Notes: www.patreon.com/posts/105279085

this video went well with my breakfast

@dinohuntr851

2 ай бұрын

Me too!

When you explain the spherical axis, I love how you explain the laserpoint to the plane

@bprpcalculusbasics

2 ай бұрын

Thanks!

You can violate ρ ≥ 0 and 0 ≤ φ ≤ π just as much as r ≥ 0 and 0 ≤ θ ≤ 2π. The opportunity doesn't come up as much in 3D; for example, writing the area and volume elements as r dr dθ and ρ² sin φ dρ dφ dθ requires r ≥ 0 and sin φ ≥ 0 (but not ρ ≥ 0) because you need the absolute value. But if you want to parameterize a surface with φ and θ, then you might want to violate these, much like when you parametrize a curve with θ.

Literally a fly moves when he demonstrated Lazer pointing analogy to spherical coordinates (5:08)

@bprpcalculusbasics

2 ай бұрын

I didn’t know!! 😆

Very useful and clearly explained. Thank you!

Great KZread channel,, I love to watch it

Yessss calculus 3!!!

Your drawing work so well in providing a 3d view

Best video I've seen on 3d coordinates. Can you do area and volume differentials deductions for integrals?

This is performance art at its best.

Mathematician have their own logic and philosophy..let them be.

R can be negative? I thought that it was a distance...so confused!

@_MATAN_

Ай бұрын

Yes, It is the distance from the origin in the XY plain. I don't know why he said it could be negative either.

在KZread 搜尋面上的x 和y axis 似乎方向錯了。

The grid. A digital frontier.

@Gordy-io8sb

2 ай бұрын

I tried to picture clusters of information as they moved through the computer.

@Gordy-io8sb

2 ай бұрын

I kept dreaming of a world I thought I'd never see...

@Gordy-io8sb

2 ай бұрын

I got in.

Next video: Velocity and acceleration in the cylidrical and spherical plane. 🤣

@pdwag198

2 ай бұрын

*vectors

I am slightly confused when I see (r, 𝜃,𝜙) with the meanings of θ and ϕ reversed (a different convention). I would probably keep making mistakes when calculating the rotation :):):)