Lec 5 | MIT 18.02 Multivariable Calculus, Fall 2007

[osmannee]

On 12:19 an Motorola batery is empty

[TaiLanorazx659]

so bin selber aus Frankfurt

[agapitoflores001]

This one is very relevant. It helps a lot.

[TheJuga]

why was everyone clapping

[LAnonHubbard]

Love this guy. I did get a bit lost on the Taylor stuff but I need to review it and was here mainly for the parametric representation part.

[sundeshP]

taylor series are awesome everyone flipped shit HAHAHA!! Stupid MIT kid

[jakeyboyGH]

"have mercy" hahahahaha

[bmx391xmb]

who are the 3 ignorant folks?

[adidasguy87]

You could tell it was a Friday.

[lsufan1234]

am i mistaken or could he have just taken the derivative of the parametrized equations, then just put dy/d(theta) over dx/d(theta) and used 2Pi as theta, instead of using the taylor expansion

[lsufan1234]

am i mistaken or could he have just taken the derivative of the parametrized equations, then just put dy/d(theta) over dx/d(theta) and used 2Pi as theta

[zanariot]

If a point is the intersection of two lines, and a line is the intersection of two planes, then is a plane the intersection of two 3-dimensional spaces? That doesn't make any sense, but it almost seems like it would be true if you kept following the initial logic.

[poseidon129266]

In 4-dimensional space, that's right.

Two n-dimensional objects intersecting in n+1-dimensional space make a n-1 dimensional intersection.

[MikeM8891]

he came up with a really round about way of saying take the derivative dx/dy.

[michalchik]

To all those saying that this is the best math instruction ever. I like this guy and find his explanations good and useful, but have had at least 4 professors that were better. I am very grateful for these videos, but don't think this is as good as it gets. this is just what competent math instruction looks like, not excellent math instruction. I hope you guys get to experience first hand really good instruction.

[michalchik]

I am amazed at the number of people that freaked out at the Taylor expansion and seemed to hate them. I thought they were one of the most elegant and powerful things I has seen in mathematics and they answered so many questions.

Now trig substitutions, those are ugly.

[Deliratio]

Funny thing is, you can find taylor expansions for the functions you want to integrate, then integrate then taylor expansion and with the new expansion, go back to an elementary function. Which is a lot less effort than trig-substitutions.

[michalchik]

@Deliratio Good point, I had forgotten about that.

[IronWolfWood]

@michalchik You're right !

[GreenAms]

@michalchik it's actually the Maclauren series...not Taylor...but Mac is a form on Taylor about 0 instead of a constant.... :)

[michalchik]

@GreenAms Ah, I have to look over that again. Thanks for the reminder

[tatfr0guy]

@michalchik i don't know....if you think about it trig substitutions in the context of the arclegnth formula are pretty intuitive

[bmx391xmb]

@michalchik trig sub is very very useful... with out it we wouldnt be able to integrate many things...

[reid300]

@michalchik I hate everything to do with summations lol, one bad calc prof ruined my chances with summations lol

[phtmexplo]

gr8 vid, thx

[michalchik]

the first term of the taylor expansion shouldn't be primed right?

[balwit]

This is the best mathematics instruction I have EVER experienced. Thanks!

[karsonson]

To treenabalds,

It's because the second derivative of sinθ is -sinθ, it is EXCATLY zero when you plug θ=0.

That is, f''(0)=0.

And for cosθ, the first and third derivatives are EXCATLY zero when you plug θ=0. That is, f'(0) and f'''(0) are zero.

[treenabalds]

Thank you, karsonson. It makes sense to me now.

[treenabalds]

Can anyone clarify why (at 48:01) he sets sin(θ) ≈ θ θ^3/6, leaving out the second degree term (θ^2/2) as it seems should have been next according to the Taylor expansion? He doesnt do that when setting cos(θ) ≈ 1 θ^2/2. I keep thinking about it but cant figure out what Im missing.

[ginogrz]

This prof is the man, seriously.

[dnm25]

i feel better about not having mastered taylor expansions now...

[Cactilio86]

Agree with the previous comments. I'm amazed about how the people reacted to that. Nice!

[CadeHerronETSU]

Hahaha!!!

Applause... Very nice!

[gregsabo]

I loved when the class applauded!

[ThePname]

@gregsabo I do have wished to not know the end … sniff