Lec 2 | MIT 18.03 Differential Equations, Spring 2006

[IndigentiaSumEgo]

Euler's high.

LOLOLOLOL

[sukhjinder101]

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.

[rustingfreight]

29:37 wtf?

[NganaJHone]

I am very happy to see the vidoe Euler's Numerical Method for y'=f(x,y) and its Generalizations. from you, hopefully the others also are happy for You

[Ondelendo]

Steady I Really Like This Video Euler's Numerical Method for y'=f(x,y) and its Generalizations

[bebeheuy]

Good, I like that you share this video Euler's Numerical Method for y'=f(x,y) and its Generalizations., I wish success always

[andreeaweed]

this is awesome

[SheilaConnieny530]

soso kuckt auf mich bin n hamster

[agapitoflores001]

Very useful equations. Very useful to me. Thanks. Deserves high rating.

[1PeaceNation]

wow. Math!

[thebigfootme]

good job! i love his form of teaching!

[ewajfaifaldoe]

he laughs like sheldon from big bang theory.

[ellliotlai]

love this <3

[ellliotlai]

i'm studying in taiwan, i speak chinese, and I have a russian professor giving differential equations lectures in english

how bad could it be? lol

[worseize]

How about ? convex => all grafik right side by e , if concave => all grafic left side by e , Euler method.

[TheOttoWH]

What the heck happened at 29:40!?

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

uHAUHuhauhUAHUhuaHUHA

[darylicked]

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

[just003]

@darylicked

using the eqn: y = mx+c

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

(delta)Y = hAn

[ARMnonymosTASHNAG]

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

LMAO



[EsXRaptor]

What's the first pitfall of numerical methods we were supposed to find?

[johnmojo86]

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



[chr0nicForc3]

haven't seen a chalk board in while

[southernsahara]

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

[bertalmighty]

@southernsahara Probably a social club.

[MetallicAus]

thanks for making this lecture available.

[krishnashethji]

very good video.....

[kauboibiboppu]

fuck yea !

[SgtBuckwald]

very good video

[comando527]

This professor is awesome, and he also has an eerie sense of humor hahahah. No matter where you go ivy league, community college or self teaching. knowledge is granted for those who look for it no matter what. And hopefully apply it to great theories in science and mathematics...thats all there is to it.

[AlwaysAndForeverPFC]

29:37 xaxaxax that was great xD

[ivionday]

LOL @ 23:24 !!

[birsutube]

He is awwwwwwwsome. My differential eqn prof in college was such a boring stuck-up and all full of himself since he was from stanford and teaching in our small liberal arts college.

[shocks007]

WOW UIUC's math department sucks balls. i actually wish I can take math classes at MIT. This lectures online are a godsend!!!

[delinquentnerd]

14:20 - 14:45 lol this guy's awesome.

[jamil7benton]

I started Diff Eq yesterday @ ju co with a prof who can't speak English. I have a feeling I'll be spending a lot of time watching these videos.

[einsteinkarthik]

Awsome... 

[analemma2345]

"Don't be late" what the hell...?

[406356690]

i love mit

[shalem8]

29:38

[fermixx]

the professor could play bowling on his desk, is really laaaaaaaaaaarge

[fvmanu570]

hello, MIT please podrian traducir o subtitularlos los cursos seria de una mejor hgran ayuda el pueblo estudiantil de paises de habla español y castellano se los agradeceria ,...

[wasssabii]

talves yo te puedo traducir algunas cosas.... que no entiendes?

[fermixx]

@fvmanu570 en tu caso primero deberias aprender a hablar castellano).

Tu texto deberia haber sido algo como:

"podrian traducir o subtitular los cursos ? Seria de una gran ayuda AL pueblo estudiantil de paises de habla HISPANA (castellano). Se los agradeceria."

[Swallow18ki]

JA JA JA Por lo soberbio, pense: este tipo seguro que es argentino.

Despues mire tu perfil y lei:

"Im Fermin from Buenos Aires, Argentina."

No falla! JA JA JA!!!!!

[fermixx]

@Swallow18ki no es soberbia chabon. Es la universidad, estas aprendiendo ecuaciones diferenciales, y no sabes siquiera escribir bien?

No estoy diciendo que me escriba como Borges, pero no se dice "paises de habla español". Que no muera la lengua castellana gracias a los sms y el msn !

