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# Lec 3 | MIT 18.03 Differential Equations, Spring 2006

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Indoor, Outdoor & Kids' Trampolines

It was supposed to be "sign of p", not "sine of p"

wow. man this professor is very good, my professor sucks. :3 man now i can Get a good mark beter than C or C+ XD

Now this is what I call lecture. My professor didn't even say a thing about all these basic stuffs. Awasome, and thanks for posting.

good silence in the lecture ..we have a rock party every lecture

I don´t think you can get anyway better explained than this …

I find it hard to believe your Professor didn't explain the Linear DE's and how to solve them. That would be a Calculus Professor skipping over continuity and jumping right into differentiation.

That is the result of chinese professor who can barely speak english and expect student to know everything before even the class started. Welcome to Stony Brook University.

come on who REALLY understands this stuff? not me.

many many many many many many many thaaanks for mit

Just a nit-pick: In the explanation of the 'linear' versus '1st order' forms, the captions state 'the sine of x'. Really, it should be the 's-i-g-n' of x… With that said, I cant believe that I'm such a loser that I'm watching, of all things, a vid on ODEs in my weekend.

God, I need a woman………..

At 28:09 he seems to imply that u'/u = du/u, so u'=du. But since u is a function of x, isn't u' equal to du/dx? Can somebody please explain this to me?

@analemma2345 @analemma2345 Actually he meant to say "du over dx (all of that) over u" (the derivative of u with respect to x divided by u itself). That is called the differential quotient (u'/u or du/xdx depending on the notation you're using) and equals (lnu)'. So then we have (lnu(x))'=p(x), we integrate on both sides with respect to x and use some simple algebra to get u(x). Hope you understand my explanation despite my crappy english.

@keijigo @analemma2345 Actually he meant to say "du over dx (all of that) over u" (the derivative of u with respect to x divided by u itself). That is called the differential quotient (u'/u or du/xdx depending on the notation you're using) and equals (lnu)'. So then we have (lnu(x))'=p(x), we integrate on both sides with respect to x and use some simple algebra to get u(x). Hope you understand my explanation despite my crappy english.

@Satchindra meeeee :DD

search 18.01 MIT on youtube… that's pretty much all the background you need (at least for this lecture)

@agentorion Professor was right, derivative of ln(1+cos(x)) is "-sin(x)/(1+cos(x))". The negative sign was not forgotten actually.

@jimmylovesyouall from 38:15 by the way.

thanks for posting these

He just makes you love math! Impressive!

About 7 minutes in, he starts talking about the errors that occur with the 'change of sine of p' (according to the subtitles). Surely it should be the 'sign' of p and not 'sine'? Just thought I would mention it seeing as its a little confusing otherwise.

Making this free on youtube… Is a gift to humanity.

@yaymynameispete The MIT transcripts have many errors, try not to pay attention to them if you can.

Prof. MATTUCK makes my previous Maths teachers like JERKS!!!

Making my previous university look like SHIT!! I mean BULL-SHIT!!

Mit maths profs. make my previous Maths teachers look like JERKS!!

My previous university was full of shits!! I mean Bull-shits!!

MIT is lucky to have Pro. MATTUCK!!

omg, so much better than my prof! thank you 🙂

God. My school teaches math as if the only people they have in class are math majors when in actuality almost every student in my class is an engineer.

heey MIT how did you find this amazing teacher this is no ordinary teacher man i would love to go to all his lectures !

heys people… i have a doubt.. at the end, when he solves the second differential equation, and he's finding the integration factor, didn't he forgot the minus? i mean, he has got : – integr(sen(x)/(1+cos(x))) … so the answer it would be (u)^-1 … it wouldn't match with the first equation … am i right?

@MrAlb0t Yeah, I saw that too. I guess we should just focus on the differential equations part of this and not the Calculus involved. But I think the problem as a whole is unsolvable because I can't do the final integration.

Love this professor. Very lucid explanations — he makes sure you know what you're supposed to be looking for. He also obviously has fun with what he's doing!

17:45 Semipermeable membrane. Sounds like the dialysis bag lab for AP Biology.

The chalk is so smooth!

I WILL be back to watch this very video in around 3 years from now, seeing as im only in calc 1 🙂

This lecture alone was more helpful than wasting my time on reading many hours of Calculus without understanding one thing.

Lucid explanation, didn't know when it completed!!..

I Really Like The Video From Your Solving First-order Linear ODE's; Steady-state and Transient Solutions

great video! right around 28:00 it got very exciting!!

@algorithMIT what does the avg home work look like after/for one of this lectures out there?

Doing these stuff in A'levels. Yeah, I'm feeling so fucking awesome right now. -_-

I like this video lecture

It's First Order Unear DE, apparently.

he has real nice handwriting

his penmanship is impecable!

