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

  Рет қаралды 298,584

MIT OpenCourseWare

MIT OpenCourseWare

15 жыл бұрын

Lecture 08: Level curves; partial derivatives; tangent plane approximation.
View the complete course at: ocw.mit.edu/18-02SCF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

Пікірлер: 143
@kingkongtiger
@kingkongtiger 11 жыл бұрын
MIT professors teach like their students have no background knowledges, and my professors assume I have learnt all shit already in High school
@rajaradi802
@rajaradi802 4 жыл бұрын
@narak leduop not cheap schools but with the worst education system
@theblinkingbrownie4654
@theblinkingbrownie4654 3 жыл бұрын
@CAVEMAN these bots are surprisingly common especially in stem channels, idk how youtube hasn't noticed yet.
@anindyaroy5692
@anindyaroy5692 2 жыл бұрын
Exactly! And they also jump from one thing to another, and students fail to understand the connection.
@marklestergesta7554
@marklestergesta7554 Жыл бұрын
I feel you
@narutouzumakix9201
@narutouzumakix9201 6 жыл бұрын
this guy is really good at the 3D drawings
@hikmatemanzil6822
@hikmatemanzil6822 4 жыл бұрын
Trigonometry for AS and A level student kzfaq.info/get/bejne/Y72qjbWpmdy6qH0.html Subscribe please
@yabannamba7678
@yabannamba7678 Жыл бұрын
Sal Khan is the goat at it but he's good too
@qbtc
@qbtc 9 ай бұрын
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.
@katee808
@katee808 14 жыл бұрын
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.
@ccosm4587
@ccosm4587 9 жыл бұрын
these kids applaud at the strangest things
@ddude957
@ddude957 5 жыл бұрын
seems you haven't been to college
@slackbabo3858
@slackbabo3858 5 жыл бұрын
@@ddude957 I have and we don't typically applaud the professors
@hikmatemanzil6822
@hikmatemanzil6822 4 жыл бұрын
Trigonometry for AS and A level kzfaq.info/get/bejne/Y72qjbWpmdy6qH0.html Subscribe please
@aashsyed1277
@aashsyed1277 3 жыл бұрын
meh im a 9 year old
@83jeffa
@83jeffa 8 жыл бұрын
this guy is a master chalk operator
@hikmatemanzil6822
@hikmatemanzil6822 4 жыл бұрын
Trigonometry for AS and A level student kzfaq.info/get/bejne/Y72qjbWpmdy6qH0.html Subscribe please
@WilliamTaylor-rr6zw
@WilliamTaylor-rr6zw 4 жыл бұрын
@@hikmatemanzil6822 bro shut up
@ChristianCentury2000
@ChristianCentury2000 Жыл бұрын
Thank you MIT for posting these excellent courses online! The professors are great! The lectures are very well done!
@TheCrappyaccount
@TheCrappyaccount 12 жыл бұрын
I love MIT so much for all of these free lectures. I have watched all of physics, this and electronics and circuits.
@idealthinker101
@idealthinker101 Жыл бұрын
So would I.
@SimmySimmy
@SimmySimmy 5 жыл бұрын
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
@koenrad
@koenrad 10 жыл бұрын
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
@justinyeo1428 9 жыл бұрын
Yup. I also wish I had that professor.
@rajaradi802
@rajaradi802 4 жыл бұрын
Hey you look like Sheldon
@awowoosas
@awowoosas 8 жыл бұрын
All these videos are REALLLY REALLY helpful. Thank you so much, MIT!
@vishnureddy3977
@vishnureddy3977 7 жыл бұрын
That sine graph is amazing.
@user-lr5we1sy3k
@user-lr5we1sy3k 9 ай бұрын
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.
@syedaliraza3476
@syedaliraza3476 5 ай бұрын
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
@MrCavitysChessCorner 12 жыл бұрын
Phenomenal lecture. Merci beaucoup Professor Auroux!
