Lec 6 | MIT 18.02 Multivariable Calculus, Fall 2007

[TheLittleTrickster]

That's so cool.

[frmsaul]

20:28 "cool trick" (:

[lillale78]

beautiful, beautiful stuff

[pedruxxx1]

I'm brazillian, and I've been watching all the 18.02 lectures with Aurox as Instructor... And I can say that I am understanding every single word that comes out of his mouth. He's brilliant! Respect for him.

[Scelenaarwen]

i think from now on in these lecture series my 10th grade level math just wont cut it :D Good part is that its summer and at the end of it i AM gonna know multivariable calculus, failure is not an option!:)

Awesome series, and professor.

[joeglimmix]

you can integrate that thing with a poseidon substitution

[joeglimmix]

he needs to do some exercise...has a belly

[pedroissler]

@joeglimmix i agree with you, but here goes how typical "independent learners" would reply to this: Look, first you get his level of education, ok? Then you can get to comment on his belly.

[Scelenaarwen]

@joeglimmix by contrast his brain probably has 8 pack abbs 

[StatelessEuphoria]

excellent. I fin his accent quite nice actually. Far better than some asain lecturers I have.

[purev1olence]

I'm surprised he couldn't integrate sqrt(2-cos(t)).

[pairalines]

@purev1olence There is no elementary integral of that.

[Liaomiao]

This teacher is great. He provides clear and concise explanations to what are potentially unfamiliar issues (to those that aren't well versed in maths such as myself.) Everybody has an accent depending on which part of the world they're from - even you. What's important is that his grammar is perfect and he knows the subject matter which makes him very easy to understand.

[amitk19]

the last part was a beauty of Keplers law!

[MatrixOfDynamism]

The lecture is incomplete? The lecture did not finish but the video did? WHY!?

[bmx391xmb]

man this guy is awesome. you can def integrate the function at @20:20 just use a Weierstrass substitution!!!!

[bmx391xmb]

man this guy is awesome.

[lsufan1234]

2 people are english majors

[Wishingstarification]

best teacher ever

[taikukaikei]

his lectures are amazing...

however... the students in that class prolly get screwed up. for someone to feel comfortable in his class, he or she should study in advance. There does exist such thing as geniuses, but people get to this point in math through many hours of studying.

[fluff125]

I highly suggest that all of the people watching the video go to the link in the description and do all of the practice quizzes. Your understanding will improve immensely.

[gorgolyt]

you can do that integral by taking out the sqrt2 and then multiplying by sqrt (1+cos/1+cos), then you factor out the resultant sin and it's of the form of a chain rule derivative.

[janitarjanitar]

He constantly stops and asks if theres questions, and he elaborates on subjects he feels are pretty trick to catch at first. good teacher. not as sharp of a dresser as professor donald sadoway though :)

[Taowhr]

Is it just me or he has neat writing?

[bebexpink]

@Taowhr yes, his handwriting is mesmerizing.

[DigitalAssassin]

Love the laugh & clap at 43:20 !

[Nezumitheumi]

17:30, "You could have your car's milage counter count backwards from the point where the car will die and start walking." Don't you just hate those walking dead cars?

[FredTheMightyFraud]

@Nezumitheumi He said ''stop working''. It's really just the french accent.

[Angiegirl2112]

i understand all of this and im only 12

[asinfulvirtue]

well duh, someone spelled out how build a triangle out of paper like they do in your classes i'd know how to do it too.

[Angiegirl2112]

@asinfulvirtue what so you mean someone spelled out how to build a triangle out of paper in my classes?

[Angiegirl2112]

@Angiegirl2112 you rock

[rgh1986aka199]

Is anybody solving the assignment sets? I need help with Assignment 2> Problem 2....

[studentLifeProject]

Why isn't the arc length from 0 to 2pi of the cycloid just the circumference of the wheel?

