"Ok, so let's talk about geometry, that should calm you down"

Lmao

43:20
"I see you guys are having fun"
I guess he was thinking something like "we'll see who has fun at the exam"

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.)

someone needs to make a compilation of the students cheering for the professors erasing the blackboard!!

The way he parameterized the directional derivative was really confusing.

For people who are confused, try studying basics of 3-D geometry. You will easily understand the equation of tangent plane. It is basically asking us to find the equation of a plane whose direction ratios of its normal vector and the a point through which it passes is given.

This guy is the man!

I love it when math gets graphic.

This video is what is keeping me going in life, god bless calculus

blackboard duster action highlights - 28:28 and 43:30

This is one of the more difficult lectures for me so far. The fact that I didn't fully grasp parametric equations is coming back to bite me up the ass....

The alternative method that he used to find the tangent plane at at 29:45 shows his amazing geometrical intuition! I would not have thought of solving it so intuitively using linear approximation of the curve at a point.

god bless u man,nice clear  lectures

oh, these classes are so awesome, I wanted to clap at the end of the video.

Need more examples on directional derivative parts. It's a bit rush in the video.

Very well explained, and this chapter is quite important for you to understand gradient descent in machine learning. Thanks, professor

@pattttttrick You see the gradient is a sort of operator, when you apply it to a scalar field, it gives a vector field. The gradient it self is not the vector.

To all those who didn't exactly got why dr/ds=(u hat), try understanding this way of explanation:
In the X-Y plane lets just take R(r vector) to be the position vector of a point in X-Y plane. Now if we move a length ds along u vector(U), the position vector of the point will change by amount dR. Thus, if you draw a picture of what I just said, you will understand this that,                                                                                                                                                             (R +dR) - (R) = (ds)(U hat). That is dR=(ds)(u hat). And thus dR/ds=(u hat).

21:18 example
25:52 (another way
30:43 Directional Derivatives

El profesor de universidad del que más he aprendido :')