@Filipe8496
@Filipe8496 14 жыл бұрын
This is the best teacher I ever seen. :D
@AdrielGreene
@AdrielGreene 11 жыл бұрын
This was so enlightening!
@A3abbadq8
@A3abbadq8 13 жыл бұрын
Great Lecture!! Helped me a lot.
@hassanhb9605
@hassanhb9605 5 жыл бұрын
Wow , Wow ! What an amazing explanation ... i felt like Multivariate Calculus is very easy as opposite of usual
@karigucio
@karigucio 6 жыл бұрын
i appreciate this guys 3D drawing skills
@imegatrone
@imegatrone 12 жыл бұрын
I Really Like The Video From Your Level curves; partial derivatives; tangent plane approximation
@yhmd777
@yhmd777 7 жыл бұрын
It's a great video because I can review what I learned this year
@LauroKirsch
@LauroKirsch 15 жыл бұрын
This helped me a lot!
@inuyashalivesbaby
@inuyashalivesbaby 14 жыл бұрын
omg.... I know this is stupid, but I have to say it. That movable board is awesome man!!! Go MIT!!!
@venkatesh-ke9ff
@venkatesh-ke9ff 5 жыл бұрын
your teaching is supper, sir, i never see before such knowledge any professor
@LAnonHubbard
@LAnonHubbard 12 жыл бұрын
Brilliant stuff.
@k0fdark
@k0fdark 15 жыл бұрын
Thanks this is very helpful, my fav teacher :D
@mohammadfallahzade2110
@mohammadfallahzade2110 4 жыл бұрын
he is a legend thanks MIT
@marklestergesta7554
@marklestergesta7554 Жыл бұрын
Thank you MIT ❤️❤️❤️
@alinapol
@alinapol 11 жыл бұрын
great lecture
@priyanksharma1124
@priyanksharma1124 6 жыл бұрын
Amazing pedagogy
@kindalindaable
@kindalindaable 8 жыл бұрын
Thanks sooo much!!
@hanzellmo
@hanzellmo 14 жыл бұрын
Spivak's calculus might be to confusing for someone that's starting, but is an awesome book.
@sac12389
@sac12389 10 жыл бұрын
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.
@GNARGNARHEAD
@GNARGNARHEAD 11 жыл бұрын
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
@alyasker2194 4 жыл бұрын
thnx a lot that was really helpful :)
@axxxyxxxx5233
@axxxyxxxx5233 5 ай бұрын
Randomly clicked this magical vdo this could be turning point of my life
@iyanev
@iyanev 11 жыл бұрын
Why does everybody hates Taylor's Series.They are a live saver and allow you to do so much with a little work.
@elamvaluthis7268
@elamvaluthis7268 2 жыл бұрын
Very nice.
@silentweapon
@silentweapon 11 жыл бұрын
I feel so fucking lost during my calculus class, and enlightened right away after watching this video. THANKS SO MUCH!
@BattleslashX
@BattleslashX 11 жыл бұрын
That's some nice handwriting.
@not_amanullah
@not_amanullah 29 күн бұрын
Thanks ❤🤍
@jogaserbia
@jogaserbia 14 жыл бұрын
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.
@ishandave3542
@ishandave3542 8 жыл бұрын
god please name lectures by the topics!!!!
@mitocw
@mitocw 8 жыл бұрын
+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
@ishandave3542 8 жыл бұрын
***** 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
@tripp3468 7 жыл бұрын
Jesus dude, learn how to spell.
@ishandave3542
@ishandave3542 7 жыл бұрын
I edited the comment ,seems fine to me now English is not my first language.
@saminzawad4677
@saminzawad4677 6 жыл бұрын
ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/
@not_amanullah
@not_amanullah 29 күн бұрын
This is helpful ❤️🤍
@datagus
@datagus 13 жыл бұрын
Well, goodbye to my old calculus teacher!!! Welcome MIT!!!!!!!!!!
