The instructor is very very good, almost feel guilty for not being able to buy him a beer lol

This guy is great, explained something I spent two hours staring at a textbook in 10 mins superbly

hit like if you didn't pause the video after 0:44

"welcome back" hehe little does he know...

Now this is my pace right here ! Good job

For example C, instead of breaking x^2-y^2=0 into (x+y)(x-y), you could set y^2=x^2. Taking the square root of both sides gives you y=x and y=-x, which are the 2 lines which form the X shape through the origin.

for someone who never knew, using x2 for youtube lecture vids is really helpful! You learn faster

One of the best math instructor I have ever learned from!

This explanation is so amazing! Thank you so much!

12 years ago and still its the best i found in youtobe

its hard to visualize 3D on a 2D board unless ur a really good artist

Who is missing 2010? While watching this video and thinking that in 2010 , how beautyful days it were....

that chalkboard is beautiful.

take different constants of z. z=0 will give you two straight lines, z=1 and onwards will give you the curved lines that are symmetric to the y-axis and z=-1 and lower will give you the curved lines that are symmetric to the x-axis

Put in different values of z. At z=0 you get a line but at any other value of z you get hyperbola's that are shifted by a certain degree.

really good video, very informative and easy to learn from. One thing though is that I believe that at 7:30 when you start to draw the hyperbola only the first two you draw are correct, if you rearrange z=x^2 -y^2 you get -/+x=(y^2+z)^1/2 so the absolute value of x will always be greater than y, the saddle you draw later on actually adheres to this idea.

This helped a lot, thanks!!

Thank you very much!!! Really helpful tutorial!!!

this video was very helpful, thank you!

my, what a big chalk you have

Very good video. Thank you, it was extremely helpful.

Super helpful! Thanks for the upload :)

I'll admit. The last time I seen or used a chalk board was 2001. And with computers, touch screen and stylus, and smartboards, I'm seeing less usage of whiteboard too. Very informative video! :)

At 6:29 David says it's a Hyperboloid of Two Sheets, but I think it is actually a Hyperbolic Paraboloid. The general formula for the graph of that Quadric Surface is z = x^2 - y^2, which matches the saddle description he gives.

im glad im not the only one struggling with 3d graphing and visualization. this guy had a hard time explaining the shape for C, understandably so. 3d->2d is a bit harsh for professors to make us do when we have computer software for it.

wouldn't part C be considered a hyperbolic paraboloid? not a hyperboloid of 2 sheets? standard form for a hyperboloid of 2 sheets is (x/a)^2+(y/b)^2=(z/c)^2-1

thank you so much. Wish you were my teacher

part C is also a called a Pringle.

Thank you!!!

in example c i didn't understand what you meant, "by moving z across we get hyperbolas"? i don't get why it would cause a hyperbola

thank you a lot !

Amazing video, I have question if x^2+y^2 < r^2 , ABS((2x^4y+y^5-5x^2y^2)/((x^2+y^2)^2)) < b and b> 0, find the value of r?

What z-value steps do we take? z=0,1,2,3,4,5...?

so helpful!

Thank you! :D

thank you

it's called recitation, and yes. even postdocs are TAs at times.

AHHHHH THANKS man

why isnt the third equation a hyperbolic paraboloid

Can't the last one being a butterfly shaped pattern of arranged bowls ?

Believe me or not , he has memorized the graph of last function as we memorise and at the end time forget our own made formula for memorization

every university math course I've ever had has been with chalk boards

BeyondSkys09 Your comment is dumb. If you attended any accredited university, except perhaps an online school like the University of Phoenix, you would find that all math departments still use chalk boards especially for large introductory classes like Calculus III, which this video is for. Blackboards are big enough to see in large lecture halls and provide professors the mobility they need to lecture easily and get rid of mistakes they may possibly make quickly.

we use them at stanford too

Tnx!i got it!!!

In Q1, why isn't his plane passing through (0,0,0)?

Muy bueno aunque si tuviera subtitulos en español sería genial ,saludos de Lima- perú(UNI)

life saver

I smell geekiness from him

powerful hand!!!

He's actually only 3'4.

Yeah. Basically we're in big troubles. It is a simple manner to let you decide how you're going to manage your life at this point. Once again. It is a guide-life you're free to just trash or whatever. Take it like a general idea of what success could be if you decide to follow what sounds thrilling to your self. It's free so help yourself. *It is entirely up to you* #bestpart

That chalk is bigger than my brain.

How do draw it if there are constraints?

MIT: sidewalk chalk for the video

OMG is this the math sorcerer?

dude how long is your blackboard

So mr Minkowski ("remember him from SR?") must have been a horse-lover ;-)

partial differential equations pde

I think there is a tiny mistake in how he drew the axes of the coordinate system: The arrow which is captioned with some variable should be pointing in the direction where the variable increases, therefore it is not crrect to draw an axis pointing in BOTH directions ;)

The first problem he does is a problem from my homework assignment.

@ryanphoon is best of the best

aha, problem number 2x10^infinty of our generation: discussing blackboards under a math video.

That is one meaty stick of chalk.

are contour lines and level curves the same thing?

i like to think of it more like a pringles chip, but ok

i thought it would be cylindrical

Some buff ass chalk.

Only person I've understood so far thank you! Very well explained. Good boy. Good little boy you. Come and have a cookie. Have a little cookie. Come her you good little boy. Have a cookie. Yes. Yes. Take the cookie. Good boy. Eat that cookie up. Such a good boy. You like that cookie don't you. Good boy. Good little boy.

freakin MIT

The cameraman is annoying. He zooms in on the graph and doesn't allow us to simultaneously see the level curves.

Thanks, it was helpful :D, by the way you look like Eminem :D

why does he looks like Chris from The Family Guy.

they still use blackboards at MIT even primary schools have moved forward lol

You could ride them

I have no fucking clue how to hell you came up with part c...

oh my, "you can put this on a horse" what a joke.

Oh no, MIT is using grad students for their video lectures!!!

Laugh so hard when he walked in after 5 seconds...

9:57 Lolz

boi

Who is here in 2023-2024 :)