Surface Integrals

[masoncobb]

For anyone wondering about the derivation of the unit normal vector for the sphere: The normal vector for a sphere centered at the origin is always <x, y, z>, as this is the vector field that points radially outward from the origin. To derive a unit vector, it is the vector itself divided by its magnitude. The magnitude of the vector is found by taking the square root of x^2 + y^2 + z^2, with the x, y, and z coming from the x, y, and z components of the vector we are finding the magnitude of, which is just <x, y, z>. As given in the equation for the sphere, x^2 + y^2 + z^2 =4. Since the magnitude of the vector is the square root of the quantity x^2 + y^2 + z^2, which is equal to 4 by the equation for the sphere, the magnitude is found to be equal to 2. The original vector then just needs to be divided by the magnitude, hence the 1/2 out in front of the <x, y, z> for the unit normal vector.

[schrodingerscat]

i don't know who spread the word that calc3 was easier than calc2 but no

[esenniiazov]

change speed to 1.25
Your are welcome!

[jonathanrivera]

Very organized and consciousness towards different audiences. Color coded, preview, nice! Well done!

[cmdrbobert]

I'm a bit confused about how you are calculating n hat dot dS. Why <-fx, -fy, 1>? did you take a derivative some where?

[EricPham-uibt]

If we use geometric element like square or circle like pixel in computer term on one dimension then intergate on a limited range and domain and error trapping method

[ModernTruthRevelation]

GOSH THAT IS AWESOME. PLEASE MAKE THAT EXCELLENT WORK CONTINUE

[boletokuchhbhi]

the best explanation of surface integrals
thank you sir

[andresmena]

BEST EXPLANATION EVER OD DOUBLE AND SURFACE INTEGRALS> I LOVE THAT YOU COMPARED BOTH OF THEM TO SHOW THE DIFFERENCE AND SIMILARITIES AS WELL AS GAVE ALL THE POSSIBLE CASE. AMAZING VIDEO!!

[frankyesjosh]

Wonderfull lf you have problem for sleeping !

[bulldawg]

You glossed over too many details in the sphere example. Could use more detail on normal vector determination, too. Overall, very helpful.

[ananurlaila]

When F= (yz + zx + xy ) through an area S which is part of a circle with radius a in the first quadrant of the xy plane. Calculate the flux?

[kewtomrao]

Not bad! But our sirs explanation is top class n he recommended everyone to check this vid out. He has 22 research papers!

[akashchaurasia]

solve one question by taking surface of ellipsoid.

[SSJPokaLink]

Doubt this will be seen before my final lol, but can anyone help explain how he derives the normal vector in the second example?
Since he's using the formula form that converts the vector field into a scalar of two variables, I want to think we need to some rphi X rtheta cross product, but I'm sure I'm just thinking about getting normal vectors wrong.

[thomasdiprima]

Surface area of a sphere = 4pir^2 which would be 16pi for this problem. How did he get 32pi?

[adosar]

why ds=dv/dρ and not ds=dv/dθ or ds=dv/dφ?

[scimitar]

When youre doing the unit vector, why dont you divide it by its magnitude?