Lec 25 | MIT 18.02 Multivariable Calculus, Fall 2007

[melisantika]

I am very happy to see the vidoe Triple integrals in rectangular and cylindrical coordinates from you, hopefully the others also are happy for You

[Onepissite]

I am very happy to see the vidoe after you give this Triple integrals in rectangular and cylindrical coordinates

[Ondelendo]

I Love The Video It Can Increase My Knowledge Triple integrals in rectangular and cylindrical coordinates.

[bebeheuy]

Steady I Really Like This Video Triple integrals in rectangular and cylindrical coordinates.

[willamricard]

Nice Video That You Share , So Very Nice Thanks You Triple integrals in rectangular and cylindrical coordinates.

[imegatrone]

I Really Like The Video From Your Triple integrals in rectangular and cylindrical coordinates.

[anakmudajaman]

after i watched this video, my insight is very open because the video is very good to give information Triple integrals in rectangular and cylindrical coordinates.

[aritrayou]

To whoever is developing the courses online - Could u edit the video, right where Prof Auroux explains how to find the x and y limits for the triple integral int(dV)?

I understood the z limits but I didn't understand the logic for the x and y limits. If he could add a snippet explaining the limits with a diagram of columns and slices like he did for the double integrals, it would be better.

Thanks in advance and GREAT VIDEOS (though u must be tired of getting that sort of comment by now!)

[pedroissler]

@aritrayou dude the x and y limits will be the level z in which the intersection between the two curves happen

so

Z1 = x^2 + y^2

Z2 = 4 - x^2 - y^2

Z1 ∩ Z2 --> Z1 = Z2

x^2 + y^2 = 4 - x^2 - y^2

2*x^2 + 2*y^2 = 4

x^2 + y^2 = 2

circle of radius sqrt(2) centered at the origin.

This is true for every curve

[aritrayou]

@pedroissler But what happens if the volume is defined by a bunch of intersecting planes?

Same method?

[ny1fanta]

@aritrayou then you can use rectangular coordinates. cylindrical method is good when there is a circle (projection) on xy-plane

[pedroissler]

@aritrayou This is clearly not a general method.. For 2 curves like paraboloids it is easy to set the bounds because you know they intersect at a given level forming a closed solid. For a bunch of planes, if they don't form a closed solid, maybe it would be better to define when these planes intersect the xy plane (when z=0) or, maybe even better, any given level z=constant for that matter. A bunch of planes that don't form a closed solid would form a pointy thing w/ nothing above it.

[newsubject89]

Now i know why they pay over $50K/year.....excellent and thorough teaching.....thumbs up to that.

[GNR214]

what kind of book does the class use?

[265HITMAN265]

The blackboard and the chalk makes me wanna become a lecturer.

[papatia]

iv'e never been more impressed by chalk

[Flygfanatiker]

3 people did not get into MIT

[HD4WG]

Georgia Tech > MIT

Our lectures and Calc 3 class is way harder...

[DoctorQuestionMark]

@HD4WG This is Calc 2. Your argument is invalid.

[DoctorQuestionMark]

@HD4WG This is Calc 2. Your argument is invalid. ocw (dot) mit (dot) edu/courses/mathematics/18-02-­multivariable-calculus-fall-20­07/

[dahmer1552000]

this guy is awesoommeee!!!!

my teacher sucks big time lol

[lorenzotrojan]

density in grams per cubic inches???? Weird! He was really in a rush towards the end though...

[gorgolyt]

every now and then i'm confused about why some of these people are at MIT.

25:00 guy, i'm looking at you.

if you cut the thing in half, you need to multiply by 2. if you cut it into quarters, you need to multiply by 4.

derp.

[99ludester]

Awesome erasing skills at 35:00

[NxyDolli]

Much better than the shit-ass lecturer I had for this module. If only I had discovered this before my exams last year...thank god I still managed to scrape my 2:1 :D

[boooringboy]

great job youtube

[cb2198]

I love these vids... but why do they cheer whenever he erases the board?

[99ludester]

@cb2198 why wouldn't you cheer? (o.O)

it's just a thing their students have been doing since 18.01, they get bored i guess...

[rocco0031]

Eh bien. Si j'avait vu cela avant le 1er semestre... j'aurais eu mon semestre ! Il explique très bien, merci MIT.

[jcgarces85]

Él la lleva!!! Excelente

[tyler121515]

I don't think this guy is a good teacher. I've already taken this class at my school so I understood this material, but, if I did not know anything about this I woud have been very confused. He's obviously a smart guy but I don't think his explanation of the material is very clear. Cool accent though.

[andydeniedyou]

this was quite informative since my own multivariable class doesn't record lectures, so this is great review. Also, the study who asked cylindrical coordinates clearly knew it would be easier, but probably just felt like showing off hahah

[cocacola443]

This videos are so informative. I love the accent. :) Thanks MIT.

[Anonymiusen]

He is French. You will struggle to find any other learning resource on multivariable calculus on the internet than this.

I think he is a brilliant teacher. I've been watching hours on hours of this course.

[69erthx1138]

@Anonymiusen I was going to wager Moroccan, but six of one and...but his English is clear, so I don't see the need for the subtext.

[jcgarces85]

@Anonymiusen What's the name of this sir? He's a incredible teacher

[Yu2Kal]

@jcgarces85 Denis Auroux

[13Septem13]

@Anonymiusen This course is great. But there are also khanacademy calculus videos, they are great too.