- Solve a linear system using matrices | MIT 18.02SC Multivariable Calculus, Fall 2010
- (New Version Available) Solving Trigonometric Equations IV

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- Solve a linear system using matrices | MIT 18.02SC Multivariable Calculus, Fall 2010
- (New Version Available) Solving Trigonometric Equations IV

29:37 xaxaxax that was great xD

i do not understand what the men in black were about. They also appeared in the electromagnetism lecture. May someone please inform me what that is about

My teacher was awfull next to this guy when I did that class

lol at 9:54 watch how he pockets the chalk.

LMAO

he needs to explain where hAn comes from a bit better.

What the heck happened at 29:40!?

What was that!? A kind of commercial or a special break!?

uHAUHuhauhUAHUhuaHUHA

@darylicked

using the eqn: y = mx+c

(delta)Y + c = m(delta)X + c

(delta)Y = hAn

this is awesome

@Tsoy1984 yay!

@fdlbeats not with grammar like that

Sir How we assume that the next Yn+1 element also comes on the same curve and has slope "An" as those of Yn.How this is possible as per Euler's.It may come with negitive slope.Consider a sine wave suppose at the maximum Yn=1 (The maximum value of sine wave) Here Yn+1 Element does not have the same slope as Yn. We cannot suppose it as An.Please clarify this.

awesome lesson

Interesting video

whats his name?

OMG you just made me understand the first three weeks of class in 50 minutes. So THIS is what you pay for at a university….wow….

Euler is too high. 😀

2:54 I actually did! XD When I was trying to deduce the equations of motion of bodies affected by gravity that's the first thing I made up to give me an approximation. I guess I'll skip this one.

@raydredX It's the first time I hear this has a name. People seem to like to give long names to simple things.

I struggled to learn all this over 4 weeks of 1 and half hour lectures and this guy made it crystal clear in 50 mins….

@euanfoster thats a typical "rook at me, im going to torronto" thing to say

@ellliotlai Haha

29:37 What just happened? I'm confused…

good stuff…

I've seen it in other MIT videos. It's so painfully awkward.

cool story bro

his chalk, his rules.

Why thank you dear sir chap.

29:36 "THAT MEANS YOU, PRETTY BOY"

It doesn't come the same curve, it only comes close (hopefully). Most solutions to deq's can't be expressed as well defined functions such as sin. Therefore they can only be approximated which is what this method is for. It is similar to irrational numbers being expressed in decimal form. It can't actually be done be it can be approximated to varying degrees of success that are often close enough for practical use.

thanks a lot, great lecture.

anyone have an idea of what the homework-pitfall could be? Something that destroys the fait in numerical methods forever… Somehow seems good to know 🙂

this is great. thanks, Prof!

I love it!

brilliant… 😛

my little box of treasures 😀

23:28 WTF?

40:47, this prof is hilarious

Why isn't his name on these videos?

let's say that I am in LOVE with this old man 🙂

MIT doesent have HD cameras or what?

We meet again 240p.

Best part of the lecture.

29:35.. what???? LOL

OKkkay will you plese tell me the reference of euler too high too low ? cuz i didnt get this joke because of being not american.

I found watching PatrickJMT's explanation on Euler's Method helped me better understand this professor's lecture.

I don't think they had HD cameras in 2003.

Perhaps you should read the title of the video again 😛

240p knew I was coming didn't it…

His notation for euler's method is incorrect. He should've use the linearization. Much more understandable.

This was actually recorded in 2003. The videos were later used for a class in Spring 2006. This info is from MIT in the comments of the first lecture.

His comments around 44:00 are completely wrong!

For a particular step size h Runge-Kutta achieves h^4 accuracy, so halving the step size improves the accuracy by 16 times.

If you use Euler's method with a step size of h/4, so that both methods perform the same amount of work, he says that Euler's method also gives a 16 times improvement, but this is NOT true. Euler's accuracy is order h so you only get an improvement of 4 times

There's a reason people use higher order methods!!!

we still used the terms concave up/down in my AP Calc class….

