Lec 4 | MIT 18.03 Differential Equations, Spring 2006

[NganaJHone]

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[Ondelendo]

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[bebeheuy]

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[willamricard]

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[imegatrone]

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[bundawartini]

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[anakmudajaman]

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[ShilaGinafy49]

geil bin ne sau

[agapitoflores001]

Mind blowing lecture. Whaaah.. but this is so excellent.

[vajitarian]

he is alright. i can honestly say that his lecture is identical to the one receive at my university. just because he teaches at MIT doesnt mean he is greatest educator of all time. he does his job slightly above average, that is all.

[Styx47ag]

@vajitarian what university do you go to? This lecturer blows mine out of the water.

[vajitarian]

@Styx47ag a small campus in the california state university system called sonoma. it is far from fancy but i also wouldnt care to guess how much cheaper it is than MIT. i would say that this professor is better than my calc 1 professor but i would say that he is either identical or very close to my last two math professors.

[Liaomiao]

great lecture as always, damn this is getting difficult lol

[CostaDelBarto]

I love watching maths nerds snicker when they teach it. Another great lecture. 

[stan021]

It is the best explanation...superb

[alexwhb122]

It seems like every MIT teacher is amazing!

[x1x2x3ct]

HE RULES

QED



[AA10Megaviv]

Arthur Mattuck's typical lectures are truly thrilling roller-coaster rides inside the hidden potential humor of energetically blazing math, and so I'm simply addicted to them. :)

[HGoodwyn]

Only a genius could mention a drug boat in a pure math class and got away with it!

[trgopan]

really maths GURU

[naturallymagic88]

great lecture!!! if you don't understand this, you probably need to watch the previous lectures or go back to high school.

[yyourfacee]

damn..that was intense x.x

[lovericecake]

I really wish all the schools would use the same book so that they teach all the same components! =/ His lectures are great though...

[paultech1988]

He is a really good teacher. I am glad that the videos were uploaded to youtube as the opencourseware site said something was wrong with the url. This is the first time I'm doing a diff 1 course and so I am trying to get a headstart on the work. Thanks MIT!!!

[ducefalo21]

Gracias maestro!

[anuragk833]

it's really poor video not able to understand anything

[ivionday]

Three seconds or three grahams. haha.

[odinheim]

Good lecture

[tennisIS4pussys]

What lecture does he explain "exact equations"?

[brco2003]

@tennisIS4pussys I need this, too. And I bet he does a damn good job.

[PukkPukk]

Its great they still use chalk.

[robinhoode]

Drug boat? This guy is ridiculous..!

[darkrathamantis]

Impressive. I live in Ecuador and I study in the best university of my country (ESPOL), and it is know that it has the same academic level as MIT, but the way this professor get's my attention is out of this world. Don't get me wrong, I am proud of my school, but I guess I will watch this lectures before attending to class, just to be a bit ahead.

[PukkPukk]

Sounds like a very good plan. These MIT vids are quite entertaining and interesting. I am pretty much lost when listening, though I think I can grasp a bit of it. Good luck in Ecuador.

[darkrathamantis]

@PukkPukk Thanks :D

[MATH462PDE]

Now why on earth would one call an equation of the form \dfrac{dy}{dx} = F( \dfrac{y}{x} ) a homogeneous eqn. Take y' = y/x + 1 or in other words xy'-y=x . NOT A HOMOGENEOUS eqn...Abusive terminology

[Hivernya]

where is the lecture for exact equations?

[BRAINONBOARD]

THE LORD says that this man works for 23 !!!!

[jsmith754]

How do you solve the problem dT/dx=1/(1-T^4)? I am very curious about this one, and i think he didn't solve it here. Thanks.

[sikory]

you multiply both sides by (1-T^4)dx, so the equation becomes(1-T^4)dT=dx then you integrate boht sides (left to dT and dx)

that results in T-T^5/5= x + C but to further reduce that to a explicit function of x is pretty much impossible

[jsmith754]

I guess I was writing it the wrong way. I meant to say dx=dT/(1+T^4). Any idea if it can be integrated over T?