[fdlbeats]

this dude is so awesome, i wish could go mit.

[aibmoloc511]

@fdlbeats

same here i wish i could there :/

[mchk2]

@fdlbeats calling him dude wont help you go there lol

[doronster195]

@fdlbeats not with grammar like that

[Diplazium]

At 13:00 when he calculates the value of "An" he gets -1. Shouldent it be 1 because 0^2 - 1^2 = 1, unless I am incorrect when you square a negative number you get a positive number. I am sure there is some reason for this being negative.

[HeresyAPC]

You're stupid.

[tuvlad]

We have the following:

1. By definition An:=f(xn,yn)=xn^2-yn^2.

2. Hence, if x0=0 and y0=1,

3. A0=f(0,1)=(0)^2-(1)^2=0-1=-1.

4. Therefore A0=-1.

The problem is that 0^2 - 1^2 = 1 is false.

[Diplazium]

Thanks Manuel,

Your comments were much more helpful than those of the pinche maricon HeresyAPC. I have only taken applied calculus due to differential equations not being a requirement for a biology major, however; due to a love of physics I have become interested in it. What better source to learn about it, without paying for it, than MIT. I didnt realize that "An" was understood to be the difference of two separate functions. It makes sense now.

Muchas gracias paisano,

-Dave

[tuvlad]

No hay nada que agradecer. Ya sabes paisano, estoy a tus órdenes. Lo que se te ofrezca. Saludos.

[sleepingeye]

When calculating, multiplications and powers go before addition/subtraction.

0^2 - 1^2 = (0^2) - (1^2) = (0) - (1) = 0 - 1 = -1

[jg2675]

You have to see it this way:

y'=x^2-y^2

y'=(0)^2-(1)^2

That's why y' =-1

That's why the professor is correct

[Phio87]

These videos are very helpful!

Oh...and I also would like to know wth happened at 29:39 o_O

[diegoramos27]

+1 who wonders what happened at that time, lol, thanks for these videos.

[Hivernya]

ok can someone explain to me what happened at 29:39

[ari100teles]

00:01

[gocymru]

oh dios, a lot of Chinese

[s1ncere619]

why does it matter if there are a lot of Chinese? you ignorant bastard.

[gocymru]

omg, i was just amazing that there were a lot of Chinese in this lecture room, and didn't mean anything offensive, but you replied me badly. I believe your mama must be pround of you.

[Avogadro1988]

s1ncere619 is a typical youtuber, without even thinking about what is said and analyzing it first, quickly insults the person who is stating his opinion. A lot of chinese, oh god, it's not like he said, holy FUCK look at all those disgusting chinese! its a good thing we bombed those sons of bitches

[schlynn]

LOL, US bombed Japan. You make Americans look stupid.

[888Xristos]

19:13... "too optimistic..."

LOL

[Tsoy1984]

This guys is funny! :D

He makes class quite enjoyable!

I wish I had a professor like him for my differential class!

[puupydoger]

@Tsoy1984 yay!

[Joez85]

MIT is so cool..

[gocymru]

yeah, always

[bahaa456]

its best lecture in odes

[ribakuka]

yes because is function of x

dont get confuse

if y=x2, then you have y2

if you want to derive y2 by respect to x

you will get2y*y'...or same like 2*(x2)*(2x)

4x3...

-----------

and also dont confuse with concave or convex, its just simply monotonically decreasing or increasing

[dennies0101]

sorry for the stupid question but someone can explain at 21:40 why y'' = 2x - 2y * y' ?

I mean why y* y' ? For convexity/concavity i should compute hessian matrix ,should not ?

I don't understand, seems he derivate respect X and in the same expression respect Y...

[dennies0101]

..sorry ,posted twice !

[tekwon2000]

The function is defined implicitly in y, from calc 1. Hessian matrices are fun, but this function is a total derivative and does not require a matrix of partial derivatives to determine any max/min parameters.

[888Xristos]

He reminds us to use the "chain rule" from when you first learned dy/dx. Here's the usual explanation:

if y' = x^2 - y^2

y'' = 2x*x' - 2y*y'

(x' = 1, since it is dx/dx, so we don't write it)

y'' = 2x*1 - 2y*y'

You could also substitute to get

y'' = 2x - 2y(x^2 - y^2)

[dennies0101]

sorry for the stupid question but someone can explain at 21:40 why y'' = 2x - 2y * y' ?