[michalchik]

Think of it this way. Let's say the wheel did not turn but was simply dragged. The curve describing the path of a point on the wheel would be equal to the displacement of the wheel. Similarly, if the wheel did not move but simply turned in place the arc length would be 2pi for each revolution. The cycloid includes both the revolution and the translation as part of its length.

[studentLifeProject]

Thanks! That makes sense. Happy new year's :)

[rgh1986aka199]

Points on the wheel do not have the same speed. Point of contact with the ground has 0 speed, the center has speed v, while the topmost point has speed 2v. By the time the centers moves some distance, the top point would have moved a greater distance. However if we fixate on a point on the rim, it will have variable speeds and would have covered various lengths in different time periods. The total length covered by one such point is arc length and it is more the circumference.

[brijeshagarwal1975]

for cycloid the proof was given in terms of angle,later it was told that at radius =1 and speed=unity, angle may be replaces with time.thus r vector of cycloid was arrived at in terms of t.

also using this r in terms of t, speed was calculated as sqrt(2-2cost).

my question is when relation in terms of t was arrived at by using speed =unity,why it is coming as sqrt(2-2cost) ?

[tharinduuuu]

@brijeshagarwal1975 in the first instance the speed at which the wheel moves to the right was set equal to 1(which was also set equal to the radius giving the magnitudes of angle and time equal to unity). The speed calculated afterwards was the velocity of the moving point P on the wheel which obviously varies with time. hope this helps.

[michalchik]

the angular speed of the wheel was set to 1. That is it completed on revolution in 2pi units of time. The speed we calculated was the linear speed of a point on the wheel.

[rgh1986aka199]

If the speed were non-unity say w, the relation would have come out to be root(2-2cos wt)...no biggie

[SamiHelif88]

the best lecture i've ever seen..... he's really >>>WOW

In addation to that, he speaks batter than native speakers'.

[andresgoens]

16:45 the s probably comes from the german word "Strecke" which basically means trajectory

[Trillske]

Love it when things start to be atleast a bit abstract agian. Hated one variable. Mostly just remembering formulas and definitions and w/e.. yuck.

[sanderroy]

As much as I may find him to be an excellent teacher, and easy to understand, I cannot rule out that he is more difficult to understand if one has learned english as a second language. Regardless, closed captioning (click the triangle in the bottom right and then click the "cc" button) should remove any problems, yes?

[hodsun]

I don't get it; he's easy to understand. How can anyone be saying they can't understand him? His accent is light, and his grammar is better than most native speakers'.

[savita1926]

Why do son of a bitches comment on his accent.

Some time people make big deal out of it may be due to prejiduce.

[roflcoptergoswoosh]

oh man I just watched lectures 1-6 in one day

[Wirrit]

As far as accents go, I'd call this a fairly light and innocuous one. It -is- important for teachers to be understandable and clear -- but I think he is. The grammar's near-perfect (at least as perfect as any native speaker), and the difference in pronunciation is very standardized and doesn't cause words to get mixed up with eachother. That's really all you can ask.

[rinwhr]

@Wirrit You be surprised how "perfect" native speaker's grammars are.

[MAFlOTU]

the teacher is super okej !

you must be a born wanker to say something bad !

[drecklia]

there is nothing wrong with him...he only has a french accent...but goes figures!!! MY mult calc prof sure has a heavy accent!!!

[jacobbis4lovers]

I would hate to have this guy as a teacher, it's really hard to understand him.

[iyiguncevik]

yeah, right. it's him not you.

[ArabicPilot]

the teacher's an IMO math winner / doctorate from france, and you're pansying out and calling him horrid because he's got an accent?

do you even understand calculus, or is this all because of the accent?

[jacobbis4lovers]

i never said he was a horrid teacher, did I? I just said it's hard to understand him because he has an accent. i can't decipher what he's trying to say...

Yes, I understand calculus. I aced calculus 1 and 2.

And I am making an A in Calculus three right now.

[x1x2x3ct]

@ArabicPilot cool story bro.