Position vector valued functions | Multivariable Calculus | Khan Academy

Using a position vector valued function to describe a curve or path
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Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.
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[@billymcgregor2067]

Wait a minute that's not grant's voice

[@chao.j]

set playback speed to 1.25 x, it starts to sound like grant :-)

[@That_One_Guy...]

@@chao.j it's only you who think of that

[@armstrongtixid6873]

That's Sal's. Sal took over for a bit, but Grant did most of the work ;)

[@donwald3436]

Grant took too much testosterone that day.

[@mukarrammallick7546]

@@donwald3436 NAILED IT. XD

[@andrewdavies5722]

graaaaaant!!! come back.... nooooooo!!!

[@souvikroy6237]

😂 i can understand your feelings

[@Mathieu-qx7bp]

Well... I prefer Grant's voice, but you gotta admit Sal's writing is way better here x)

[@y.a.46]

I feel betrayed. Comeback Grant. His enthusiasm really made it easier to understand.

[@theovisbecq33]

Does Grant come back in future videos of the serie ?

[@MayankGoel447]

Yup just 2 videos later

[@kamalb]

Sal?

[@iwtwb8]

The transition is jarring.

[@bhavna6565]

Kamal Banga nooooo man i need grant back on this one

[@nickmilkshake2661]

Agreed

[@micahdelaurentis6551]

what work have we been doing with line integrals?

[@carultch]

Probably in a previous video, he gave other examples of how to do line integrals.
An application of line integrals, is physical work. If the vector field represents a force field, then a line integral along a space curve will give you the work done by that force field, as an object takes that path.

[@tielessin]

No panic! It's just 4 videos that'll prepare you for the coming multi variable calculus concepts that Grant will teach you after that.

[@oneinabillion654]

*SAL APPEARS*

[@iekenta03]

Awesome dude. You have no idea how many people you help out with this :).

[@bat102]

at the beginning of the video "line integral " is mentioned which hasn't been covered in the videos prior to this in the playlist, is it due to a mistake in the items' order?

[@ihibthegreat5343]

its same way on the actual sight. Probably an artifact from before Grant from 3blue1brown did the first part.

[@sams6454]

if you watch it on khanacademy.com it is fixed and edited out.

[@smolytchannel5062]

This video is 6 years before the previous one. So yeah maybe

[@sheldonwu1285]

scalrrrrrr, vectrrrrrrrrrrrrrrr🙃

[@BareClause]

me not happy atm lolz

[@esmondlucan4269]

GEOMETRIC FORMS CAN BE REDUCED. TO LOGARITHMIC. FORMS WHICH CAN BE FURTHER REDUCED TO ALGEBRAIC FORMS

[@jaakkokuu]

Once again. you make this so easy to understand.

[@michaelhernandez2724]

The vector-valued function generates each of the terminal point of the position vectors evaluated at t- value specifying a point on the plane curve.

[@kaustubhpandey1395]

Hello Sal, where was Grant?
Edit: Oh this was years prior

[@dreia2405]

You are a great teacher, thank you

[@tomaslopez814]

Grantdaddy?

[@johnr1875]

does it matter that the curve, C, is not a function? is it because its parameterized?

[@elvinespino5957]

Thanks, man! The transcription at the bottom helped a lot

[@samuelleizerman5832]

***** click on the cc logo that says captions when you mouseover it, then click off.

[@v7e4n8om]

Vector Equation of a line!!!! pls

[@hermonokhidievbie6593]

ikrr

[@That_One_Guy...]

Check linear algebra playlist

[@nevilholmes5900]

Thanks

[@sidindian1982]

Finally sir is back 🙏🙏🙏❤️❤️❤️😍😍😍

[@yichizhang795]

Awesome!

[@halogenhali583]

Greaaaat

[@emmanuellagalley7914]

I love it😍🤭

[@scholar-mj3om]

Marvellous💯

[@Raikaska]

I thought the curve was "C", not "S"

[@agrimsingh001]

sal is back

[@matthewwroblewski8752]

Kewlio dadio

[@HabiburRahman-xs9gb]

in simple language, position vectors must have an starting point which is (0,0)...right?

[@Suarsaa69]

Somehow I am able to understand Sal's videos even at 1.75x, but not grant's 8(