve. If we imagine our field is a velocity field, the flow is measuring the degree to which a curve just naturally flows along with that velocity field. As a line integral, this is identical to our formula for work, it is just interpreted differently physically. When the path is a closed curve - i.e. starts and ends at the same point - then the flow integral is called the circulation of the vector field along a path. We see as examples a source field which has no flow and a spin field which has lots of flow.

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[tomscholten]

At 4:33, the last integral has boundaries a to b, but shouldnt that be C. Atleast accoording to the book it is C

[peterfriedman]

I'm not sure why Mr. Bazett's videos don't have more likes. All these (Multivariable Calculus) videos are fantastic! Thank you so much!

[adamsusel]

This man saving my life right on time. Doing vector calc in calc 3 right now. Could not have been better timed to post!

[CaptchaSamurai]

The joy of feeling vector calculus is immense. Thank you for this concise, amazing series! ε>

[mbelekamohelo]

We appreciate the visualizations, they jus blend perfect with the concept.

[juncarlin]

I have to admit that this video is the best one I've ever watched about flow integrals.

[leadtoexemplify]

I like the energy and the passion with which you are explaining them. thanks

[qamarmoavia]

Thanks a lot :) . Dr. Trefor you always change implicit into explicit . LOVE YOU

[harshaniperera]

Thank you sir !I am following your videos since 2 years .Now I am studying physics as my major subject. Still helpful to fulfil the foundation of every theory in physics and mathematics . Live long with good

[abstractnonsense]

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[cosmefulanito]

Greetings from Argentina!!! keep on the good work, thank you

[xandiczr]

Those videos are just priceless! Thanks for the time!

[leadtoexemplify]

God and Knowledge is always with those selfless individuals who spread knowledge. God bless you

[continnum_radhe-radhe]

Thank you so much sir for making these wonderful awesome videos 🙏🙏🙏

[hectorgalva]

Awesome doctor, I like a lot your videos, your are very intuitive and I can understand better the wonderful of math.

[momen]

this is the best channel for math ..
I have some questions
* Is ds =|dr| ?
& ds=|dr/dt|*dt=|V|*dt
& dr=dr/dt=V*dt ?

[julioreyram]

Nice examples. As always, good concept discussion and illustration. Thanks! :)

[hubenbu]

First time to see the integral finger with a ring. haha
Calculus: An Intuitive and Physical Approach by Morris Kline appears to be a great read.

[continnum_radhe-radhe]

Sir, please make videos on gamma and beta function
.... 🙏🙏🙏

[abdelstar]

really love you, thak you so much. very useful