@cristh2311
@cristh2311 10 жыл бұрын
I hope most of you noticed that at 42:21 we were dealing with a "toilet function" ;)
@cristh2311
@cristh2311 8 жыл бұрын
+Mei Yifu I guess someone didn't notice ^^
@cristh2311
@cristh2311 8 жыл бұрын
+Mei Yifu look at how the function is drawn.
@cristh2311
@cristh2311 8 жыл бұрын
+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
@cristh2311 8 жыл бұрын
+Mei Yifu Yes, in minimum period. I started in Summer Semester 2013, wanna see my grades? I have 3 and half years of them :)
@md.nasimreza3029
@md.nasimreza3029 9 жыл бұрын
nice
@BareClause
@BareClause 10 жыл бұрын
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
@maxsash 7 жыл бұрын
I don't think so. They say they will but they never come back.
@BareClause
@BareClause 17 күн бұрын
@@maxsash I ended up getting a phd bitch
@inuyashalivesbaby
@inuyashalivesbaby 12 жыл бұрын
@hellomate639 Good for you and your university. :)
@elamvaluthis7268
@elamvaluthis7268 2 жыл бұрын
Basics of vector calculus understands properly.
@skylarshi1040
@skylarshi1040 Жыл бұрын
lifesaver and im going to cross register every math class at mit. dont know why my professor assume im smarter than mit students
@user-gt2th3wz9c
@user-gt2th3wz9c 7 жыл бұрын
Are graphs build in Mapple? Recognized the commands, that were used
@ZbladeVX
@ZbladeVX 10 жыл бұрын
Great lecture but itd be cool if the camera movenment is less. He writes reasonably clear and very neat. Great prof too
@ashokedas1552
@ashokedas1552 8 жыл бұрын
good
@orangasli2943
@orangasli2943 Жыл бұрын
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
@suffixable
@suffixable 9 жыл бұрын
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
@proghostbusters1627 4 жыл бұрын
I can't see what you mean. Prof. Jerison is fricking great.
@semjoneschweiler2229
@semjoneschweiler2229 5 ай бұрын
Strongly disagree, Prof. Jerison did a great job in my opinion.
@SUBASHCD
@SUBASHCD 6 жыл бұрын
25:37 Horizontal lines plotted is incorrect?
@dnm25
@dnm25 15 жыл бұрын
41:26 differenti-able :D 5/5
@rebeccalee120
@rebeccalee120 5 жыл бұрын
This is what we learn in 4 classes of same length
@zyrohnmng
@zyrohnmng 12 жыл бұрын
You still have to admit...it is cool, common or not...it. is. epic.
@eldernos
@eldernos 14 күн бұрын
That dude sure can draw a sin curve.
@AndresGomez-pw4fs
@AndresGomez-pw4fs 3 жыл бұрын
what's the program he's using for plotting the functions??
@somnathmondal724
@somnathmondal724 4 жыл бұрын
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 ??
@fermixx
@fermixx 14 жыл бұрын
any to recommend me?
@sebastiandiazvivas613
@sebastiandiazvivas613 3 жыл бұрын
How I would wish to stay at MIT studying right now
@benjames2266
@benjames2266 8 жыл бұрын
What graphing program were they using to plot the graphs and contour plots?
@mitocw
@mitocw 8 жыл бұрын
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.
@xinyuli9423
@xinyuli9423 3 жыл бұрын
44:42 "Applied math is just physics with different notation" LMAO
@hellomate639
@hellomate639 12 жыл бұрын
@inuyashalivesbaby There are boards like that at my school. Not that special of a device. Common at large universities.
@josephlee392
@josephlee392 5 жыл бұрын
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
@axxxyxxxx5233 5 ай бұрын
If u take horizontal slice for z=c the slope will be same for any vertical slice y=k
@faizzzzan
@faizzzzan 11 жыл бұрын
same
@aashsyed1277
@aashsyed1277 3 жыл бұрын
what is a relation in 3 d?????
