Parametrizing Surfaces, Surface Area, and Surface Integrals Part 3

[@davidyenni3455]

You are great!!!! Very good video!! Thank you soooo much!!!

[@Don-jo8gn]

Now this was an explanation if I've ever seen one

[@jonathanfarnum4884]

Why can't all women be logical like you? Great job. Absolutely wonderful.

[@amatoallahouchen5894]

ooh my lady you really nail it !!! thanks a million !

[@nathandiehl9019]

Thanks, I couldn't figure this out before watching your video.

[@zarehdarakjian2476]

May God keep you and protect you!

[@bisharakevin]

You're awesome

[@mathewj2009]

shouldn't it be dv du since the u is outer bound and v is the inner one? or is it flipped in this case? at 7:09

[@jeffgodfrey4359]

I was going to ask this same question

[@diptachatterjee8717]

very nice explanation

[@omer19telli]

god bless you!!!

[@barryhughes9764]

A little confused ! How can the surface integral result in the mass of an infinitely thin surface? Or does it compute the mass of the volume contained under the surface , given by the density function. I am not a mathematician....obviously.....it's just a hobby of mine.Any clarification would be greatly appreciated and thanks for these great videos.

[@AraDeanMaffy]

She should have said "areal-density" to be (more) precise. You could check the units to be sure: Mass/area multiplied with area = Mass . One could think of a very thin surface consisting of just one layer of atoms, summing all up you have the mass of the surface. Although you are right that mathematically an infinite thin surface should have mass zero. This is were Physics and maths collide - use your imagination ;)

[@barryhughes9764]

Much obliged for your clarification. It's instances like these that I feel impair my progress In my hobby of mathematics. For me, there should be no ambiguity in mathematical statements....it impairs comprehension of the subject. Thanks again for your reply.

[@thanhtantruongvinh99]

Very helpful! Thank you :D

[@mpyse]

answer is18pi u forgot to mulitiply the 2 from the normal vector by the v

[@TheBigBanggggg]

Not defining a physical concept like density in a math-class is pretty .... unusual.