These are too good. I spent days reading abstract definitions and formal explanations in books to understand concepts this professor explains so vividly and creatively with 10 seconds! Thank you!
30:00, the way to remember it is that the work is a straightforward dot product of F with , M goes with x and N goes with y and we add, and the flux is a dot product of F with the same vector rotated pi/2 so N goes with x and a minus sign with few choices left for M. Auroux missed a nice opportunity at the beginning to clarify the sign convention for flux by foreshadowing the result for closed curves with + being from the inside, out. I'm not faulting anyone, I couldn't give a lecture on this and keep possession of both my hands when erasing blackboards operated by hazardous machines. If he loses his hands, he'll never erase anything again. Be careful out there, Denis, we don't want to lose a great teacher.
I never thought about the fact that Gauss' theorem could be expressed in the plane, although it is pretty obvious. Same like Green's is just a form of Stokes' in the plane.
movement is relative. It doesn't matter whether the curve or the gradient is what's moving. If you mean that the gradient is changing then you would add another dimension to describe the change and calculate flux along a surface instead of a line (the surface being the line drawn out along a third dimension representing time, along which the gradient varies appropriately to describe the changing position of the gradient and curve relative to each other)
These are too good. I spent days reading abstract definitions and formal explanations in books to understand concepts this professor explains so vividly and creatively with 10 seconds! Thank you!
This fellow makes things crystal clear.
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 and Curl Of Vector 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.)
30:00, the way to remember it is that the work is a straightforward dot product of F with , M goes with x and N goes with y and we add, and the flux is a dot product of F with the same vector rotated pi/2 so N goes with x and a minus sign with few choices left for M. Auroux missed a nice opportunity at the beginning to clarify the sign convention for flux by foreshadowing the result for closed curves with + being from the inside, out. I'm not faulting anyone, I couldn't give a lecture on this and keep possession of both my hands when erasing blackboards operated by hazardous machines. If he loses his hands, he'll never erase anything again. Be careful out there, Denis, we don't want to lose a great teacher.
29:48 famous Auroux speed erasing :-)
never breaks a smile, ever over this
I learned Flux for years already -- only this is my first time really understand how it is defined and works.
This is so good. shocked, so clear, so clear, so easy
Studying Mathematics for knowledge. And I found the best resource!
I never thought about the fact that Gauss' theorem could be expressed in the plane, although it is pretty obvious.
Same like Green's is just a form of Stokes' in the plane.
i flexed in my class telling this to my physics teacher 🥲
All the vector calculus integral formulas are unified in a general Stokes Formula. Maybe check out differential forms if you are interested.
25:11 amazing
Funny and very intuitive lecture
I Really Like The Video Flux; normal form of Green's theorem From Your
it's because of his skill at erasing berofe the next blackboard cover it... just funny staff
Why did they clap when we was moving the line through the vector field at around 10 mins? =D
maybe because of the great didactics when teaching
25:11 outrageous
My textbook covers flux in 10 sentences. Thanks for making this public so it can bolster this kind of trash textbook.
at around 14:04, regarding flux what if curve is also moving? how to tackle that?
movement is relative. It doesn't matter whether the curve or the gradient is what's moving. If you mean that the gradient is changing then you would add another dimension to describe the change and calculate flux along a surface instead of a line (the surface being the line drawn out along a third dimension representing time, along which the gradient varies appropriately to describe the changing position of the gradient and curve relative to each other)
then the flux also changes with time
Thanks ❤🤍
@huanyanqi Because he explained it well.
This is helpful ❤️🤍
ty for lectures
Why doesn't he use symbols for divergence and curls?
Cause its maths not physics
I like this professor
Where you at now?
Where you at now?
11年前就翻墙听这个，有趣
22:33
Why, because they'are not finished with writiing it down on their papers ...
hey are you alive
why did people cheer when he wiped the upper blackboards??
The race between the teacher's erasing skills and the auto-dropdown chalkboard is somehow amusing. It's a running gag, starting from lecture 1.
oh i see, thanks!
I cannot post. hmmm
The notes made no sense. This lecture made it seem so simple
Your own notes of this great lecture make sense. Otherwise, you don't learn
never realized how immature MIT students were....
they have a sense of humour and their applause comes out of their respect and adoration for their professor.