@eafindme
@eafindme 11 жыл бұрын
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!
@Souliee
@Souliee 15 жыл бұрын
Hes really good at explaining, not like my professor :
@sarahdaud
@sarahdaud 13 жыл бұрын
@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
@SevenRiderAirForce
@SevenRiderAirForce 13 жыл бұрын
Math - this is how you do it. Oh, and I lol'd at 22:48 when they clapped for him.
@jacklyons5888
@jacklyons5888 6 ай бұрын
things are now getting exciting :P vectors are bleh
@yuhanwang7122
@yuhanwang7122 5 жыл бұрын
Applied math, which is the same thing as physics but with different notations. Comedy gold.
@gautamgopal3517
@gautamgopal3517 3 жыл бұрын
Anyone else Bingewatching all these lectures?
@soubhadramaiti1996
@soubhadramaiti1996 6 жыл бұрын
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.
@nchaconn79
@nchaconn79 15 жыл бұрын
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
@TheTranceWhale
@TheTranceWhale 11 жыл бұрын
Is Taylor really that unpopular? (@ 38:20) We tend to use 'taylor' as a verb: "Doesn't integrate? Just taylor that shit."
@malihareza4754
@malihareza4754 3 жыл бұрын
In a previous lecture the whole class gasped when the professor mentions Taylor series. So it's coming from there.
@hellomate639
@hellomate639 12 жыл бұрын
@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.
@iitjee3813
@iitjee3813 2 жыл бұрын
24:09
@UnjojoHalas
@UnjojoHalas 13 жыл бұрын
lol. i like the way he says temperature. (hope i spelled it correctly) he's awesome!
@somebodyhere3160
@somebodyhere3160 3 жыл бұрын
9:35
@pufifa
@pufifa 11 жыл бұрын
30:40 that thing won't stop staring at me :O
@saubaral
@saubaral 4 жыл бұрын
thats not the graph we need, but the graph we deserve
@themastershadowx
@themastershadowx 15 жыл бұрын
i think it's obviously seen that he is from france as he pronounce "r" with french pronunciation
@inuyashalivesbaby
@inuyashalivesbaby 12 жыл бұрын
@hellomate639 in a quite plainly condescending pompous way... That's all.
@orangasli2943
@orangasli2943 Жыл бұрын
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 =?
@eligray
@eligray 14 жыл бұрын
@katee808 Starting next month, I'll be paying the price for you =)
@realcirno1750
@realcirno1750 3 ай бұрын
there was no tangent plane
@inuyashalivesbaby
@inuyashalivesbaby 12 жыл бұрын
@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.
@hellomate639
@hellomate639 12 жыл бұрын
@inuyashalivesbaby I'm not judging. Lol. I'm just saying quite plainly that those boards aren't a very impressive feature.
@robertsguitar
@robertsguitar 13 жыл бұрын
Fun fact: This prof started his masters leading to his Ph.D when he was 14 :|
@proghostbusters1627
@proghostbusters1627 4 жыл бұрын
And here am I watching this at 14. Man I feel I've fell behind already (I'm semi-joking)
@fermixx
@fermixx 14 жыл бұрын
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 !
@dongel1001
@dongel1001 15 жыл бұрын
is he french? his accent is so funny
@lefuglyduck
@lefuglyduck 3 жыл бұрын
Man, there is a LOT of coughing happening in the background. In 2021, if someone is coughing that much then clear the fucking room!
@alperener460
@alperener460 9 жыл бұрын
is there one who know this guy's accent
@GorkemArar
@GorkemArar 9 жыл бұрын
alperen çağrı er Fransiz
@zhangqinghui3546
@zhangqinghui3546 9 жыл бұрын
Alperen Çağrı ER french....
@Greg_Ulmer
@Greg_Ulmer 9 жыл бұрын
coughing
@hellomate639
@hellomate639 12 жыл бұрын
@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.
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