Level curves | MIT 18.02SC Multivariable Calculus, Fall 2010

[@DrYes220]

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

[@5gallonsofwater495]

i did the same...

[@mikemuponda1781]

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

[@munya_wto]

Wangu😂😂

[@coleyoutubechannel]

fr , he doesn't over complicate things

[@pavanvimmii9154]

😂

[@sunr8152]

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

[@joeschey]

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.

[@EmpyreanLightASMR]

True, though that's the easy way. I appreciated he factored it as it's not something commonly seen

[@noobmaster-dm7tu]

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

[@fast_gtr]

noobmaster69 I’m a rebel.

[@tawosabdalla697]

I didn’t know there were many like me hahaha. I didn’t pause, my reaction was oh man stop the crap and keep going.

[@j0mezzy]

Now this is my pace right here ! Good job

[@ThongNguyen-sm8sn]

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

[@sarwarmohammed3769]

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

[@HiddenShaco]

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

[@yadpreetcheema4806]

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

[@rwharrington87]

Doing good for humanity, one 360p lecture at a time.

[@bwibwi5]

that chalkboard is beautiful.

[@kamrankhankami7793]

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

[@chrisrock1990]

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.

[@MrMalding99]

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.

[@zeinabfarhat3380]

thats the engineering system day by day theyre changing the curiculum maybe when our generation have kids we will see that changing in the science department courses

[@fredericostrasser843]

Thats an unusual way to sketch a plane. If people are watching this video they should be aware of the normal vector. Great video 10/10.

[@ClassyJohn]

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

[@valerieshearsmith3136]

my, what a big chalk you have

[@anirudhsharma9802]

😏

[@anchu63]

part C is also a called a Pringle.

[@Rahul-uk4su]

Yeah a reverse pringle..

[@mathildeottele1320]

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

[@instinctscooter]

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.

[@nicholasthope]

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! :)

[@timepass4783]

We still use chalkboards here in India😂 though whiteboards are taking over

[@jbrookes1995]

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.

[@brandoncamarino3127]

Jeremiah Brookes I think it is too. A hyperbolic paraboloid has the saddle shape and the form z=(x/a)^2-(y/b)^2. For it to be a 2 sheet hyperboloid it'd have to be equal to 1 and all variables squared.

[@tejasgajra2731]

when z is a constant the curve is a hyperbola, he is right !

[@mariogutierrez2793]

Yes, you are correct. That would be a hyperbolic paraboloid and not a hyperboloid of two sheets.

[@marishaghosh6611]

This explanation is so amazing! Thank you so much!

[@TheAwilks10]

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.

[@broctorres3658]

Not necessarily. My university uses whiteboards for all math classes. Comments about chalk boards being old = bad are pretty silly though.

[@BeyondSkys09]

Are you honestly defending the black board? Oh god, you aren't even worth my time.

[@TheAwilks10]

BeyondSkys09 Dawg are you for real. Its MIT. They can write on toilet paper for all I care. If it wasn't for opencourseware I and many other engineers/ scientists would be screwed. And yah I dont mind white boards. My only problem is that I have been unfortunate enough to have most of my professors right in green marker in a room that has an overall green tint. It just straines the eyes after a while.

[@LeinysandMassey4life]

+Michael Donovan same here at University of Wisconsin - Madison. All math and chemistry lecture halls/classrooms all use chalkboards. They don't smell bad like whiteboards lol.

[@Brono25]

They use projectors at my uni. They lecturer can switch between slide shows or a camera which can show them working things out on pen and paper. Its good for us who only watch lectures online.

[@erjonatopalli954]

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

[@aldensova7537]

thank you so much. Wish you were my teacher

[@koalabear444]

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

[@kamrankhankami7793]

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

[@s1ight]

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

[@OmerSuleymana]

except Leonard :D

[@cashews9]

this video was very helpful, thank you!

[@ww8720]

why isnt the third equation a hyperbolic paraboloid

[@emmak8079]

so helpful!

[@gabrielcenteno2797]

the chawk he use was so incredibly thick, other than that great instructor

[@blueblutterfly02]

This helped a lot, thanks!!

[@someperson8249]

OMG is this the math sorcerer?

[@KabeloNgwenya]

Super helpful! Thanks for the upload :)

[@seriousmax]

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

[@GreyBillie]

Thank you!!!

[@maktub_txt]

AHHHHH THANKS man

[@DMSAProductions]

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

[@redahawse]

thank you

[@bryanquintana]

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

[@heyhey611]

Thank you! :D

[@temp___]

He's actually only 3'4.

[@zahraaljami]

thank you a lot !

[@spidieman2393]

@ryanphoon is best of the best

[@spidieman2393]

Best MIT student

[@Shafique96]

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

[@rayparker7554]

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

[@PRIYANKASINGH-hv8ri]

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

[@danbenjamin95]

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.

[@Crelicx]

What The Fuck

[@greenleaph5145]

Dan Benjamin Hush boi.

[@thebeaditya]

I laughed so hard to this :D Thank you

[@mro2038]

What's this 😂😂😂

[@Shyzah]

*_P E D O P H I L E A L E R T_*

[@mohammadhoseinrivandi5657]

Tnx!i got it!!!

[@mytommy]

life saver

[@lloydlucin528]

we use them at stanford too

[@brayamhuamanta1712]

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

[@161723516]

powerful hand!!!

[@amitrajo]

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?

[@ibile2922]

i thought it would be cylindrical

[@DAleftLANEplz]

MIT: sidewalk chalk for the video

[@nikurisuidk7526]

That chalk is bigger than my brain.

[@militantpacifist4087]

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

[@29leej]

I smell geekiness from him

[@unleashedwillyy]

dude how long is your blackboard

[@XQuber]

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 ;)

[@jacobvandijk6525]

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

[@mohammadjj]

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

[@h0333]

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

[@ryanchiang9587]

partial differential equations pde

[@prateek523]

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

[@mustafakamal8106]

why does he looks like Chris from The Family Guy.

[@BeyondSkys09]

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

[@Fishtail3]

That is one meaty stick of chalk.

[@jhat2014]

Some buff ass chalk.

[@aimeedarling12]

are contour lines and level curves the same thing?

[@Anahdhhsxjfh]

Yes

[@joesr31]

How do draw it if there are constraints?

[@김선호-l8i]

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

[@pavanvimmii9154]

❤

[@yogotah]

freakin MIT

[@itsssxxxpunit]

You could ride them

[@henikeneshetu4774]

Who is here in 2023-2024 :)

[@99Leo]

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

[@OriakoPhi]

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

[@ICOD73]

9:57 Lolz

[@videougur]

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

[@YTEmphi]

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

[@noobmaster-dm7tu]

boi