29:37 lol whaat

Funny professor 🙂

I can't help but think, as I watch lectures from Yale, MIT, etc., that the material at my lowly Midwestern state university contain the same material covered in a similar manner (only much, much cheaper). There is also a much lower suicide rate at my university than in the Ivy League.

……….and also much less prominent intellectual leaders

these lectures are great!

Calculous to the rescue!

In calculous we trust

Great Lecture!, thank You MIT!

shouldn't y" = 2x because the derivative of y^2 in terms of x equal zero?

holy crap these lectures are so much easier to follow than at my school!

I love Mattmatic its only way we can talk to – Aliens in space =)..

thanks for making mathematics simple prof

Euler too high

"halve the step size, halve the error"

Shouldn't that mean that if you halve the step size once, you know how big half the error is. And if you then add/subtract that error twice you should get the true (almost) value of the function?

i don't get how he got the other side of the triangle to be h*An. That would only work if the slope was equal to the hypotenuse and I just don't see how that's true.

I've started quoting these lectures like movies… I might be a nerd. "SAME!" "My little box of treasures."

22:39 26:53 29:36 LOL, I love this guy. 😀

dont be late~~~~~~~~~~~~~~~~~~~~

Of course the comment that euler being exactly right is not an option is said tongue-in-cheek, but the humor to be noted is that the points on the annoying line from earlier that is both an integral curve and an isocline (but not easily drawable) is the gift that keeps on giving, as it corresponds to such a situation, since y''=0 for all x along its length.

Thanks Prof,you are great!!

Such a great teacher…What a pleasure to learn maths with you. Thanks!!

A quick question. What if there are 2 differential equations? Such as dx1/dt = f(x1,x2) dx2/dt = g(x1,x2). Anyone please…

对理解微分方程很有用，来自BUPT。

Why can't one use a numerical method incorporating the second derivative [from the Taylor series] so that accuracy is better [which for second order function will give accurate results]. i.e. y(n+1)=y(n)+h*y'(n)+h^2*y''(n)/2

The second derivative can be induced from the first derivative as shown in this lecture at 21:45

Why y(n+1)-yn= h.An??????

love how mit perform the lectures with chalks .no one these days take the trouble of writing on the board and actually do their jobs . great lecture ^^

27:00 PRECIOUS

GATE examination tension brings me there,thans prof

We say 'plus' and 'minus' in the U.K. Not just in mathematics either, I work in aviation, 'outside air minus 2'. I only use 'Negative' as an adjective, "the value is negative" but I consider the value '-2' to be more of a complete identity. I don't think that we're describing 2 as negative, we're identifying a unique value that is 'minus two'. That's just our convention though.

This Euler is a genius. He has contributed in every form of math. Graph theory was his child. Father of Number theory. Also in DE. He must have been a genius among geniuses.

I like the lecture.

BUT I didn't like the jokes.

Does anyone else find his attempts at being funny and entertaining a bit annoying? I understand it that the great majority really likes all this "Euler too high" jokes, and I'm ok with that. It just seemed strange to me that nobody said that they can be irritating when you are following the line of math reasoning and have to constantly stumble upon these. I mean, otherwise he's going with the material at a good pace, then suddenly out of the blue: "feed the cold" etc. and you have to wait until he's done with it.

What's the first pitfall that Prof. Arthur wants us to find out? Is it the 'error accumulation'?

don't be late…

23:28 "UEHEUEHO" love those vocalizations

23:37 LOL

Sir, commendable job!! 👏🏽

Euler too high made my day 🙂

a great teacher

Can't we use the second derivative to calculate y_(n+1)?

Bolsonaro 2018 ! See ya !

13:24

teachers like him are angels i wish i could have got the same

DON'T BE LATE!!!!!

Idk how to express it.. but the way he explains the concepts is just so clear and straightforward. Truly this must be what it means to be a really good professor.

DON'T BE LATE lmao

Great lecture

I clicked on this video to make me sleep and yet I watched the whole video learned something 😂

Thank you for the clarity.

We can calculate the energy of a spinning gold ring where the integral is the energy of the speed of the charged platinum spinning in the center of the ring magnetally separated.

What was the Pitfall #1? Any1?