[sikory]

I typed it in Wolfram Mathematica and that gives me a integral that i guess nobody would have found otherwise:

1/(4 Sqrt[2])(-2 ArcTan[1 - Sqrt[2] T] + 2 ArcTan[1 + Sqrt[2] T] - Log[-1 + Sqrt[2] T - T^2] + Log[1 + Sqrt[2] T + T^2])

Log being the natural logarithm, but i don't think this would be something you would guess or get by things like integration by parts

[sikory]

I now found out that by the method of partial fractions, you can write 1/(T^4+1) as the sum of four terms of the form a1/(T+q1) + a2/(t+q2)+..., where q is a fourth root of -1,

[nirmalagrawal]

it's pretty simple

take the term(1-T^4) to left,integrate both sides to get T-T^5=x+arbitrary constant

[jsmith754]

I meant the less obvious dx=dT/(1-T^4). I think it is using mixed fractions up to some point. Any ideas? Is dT/(1+T^4) solvable by formula?

[nirmalagrawal]

that also is samefor dx=dt/1-t^4 wwrite the denominators as product of 1+sqrt (T) and 1-sqrt(T)

applying partial fractions method,then similarly do for 1-t^2 as product of 1+t and 1-t,also dt/1+T^4 can be solved by dividing numerator and denominator both by t^2

then writing denominator (t+1/t)^2-2,then use substitution z=t+1/t,so it simplifies to -dz/z^2-2,hope now u can solve it

[HoNiAn]

En el denominador sumale 2T^2 y restale 2T^2, con esto tienes en el denominador (T^4+2T^2+1)-(2T^2) = [(T^2+1)^2-(SQRT(2)*T)^2], esto te va ayudar muchísimo para formar, las fracciones parciales, y comenzar a integrar.

[wasssabii]

try tangent inverse (1+ (T^2))

[loafair]

he speaks english!... unlike all my profs.

[laiwencong]

why no longer available.Help!

[rpdwpb]

I wonder if this is the first class in the math sequence at MIT.

[kmharrower]

At the very end he say's the arctan(y/x) was theta,, does he mean alpha plus 45 degrees is theta?? Seems weird cuz y/x is theta??

PS Do enjoy these MIT lectures.

[in00bee]

Theta is the azimuth in polar coordinates. See wikipedia's article on the polar coordinate system

[kmharrower]

in00bee, Thanks for your answer, my question should be written better,

1) Restatement of first question, at the end he talks about theta as a function of arctan y/x, isn't this alpha?? But he talks as if he is descibing the curve of the "boat". I do not understand what angle "Theta" he is talking about.

[kmharrower]

Also, Question 2) Just prior to the Theta calc, he uses the law of logarithims, and gets arctan z= ln(1 + z^2)^1/2 + ln x + c, shouldn't the power be a negative 1/2 for the first term on the right??

Thanks for your help.

[kmharrower]

Opps, I just noticed he moves that term from side of the equation to the other, making it a positive term.

[ribakuka]

yes i think he missed that part...actually is a different y..

[xxsmangiexx]

This guy is good and he has legible handwriting!

That's it...I'm never showing up to class, I'm just going to watch these videos. I wish I went there :(

[yosonie]

MAn, I am totally lost in my dif. eq. course. I wish this man was my instructor!

[pollardrho06]

Professor Arthur is the best!

[Royalshippie]

HOW WILL I GET ADMISSION IN mit?????

[kingslice75]

Why can't my math profs be like this guy? :(

[rpdwpb]

Because most professors don't like their job teaching. I am pretty sure that MIT prof's love their job, or well they are damn smart at the very least.

[amhara23]

He is the best teacher!

[stokeajh]

how come when he find v prime, he always adds the extra y prime on the end? is the some chain rule going on there or sumin??

[MathMikie]

yes it is the chain rule

[tehdennis]

these are going to save my ass for my final..

[LongShlong125]

I noticed there were over 20 lectures , I got time today so...

[BRAINONBOARD]

THE LORD says that you are stupid.... don't say that you even understand one of hes lectures not even in one year!!!!

[BRAINONBOARD]

*( -1) sorry, thank you for reminding me....

[lhyd7hak]

congratulations MIT!!