Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07

Lecture 08: Level curves; partial derivatives; tangent plane approximation.
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[@kingkongtiger]

MIT professors teach like their students have no background knowledges, and my professors assume I have learnt all shit already in High school

[@rajaradi802]

@narak leduop not cheap schools but with the worst education system

[@theblinkingbrownie4654]

@CAVEMAN these bots are surprisingly common especially in stem channels, idk how youtube hasn't noticed yet.

[@anindyaroy5692]

Exactly! And they also jump from one thing to another, and students fail to understand the connection.

[@marklestergesta7554]

I feel you

[@narutouzumakix9201]

this guy is really good at the 3D drawings

[@Dawatehaq786]

Trigonometry for AS and A level student kzbin.info/www/bejne/Y4jdi4WuaduJrqs Subscribe please

[@yabannamba7678]

Sal Khan is the goat at it but he's good too

[@qbtc]

MIT students are smart and know they are being taught by a great professor here. They even applaud when he figures out the blackboard buttons.

[@ChristianCentury2000]

Thank you MIT for posting these excellent courses online! The professors are great! The lectures are very well done!

[@TheCrappyaccount]

I love MIT so much for all of these free lectures. I have watched all of physics, this and electronics and circuits.

[@idealthinker101]

So would I.

[@koenrad]

Much easier to understand now that I have a second person explaining it, what a great professor! Also helps that I can rewind and listen however many times I want :p.

[@justinyeo1428]

Yup. I also wish I had that professor.

[@rajaradi802]

Hey you look like Sheldon

[@katee808]

Jesus Christ he's great at teaching. I now understand the difference between spending $50,000 per year and $10,000 per year. At least they're paying for the tuition so I get to watch these videos for free.

[@83jeffa]

this guy is a master chalk operator

[@Dawatehaq786]

Trigonometry for AS and A level student kzbin.info/www/bejne/Y4jdi4WuaduJrqs Subscribe please

[@WilliamTaylor-rr6zw]

@@Dawatehaq786 bro shut up

[@awowoosas]

All these videos are REALLLY REALLY helpful. Thank you so much, MIT!

[@ccosm4587]

these kids applaud at the strangest things

[@ddude957]

seems you haven't been to college

[@slackbabo3858]

@@ddude957 I have and we don't typically applaud the professors

[@Dawatehaq786]

Trigonometry for AS and A level kzbin.info/www/bejne/Y4jdi4WuaduJrqs Subscribe please

[@aashsyed1277]

meh im a 9 year old

[@vishnureddy3977]

That sine graph is amazing.

[@SimmySimmy]

One of the reasons I truly like this awesome teacher is he always erase three pieces of blackboards in a row, so I get a chance to skip

[@syedaliraza3476]

Incredible lecture. Professor Denis Auroux is brilliant. He says his drawings on the board aren’t on point but they are way beyond great.

[@MrCavitysChessCorner]

Phenomenal lecture. Merci beaucoup Professor Auroux!

[@MarioS-v7b]

Thanks to MIT for posting this and other math videos. For a math hobbyist these videos are an excellent resource for deepening the knowledge about math. Prof Auroux is really awesome.

[@Filipe8496]

This is the best teacher I ever seen. :D

[@GNARGNARHEAD]

just in-case anyone was wondering the program he used to generate those parabola is 3D-XplorMath its a really fun program relatively easy to use its even how i generated my display picture :)

[@alyasker2194]

thnx a lot that was really helpful :)

[@hassanhb9605]

Wow , Wow ! What an amazing explanation ... i felt like Multivariate Calculus is very easy as opposite of usual

[@imegatrone]

I Really Like The Video From Your Level curves; partial derivatives; tangent plane approximation

[@sac12389]

and the sidewalk chalk is a great idea. I sit in the second (out of 4) row in my calc 3 class and often can't tell what is being written on the green board. also green boards are a terrible idea.

[@karigucio]

i appreciate this guys 3D drawing skills

[@marklestergesta7554]

Thank you MIT ❤️❤️❤️

[@hanzellmo]

Spivak's calculus might be to confusing for someone that's starting, but is an awesome book.

[@inuyashalivesbaby]

omg.... I know this is stupid, but I have to say it. That movable board is awesome man!!! Go MIT!!!

[@venkatesh-ke9ff]

your teaching is supper, sir, i never see before such knowledge any professor

[@suffixable]

such an awesome professor. MI,T could you also upload single variable calculus lectures from him. The one you have, right now, is very confusing.

[@proghostbusters1627]

I can't see what you mean. Prof. Jerison is fricking great.

[@semjoneschweiler2229]

Strongly disagree, Prof. Jerison did a great job in my opinion.

