dr peyam, could you make a video about the "metric tensor" and general orthogonal coordinates? it's talked about in physics a.l.l t.h.e t.i.m.e and this would fit nicely to what you're covering right now.
Excellent video, genius at all... I made a challeng in an earlier video, cilindrical coordinates... it is really an ask, I arrived to infinity using pure calculus, without Gauss. Thanks a lot, go on with maths.
Showing z^2 = y^2 + x^2 is a cone is an important step. Of course, it is obvious that x^2 + y^2 = r^2 is indeed a circle, and that for x = 0 or y = 0 we obtain w^2 = z^2 where w = ( x or y ). But it should be shown as well that for any vertical (fur-tickle) plane those two lines are just rotated or spun (more fun!) around! Otherwise we have circles that are fixed by the x-z and y-z planes.... which does define the cone in a rigorous manner, but still, there are some savory tid-bits to munch on in that analysis. Showing that w^2 = z^2 are w = + or - z and z = + or - w is the easy part. Intersecting an arbitrary fur-tickle plane with the cone and finding the equations of those lines is a bit more challenging exercise.
I have 1 question. If a double integral of a function having variables gives the volume under the function, then what does the triple integral gives us? Does it give us the volume under a function with 3 variables?
dr peyam, could you make a video about the "metric tensor" and general orthogonal coordinates? it's talked about in physics a.l.l t.h.e t.i.m.e and this would fit nicely to what you're covering right now.
Excellent video, genius at all... I made a challeng in an earlier video, cilindrical coordinates... it is really an ask, I arrived to infinity using pure calculus, without Gauss. Thanks a lot, go on with maths.
Nice Dr
Excellent video! Wonder what the integral would look like in Oblate Spheroidal coordinate system. Cheers
I love this videos in which you integrate an icecream
wow...perfect
Showing z^2 = y^2 + x^2 is a cone is an important step. Of course, it is obvious that x^2 + y^2 = r^2 is indeed a circle, and that for x = 0 or y = 0 we obtain w^2 = z^2 where w = ( x or y ). But it should be shown as well that for any vertical (fur-tickle) plane those two lines are just rotated or spun (more fun!) around! Otherwise we have circles that are fixed by the x-z and y-z planes.... which does define the cone in a rigorous manner, but still, there are some savory tid-bits to munch on in that analysis. Showing that w^2 = z^2 are w = + or - z and z = + or - w is the easy part. Intersecting an arbitrary fur-tickle plane with the cone and finding the equations of those lines is a bit more challenging exercise.
Of course, I’ve ignored circular symmetry here :). z^2 = r^2. However, the exercises suggested above are still of interest. Linear transformation!!
❤️
I have 1 question. If a double integral of a function having variables gives the volume under the function, then what does the triple integral gives us? Does it give us the volume under a function with 3 variables?
Hyper volume
@@drpeyam ok, thank. Need to check this
@@drpeyam Couldn't we say it's the mass if the function describes the density?
After using double angle formulae to integrate sin(phi)cos(phi) I got a little confused as to why I was getting a different result, ah well.
Rho equals plus or minus one! Fur-tickle angle? :). Rhodius? Using Rhodium? (Don’t slip on the Plasmodium!)
en.m.wikipedia.org/wiki/Plasmodium