Line integrals and vector fields | Multivariable Calculus | Khan Academy

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Using line integrals to find the work done on a particle moving through a vector field

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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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You know why I like Sal, he assumes you know nothing, then he makes you feel like a genius because he makes you think about what's going on rather than having to rotely memorise everything that he says. Never quit Sal, this is God's work you are doing.

turbothrottletrouble
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"The only really valuable thing is intuition" [Albert Einstein]. Most professors don't seem to understand it but Mr. Khan Academy teacher does.

howmathematicianscreatemat
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You explained this is a 20 minute video so much better than my 1, 170 page textbook

mariannejasmijn
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Thank you so much for these videos, it's absolutely incredible how intuitive this is, and to think you do this for almost every level of every subject....

passivlyassertive
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Thank you so much for these videos they are helpful and insightful. They help me understand the foundation of the math I'm using!! Amazing work

kiley
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you are so funny dude. you're great! your videos touches a little of everything watching you is funny, entertaining and educational!

AntonioMudge
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Thank you so much, now I actually understand what Im integrating!

ScilexGuitar
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Because of you I'm loving maths more! Thank you very much!

Rajbhandari
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you are great, i love your vids, simple and very nice for review and to learn, thank you very very much for posting them ive learned a lot .. god bless you

kavoos
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Amazing Video!!! Really understand this now!

joshuasegal
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Great video ....simple enough to understand detailed enough for indepth knowledge.

blackwolfkills
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Thank you for these wonderful tutorials

NehadHirmiz
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This was much more concise than my professor's explanations. I appreciate it a lot. I was really worried about my quiz tomorrow.

JaredBGoode
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This video is simply awesome man Thank you very much

weiyangli
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GREAT VIDEO T.T you're a life saver

ManBearPigMike
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Sal i like the way u talk to us, u talk like a BUDDY or a friend not as a teacher or a tutor. I felt like i was listening to a friend of mine which makes it easy!

jakeaudi
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thank you so much. you are saving my life

sivhopj
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whooaaa omg everything just clicked for me! thanks so much!

silverchair
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Hi, thank you ! love your courses !

I have a small question, hope you can help me . At 8:00 in the video, the graph is a x-y plan . but why not a i - j plan ? I see the x and y is only parameter while the axel sould be i and j ? Here the x and y is like parameter 'a' and 'b' in a f (a, b) funktion?

joycewang
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you’re the best Sal, you’re the only reason I haven’t failed my physics degree so far

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