[@mohammadfallahzade2110]

he is a legend thanks MIT

[@ishandave3542]

god please name lectures by the topics!!!!

[@mitocw]

+Ishan Dave Sorry, all of our early videos are titled like this (thousands of them, so the odds of us going back through to change them aren't very high). We changed how we named them starting in 2012. To get a list of topics, see the course on MIT OpenCourseWare at: ocw.mit.edu/18-02F07.

[@ishandave3542]

***** please there is no need for sorry.I am under great debt from professors from MIT especially professor walter lewin he is my favorite professor of all time he came to my college last year I am sad that I didn't have the chance to meet him.

[@tripp3468]

Jesus dude, learn how to spell.

[@ishandave3542]

I edited the comment ,seems fine to me now English is not my first language.

[@saminzawad4677]

ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/

[@BareClause]

I'll add this to my watch later list, because I am going to need this when I do Mathematical Methods at UWA next year.

[@maxsash]

I don't think so. They say they will but they never come back.

[@BareClause]

@@maxsash I ended up getting a phd bitch

[@iyanev]

Why does everybody hates Taylor's Series.They are a live saver and allow you to do so much with a little work.

[@skylarshi1040]

lifesaver and im going to cross register every math class at mit. dont know why my professor assume im smarter than mit students

[@jogaserbia]

Awesome videos. Just to let everyne know, you can donate to the open course ware through their website. Also, you can buy books through amazon where MIT gets money. I dontated because I really believe in what they are trying to achieve.

[@AdrielGreene]

This was so enlightening!

[@priyanksharma1124]

Amazing pedagogy

[@TheJesseWu]

That's some nice handwriting.

[@nchaconn79]

This is fantastic, very clear explanations. I'm currently taking Calculus 3 in Summer session and I work a full time (40 hours per week) so I have no life... well Calc 3 is my currently life. But I love it

[@yhmd777]

It's a great video because I can review what I learned this year

[@A3abbadq8]

Great Lecture!! Helped me a lot.

[@orangasli2943]

Ok now we understand x axis when plotting against y axis is actually looking at an object from the top.. If we add the z axis we can understand that object little bit more

[@silentweapon]

I feel so fucking lost during my calculus class, and enlightened right away after watching this video. THANKS SO MUCH!

[@ZbladeVX]

Great lecture but itd be cool if the camera movenment is less. He writes reasonably clear and very neat. Great prof too

[@alinapol]

great lecture

[@LAnonHubbard]

Brilliant stuff.

[@not_amanullah]

Thanks ❤🤍

[@elamvaluthis7268]

Basics of vector calculus understands properly.

[@not_amanullah]

This is helpful ❤️🤍

[@k0fdark]

Thanks this is very helpful, my fav teacher :D

[@cristh2311]

I hope most of you noticed that at 42:21 we were dealing with a "toilet function" ;)

[@cristh2311]

+Mei Yifu I guess someone didn't notice ^^

[@cristh2311]

+Mei Yifu look at how the function is drawn.

[@cristh2311]

+Mei Yifu :D this math is old good night stories for me now. I am quite far in my masters now, physics. I just couldnt resist commenting about it at the time ^^

[@cristh2311]

+Mei Yifu Yes, in minimum period. I started in Summer Semester 2013, wanna see my grades? I have 3 and half years of them :)

[@LauroKirsch]

This helped me a lot!

[@elamvaluthis7268]

Very nice.

[@kindalindaable]

Thanks sooo much!!

[@eafindme]

Arrr, finally I found a key to understand multivariables! My lecturer is just screwing it up! I couldn't understand it even I study by myself. Is worth a waste of 46 minutes on watching this recording!

[@datagus]

Well, goodbye to my old calculus teacher!!! Welcome MIT!!!!!!!!!!

[@zyrohnmng]

You still have to admit...it is cool, common or not...it. is. epic.

[@dnm25]

41:26 differenti-able :D 5/5

[@inuyashalivesbaby]

@hellomate639 Good for you and your university. :)

[@benjames2266]

What graphing program were they using to plot the graphs and contour plots?

[@mitocw]

The course occasionally relies on a series of specially written interactive math applets ("mathlets"), which let you visualize and experiment with various concepts seen in lecture. See the course on MIT OpenCourseWare for the mathlets and more course materials at ocw.mit.edu/18-02F07.

[@TheTranceWhale]

Is Taylor really that unpopular? (@ 38:20) We tend to use 'taylor' as a verb: "Doesn't integrate? Just taylor that shit."

[@malihareza4754]

In a previous lecture the whole class gasped when the professor mentions Taylor series. So it's coming from there.

[@md.nasimreza3029]

nice

[@hellomate639]

@inuyashalivesbaby There are boards like that at my school. Not that special of a device. Common at large universities.

