@shakesbeer00 The parabola doesn't matter in terms of bounds because we know it becomes the unit circle in the xy plane. The double integral cares only about the xy plane, and so that's all you need to know in order to set up the integral.
18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying "above the unit disk".
Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?
I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?
@@antikomunis886 1) His field of research is mainly topology 2) He can propably teach most math classes 3) He didn't ask for real analysis classes specifically by Auroux
Finally at th-cam.com/video/WfEQabCGAqI/w-d-xo.htmlm10s the professor has a moment of joy. Interesting how he chooses to explain using either the phases or
Am I the only one to feel that cameraman is obsessed with zooming in things? That's really annoying - I am more confident in his camera('s resolution w/o zooming) than he is...
Someone please give a medal to Prof. Auroux. Genius indeed how he closed the lecture with Divergence...
20:00 "There are many paraboloids in life" ~Auroux
Man, I miss calculus! So good to see these lectures!
I love when he erases the blackboard.
@shakesbeer00 The parabola doesn't matter in terms of bounds because we know it becomes the unit circle in the xy plane. The double integral cares only about the xy plane, and so that's all you need to know in order to set up the integral.
Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)
that source minus sink analogy is really intuitive at the end
Why can't Cornell professors be this good?
Thanks for the proof of nds = dxdy
The best math teacher
Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?
In India engineers/physics students take a course like this and maths studenst atke 18.024
@@cantfindagoodchannelname7359 Which institute bro?
yeah this guy is great!
great stuff...
regards from australia!
18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying "above the unit disk".
exactly
He means the part of paraboloid which is Above the disk on the xy plane
One person disliked this video because he realized once 3d flux was explained excellently he still didn't understand it
Great lecture. Thanks for uploading.
Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?
In the formula, N appears both on top and on the bottom it is not necessary for vector N to be a unit vector.
I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?
Remember that dA is the shadow of dS, so dx and dy are the dimensions of dA.
Splendid lecture.
my lecturer covered this topic within 10 powerpoint slides-.-
@shakesbeer00 Because it's over the unit circle.
This is helpful ❤️🤍
I Really Like The Video Divergence theorem. From Your
Thanks ❤
43:00
MIT plz provides lecture of real analysis...
He is vector analysis lecturer. He can't teach other subject.
@@antikomunis886 1) His field of research is mainly topology 2) He can propably teach most math classes 3) He didn't ask for real analysis classes specifically by Auroux
This is not on the divergence theorem..
Isn't this theorem called after Ostrogradsky, since he is the first one to prove it?
yeah but pronunciation issues rose, so they changed it to divergence theorem, instead of ostorgradagsaskgsy
Antonij Mijoski why the fuck u care this man?? Jesus fcking christ, are u disrespecting Sir John Denis Auroux????
@hmpcon you have kassabov?
Finally at th-cam.com/video/WfEQabCGAqI/w-d-xo.htmlm10s the professor has a moment of joy. Interesting how he chooses to explain using either the phases or
Am I the only one to feel that cameraman is obsessed with zooming in things? That's really annoying - I am more confident in his camera('s resolution w/o zooming) than he is...
+Danny Bear Maybe his dream was to be a proffesional cameraman and he just loves to zoom in stuff dramatically (31:01)
When you clear black board sir awesome
After 25 minute lecture I not understand what you have done,please sir explain it
Mmore Olympic erasing by Denis Auroux!!
Nice
32:22 :D
He teach me how to draw
32:28 I think he missed...
lol @ 32:20 and the class reaction...
sorry to disappoint you but it's d(sigma) not dS. that MIT guy needs a reanimation.
This guy needs to take an English course.
imagine thinking having an accent means you don't know the language
Four years late but as a native English speaker, he speaks flawless English
@@atehortuajf yeah, common misconception of people who only know 1 language, pathetic monolinguals...
Please @mitopencourseware. Please label each video with the content covered in the video! I'm begging you!