18 thoughts on “Surface integral example part 3: The home stretch | Multivariable Calculus | Khan Academy

  • May 28, 2012 at 9:52 pm
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    Khan might consider not using t as a variable. It looks a lot like a plus sign to me a lot.

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  • May 28, 2012 at 9:56 pm
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    They aren't boring to people who want to learn advance multivariable calculus.

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  • May 28, 2012 at 10:26 pm
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    You'll get there.

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  • May 28, 2012 at 11:04 pm
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    then don't watch it if you're not interested in it..

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  • May 28, 2012 at 11:17 pm
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    Eh, it's a little more than two years. This is beyond AP Calc BC.

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  • May 29, 2012 at 12:09 am
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    y is the surface are of a sphere 3 x the surface area of the base of the hemisphere of the same sphere?

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  • May 29, 2012 at 12:10 am
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    Not sure which class this is. I haven't actually taken these classes, but I did do some surface integral stuff in AP Physics, so I was curious as to how it's actually done.

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  • May 29, 2012 at 12:12 am
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    Calculus III

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  • May 29, 2012 at 3:07 am
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    That awesome moment when your in algebra 2 and you understand this!

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  • May 29, 2012 at 4:18 am
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    wish this came out 1 month earlier, even 2 weeks

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  • May 29, 2012 at 8:26 am
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    I haven't had this yet, I'm doing Calculus 2.

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  • May 29, 2012 at 2:05 pm
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    This is my study music!

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  • May 29, 2012 at 5:35 pm
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    Multivariable calculus is dealing with more complex shapes than normal calculus (1D [just x varies] vs 2D [x and y vary] vs 3D [x, y, and z vary] for example). It's extremely useful for surface analysis and fluid-dynamics where things are changing over time. Differential equations are a technique often used in conjunction with multivariable calculus.

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  • May 31, 2012 at 8:42 am
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    In my opinion you spend a bit too much time on the manipulations.. like I can see cos^2+sin^2=1, I dont need you to redistribute and then cancel it out in that much detail. I would like a bit more time spend on the concepts, like what is the cross product, why do we need |r_s x r_t|, etc.

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  • December 10, 2012 at 5:29 am
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    You are so great. Thank you so much for this and other videos. You teach with such clarity, and you teach us more than the concepts. The pictures and explanations put the formulas into reality. I LOVE your explanation of the parametrization of surfaces. I really see now how the t-component behaves, and how it relates to sin and cosine, and r. Thanks a million.

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  • July 11, 2013 at 7:41 pm
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    Is Sal color blind!

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  • August 23, 2015 at 2:00 pm
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    The s's and t's got all scrambled in the last minute or so. The blue should have been only s's.

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  • July 16, 2016 at 11:41 pm
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    great video ever

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