[@sebastiandiazvivas613]

How I would wish to stay at MIT studying right now

[@fermixx]

im doing distance learning and this guy is saving my ass. you cant imagine how hard is to learn calculus 2 from a book ! (or BAD book). Its easier for me to hear this french talking in english than to read the book which is written in my mother tongue (spanish), so figure it out ! thanks dude !

[@xinyuli9423]

44:42 "Applied math is just physics with different notation" LMAO

[@AndresGomez-pw4fs]

what's the program he's using for plotting the functions??

[@orangasli2943]

Finally we can understand "with respect" means "small changes of" For example let find the derivative of the function f(x)=x+y with respect to x.. Means when x is moving slowly .. What is the gradient between z and x i.e z/x =?

[@ashokedas1552]

good

[@ДімаКрасько-с7м]

Are graphs build in Mapple? Recognized the commands, that were used

[@josephlee392]

At 43:46, what if you chose a different slice in the xz plane? Wouldn't df/dx change because you would get different curves? Or, would all the curves be the same general shape: a parabola, making it not change after all? Thanks.

[@axxxyxxxx5233]

If u take horizontal slice for z=c the slope will be same for any vertical slice y=k

[@rebeccalee120]

This is what we learn in 4 classes of same length

[@SevenRiderAirForce]

Math - this is how you do it. Oh, and I lol'd at 22:48 when they clapped for him.

[@Souliee]

Hes really good at explaining, not like my professor :

[@yuhanwang7122]

Applied math, which is the same thing as physics but with different notations. Comedy gold.

[@jacklyons5888]

things are now getting exciting :P vectors are bleh

[@gautamgopal3517]

Anyone else Bingewatching all these lectures?

[@soubhadramaiti1996]

I've watched and really enjoyed the previous lectures, but I have some doubts regarding this lecture.... what I have learnt from the book by J. Coley is totally opposite (interchanged) to what professor explained about Contour plot and Level curves...... Hoping for anyone's kind reply. Thank you.

[@sarahdaud]

@inuyashalivesbaby haha i know what you mean! i study at LUMS univerity, Lahore, Pakistan and our science department is inspired by MIT.. we have moving boards here too its so much fun haha :D

[@iitjee3813]

24:09

[@SUBASHCD]

25:37 Horizontal lines plotted is incorrect?

[@faizzzzan]

same

[@UnjojoHalas]

lol. i like the way he says temperature. (hope i spelled it correctly) he's awesome!

[@somnathmondal724]

If I don't get any point in a small region of topographic map of a mountain, it indicates there is no peak . Is this true ??

[@hellomate639]

@inuyashalivesbaby Nah, just saying that my university isn't a great one (it's great by some standards, nobel prize winners have taught here), but it's easy to get into this one.

[@eldernos]

That dude sure can draw a sin curve.

[@pufifa]

30:40 that thing won't stop staring at me :O

[@saubaral]

thats not the graph we need, but the graph we deserve

[@themastershadowx]

i think it's obviously seen that he is from france as he pronounce "r" with french pronunciation

[@aashsyed1277]

what is a relation in 3 d?????

[@robertsguitar]

Fun fact: This prof started his masters leading to his Ph.D when he was 14 :|

[@proghostbusters1627]

And here am I watching this at 14. Man I feel I've fell behind already (I'm semi-joking)

[@realcirno1750]

there was no tangent plane

[@inuyashalivesbaby]

@hellomate639 I made that comment two years ago. Can you imagine me saying that aloud in a MIT classroom?? lmao. That's why I don't go there... Believe it or not, I'm not that shallow. Don't judge my character based on that one comment. I'm teacher's assistant for a calculus lab at my university now. I have 23 students. lol.

[@somebodyhere3160]

9:35

[@fermixx]

any to recommend me?

[@inuyashalivesbaby]

@hellomate639 in a quite plainly condescending pompous way... That's all.

[@hellomate639]

@inuyashalivesbaby I'm not judging. Lol. I'm just saying quite plainly that those boards aren't a very impressive feature.

[@eligray]

@katee808 Starting next month, I'll be paying the price for you =)

[@dongel1001]

is he french? his accent is so funny

[@alperener460]

is there one who know this guy's accent

[@GorkemArar]

alperen çağrı er Fransiz

[@zhangqinghui3546]

Alperen Çağrı ER french....

[@Greg_Ulmer]

coughing

[@hellomate639]

@inuyashalivesbaby Oh, get over academia already. I'm not being condescending and pompous: I think it's cool that you're a T.A. You're probably sensitive because you're in academia. I am too.

[@fermixx]

oh and by the way, that intro starts to piss me off after watching so many lectures !

[@stefanzdrnja]

CORONA