I mean why y* y' ? For convexity/concavity i should compute hessian matrix ,should not ?

I don't understand, seems he derivate respect X and in the same expression respect Y...

[kelvinella]

i never learn the numerical method in this detail. i guess my prof wasnt numerical guy

[kelvinella]

i thought those guys in black are gonna sing a song. but they are funny

[nit323]

Can sum1 tell me how at 6:57 he shows that the 3rd side of the right triangle is h times A n?

[legendofzoltar]

the Slope=rise/run or as he has it An=RIse/h solve for rise, and you get rise=An*h  hope this helps

[scorpion007]

Thanks! I had the same question :)

[Liartar]

@legendofzoltar thanks man, I thought An is the length of hypotenuse, not the slope.

[nit323]

can ne1 explain how the 3rd side of the rt Triangle @ 6:57 has come out as hAn???

[tigernov6]

Asians are the best at Calculus in the United States especially the Chinese.

Does anyone know why?

[Taylz69]

that was great, cheers. I have to ask, what the hell was with those guys in the matrix costumes?

[hgeithus]

Calculus to the rescue!!! :D

[MegaPhysicist]

I would like the video had subtitles u_u

Excellent material!!!

[freaginA]

Thanks for this

[Fortinbras85]

This is a great supplement to the differential equations course I'm taking now. I wish they would continue to post higher level math courses...

[callmejosiah]

agreed... this series is definitely going to come in handy when I take Diff-Eq this Spring.

[gamesguru]

Yea...the higher level math courses are hard to learn without good lectures. I really like that MIT is doing this and I hope they post some more advanced courses soon.

[qubix2008]

Who were those matrix guys ???

[batteekha]

They thought it was the Linear Algebra class.

[qubix2008]

So that's what they do in Linear Algebra? :))

[batteekha]

Yepppppppperzzzz

[qubix2008]

what the hell does yepperzz suppose to mean? :))

[batteekha]

It means yes.

[qubix2008]

oh...and the word "yes" was too short to have a meaning :D ok, thx :)

[freaginA]

yepperzz

[MathMikie]

this video does not explain things very well

[batteekha]

I agree.

[catalinaguerrero]

The video is fine. You are dumb that's all.

[MathMikie]

were not it is useful to get more knowledge

[atiq124]

excellent, i have learned a lot from this video and my concept about this topic is much clear now.

thanks for posting this

[MathMikie]

it is good the theory part and the explanation but you really need a few more examples

[jahdallah]

I am a math major in a university and i have just finished my third year and I took Euler's Numerical Method for y'=f(x,y) and its Generalizations in a course called Numerical Analysis and not in the course Differential Equations that I took.

[JammyTom]

good luck. Math is a strange and special thing

[Royalshippie]

the so called numerical meathods is just a meathod for solving the diff equations...so weather they are taught under a seperate heading or nder the title diff euations is same cmon..u r a math major rt

[cruzpercy]

how do you solve dy/dx=1/(x-e^x) ; y(0)=1 ?? I tried integrating 1/(x-e^x)dx but the calculator doesn't give me the answer. Neither any of the analytical methods I know helps me out (substitution, per parties, etc)... which method should I use for this? anybody can help out plz?

[gavnila]

i just finished my cal3 in a community college. goin to take differential equa... next fall.

[mhkazemi3]

OMG that so awesome!

[Mustardo2]

I think he might have mixed up concave and convex.

[nemo1620]

Nope. See "concave functions" in Wikipedia.

[Mustardo2]

You are right, my teacher taught me wrong.

[gouki02]

good

[gouki02]

thx you MIT!

[gouki02]

thx you MIT!

[LongShlong125]

That lecturer (although very good) talks very slowly , I wish youtube had a fastforward option...

[LongShlong125]

Good lectures , sad thing only so few people use them.

[ssavelan]

I'm grateful for this.

[Saskachewan]

LOL what were those Man in Black there? :P

[gezginpa]

Perfect source! Thanks for doing this!

[tokamak9master]

nobody should ever say they cant get afford a good education in america..

if you can get to a library, you can take MIT classes for free.. 'nuff said.

[kevinkuei]

@tokamak9master That may be so, but being able to say that you graduated from a good school is a big determinant in the job you get. These online MIT videos are great--but you can't put that on your resume.

[daganboy]

This is so helpful!

-Dagan, 14