Computing the Surface Area of an Implicitly Defined Surface

[@noahbarrow7979]

i've watched a multitude of math videos but none are both as illuminating and as digestible as yours. Your enthusiasm for the subject makes learning rather opaque concepts easier!

[@DrTrefor]

thank you so much!

[@garmands]

This channel will be massive, no doubt about it. This is straight to the point!

[@DrTrefor]

I hope so, thank you!

[@geekoutnerd7882]

😂 I spent 1 week looking through your videos to find the volume bound by an implicit function....learned spherical coordinates and triple integrals in the process, finally I also made a summation formulae to test my results with n cubes. Thank you very much!

[@vitroid0]

ありがとうございます！

[@DrTrefor]

Thank you!

[@qutaibaaraj6416]

Top math channel ever

[@joyghosh3858]

Why gredient of z normal.we learned it to be the Stevest direction... Plz explain sir.

[@Tsoenyana]

Doc, you are the best. This is impossible. 😂🤣

[@monu_7712]

How to find surface area of the solid of intersection of two surfaces ?

[@DrTrefor]

This is basically two surface sea problems. The main difficulty is describing the boundaries of each portion

[@hrodgeeir_0259]

Respect, Sir

[@th.n.5502]

If i have a wear surface which wear has given way to the material and has created step, material retreat, then i can't describe this wear and gouge?????

[@NOR_AZIM]

Hi doc...im thinking about dS conversion to dA...what is going to be if the surface not in k-hat direction say the wall of cylinder....in this case, i wanna solve using cartesian coodinate olny neither paramaterization nor polar/cylindrical coordinate system...thanks

[@Festus2022]

What if we had a z-component function in our Gradient eg. delF= , then the denominator would be a function of z, and the numerator would also have a z-function in it. Would we want to convert to SPHERICAL coordinates to solve the integral?

[@appybane8481]

If that happens, use F(x,y,z)=c to remove z

[@j.o.5957]

Eyyy, managed to do this one on my own as well after a little thinking. Builds my confidence in mathematics. Question to self: does that mean we can ignore the 1 in z + x^2 + y^2 = 1? Sine we only look at the gradient, that constant cancels out each time, so based on this, I'm quite sure we can do so. Our parameterization also ignores it, so we're happy in that regard. But like, if that isn't 1, but a larger number like 4, then the area is clearly larger, so this doesn't make sense. Ahhh, no it does, because then the range of r would change. Yes, now it makes sense. Nice.

[@thekorben]

Hey, I'm watching all these videos - congratulations to Dr. Bazett by the way, these are just excellent - quite some time after you did and I just wanted to say that I really enjoy all your "questions to self". It's like having a class mate that always asks the interesting questions. ;)

[@quicktripgas]

Which math software do you recommend? Maple, Matlab, or Mathematica.

[@DrTrefor]

I don't honestly have a preference. I'm currently using MATLAB for most of my animations, but this is more because it is available to students at my university. I think all three are great.

[@papadatoss]

What if the we have something like a sphere? What am I going to do with the z component there? Should I add 2 explicit integrals for positive and for negatuve z?

[@klas7988]

Hello i have the same question. If you found a awnser i would be very greatful if you cound point me in the right direction.

[@Karatemaci]

In the u substitution at 6:10 the boundaries of the integral should be 1 and sqrt(5) instead of 0 and 1.

[@arunkumarpal9605]

Really sir you are great,awesome❤❤

[@DrTrefor]

Thank you so much 😀

[@sumitkumarsahoo7601]

great salute from me

[@blandconstant5548]

I might be having a brain fart(if u know what i mean by that) but when u integrated with respect to theta why didnt u actually integrate? Like if we have integral of 5z and we integrare wrt theta shouldnt it just be 5z*theta?

[@DrTrefor]

I did, but then I also evaluated theta between the two bounds

[@blandconstant5548]

@@DrTrefor just saying its nice that u anwers comments on older videos

[@consumeentertainment9310]

Can anyone verify what I am going to say? F(x, y) = combination of x and y. The gradients of F lives in 2D plane. In this case, F(x, y, z) = constant The gradients live in 3D space and tangent to the surface because all points because all points of the surface get mapped to 1.

[@husseinmhammad54]

🥰😍