I wish that was true for us. Our calculus lecturer treated us like retards because we were engineers, and obviously couldn't appreciate or understand a proof.

brilliant teacher, imo

From 48:15 onwards, why does 'all of this automatically disappear'? As in why does the integral etc. on the left go to zero when t = 0? I get why he turned it into a definite integral, just not why it equals zero when t equals zero.

nice sir

Nah mate, I'm not trying for Cambridge hahaha. But I did have FP1, FP2 and FP3 in Further Maths besides the normal general maths.

americans are so stupid arent they? They went to the moon, have the most technologically advanced military in the world, developed and field tested nuclear weapons first, and created financial instruments that have a global effect on the world economy.

i would characterize "developed and field tested nuclear weapons first" as stupid

the things you mention has more to do with money than with smart stuff. switzerland could have also went to the moon, if they would spend more money on it^^

He is a good lecturer!

How can we find the differential eq of order 3 with nonconstant coefficients? e.g. y''' + P(x).y'' + G(x).y' + L(x).y = F(x).

38:27, where does the minus sign go when he does e^ln(1+cosx) :S

lovely lecture tho imo 😛

they know how to teach at MIT

Did he forget the y at 39.30 in equ. (1+cosx)y'-sinx"y"=2x?

Thanks for answers.

without the "nerds" you wouldn't have a computer to post your ignorant comments…

your voice is awesome !

It's interesting comparing this lecture to what my own are like with the University of Toronto's Engineering Science. It seems this professor explains things a lot more than my own, but on the other hand it's more of a challenge to have to discover these things independently.

The integral of 1/x is ln(|x|).

i don't think u even read my question there xD but nvm i saw what i didn't understand

Yeah, you're right, that's not really relevant =]

Fantastic 😛 Thanks

This guy is so solid.

didn't he miss to multiply 2x by (1+cosx) in the example # 2 ….???

I wish they were able to improve the video quality. Is there anyway MIT can get this up to 480?

WARNING: The subtitles around 7:00 state that the sin(p) should be carefully scrutinized when deciding which way to represent this equation (and ultimately solve it). The subtitles should have stated the SIGN (e.g. +/-) of p. He is referring to the algebraic manipulation of the equation and dropping the (-) sign from the p(x)y portion of the representation, which is perfectly OK to do as long as one keeps them straight.

omg he counts from 0! <3

Using scientists poached from germany and other countries.

What if you can't integrate p

Then you have to use a different method.

Nope he din't…. It was 2x/(1+cos x) Which he multiplied with (1+cos x) giving back 2x.

-sinx is the derivative of (1+cos x) And thus integrating -sinx/(1+ cos x) .dx we get ln(1+cos x) whi9ch is then exponentiated to e^ln(1+ cos x)

MIT needs to pass out some lozenges to those students…

the teacher is so clear with explaning. everything sounds so simple and reasonable.

I'm surprised no one picked up on his mistake

@38:41 what hapend there?????? i think he got that wrong and what will happend if its negative??? todo cambiaria por que tendras -(1+cos(x)) de facor integrante, – ( 1 + cos(x)) y' + sin(x) y = – 2 x

Diffusion …isnt it 2nd order usually???

great clear explanations (just bad video quality). if someone could re-digitally fix the video, it would be awesome.

In fact, Newton's law of cooling governs heat transfer by conviction not by conduction as stated in the lecture. The law governing heat transfer by conduction is Fourier laws and it says the the rate of change of temperature is propostional to the temperature gradient.

Also, steady state means, as far as I know, that the temperatures becomes constant i.e. fixed not as mentioned approaching infinity!

Excellent lecture….I learned a lot .

Great video

awesome lecture…

This lecture is really flawed on many levels. First of all Te is not a function of t (it was declared a constant in the beginning……then he changed his mind) and also, when he applies the definite integrals (at the end of the lecture), there shoulnn't be any constants. He is a good mathematician of course, but maybe, he should prepare for his lectures better

"to ethnic groups" wtf?

tomorrow ?? how many maths lectures does this guy gives each week ??

His explanation for finding the integrating factor was simple and elegant – very nice.

Sir you are great

Hi, anybody knows which book they use ??

31:05 Integrating Factor Method

Really excellent lecture… wish my teachers were this good at explaining.

Models (heat diffusion, salt concentration), and Integrating factor determination and solution of first-order linear differential equations..

Is Jello a solid or liquid?

The diff.eq. he attempted at 44:36 is also separable. He could have solved by seperation of variable. It turns to logarithmic and exponential form later.

i could finaly understand the theory behind this method just by the way he ponders his calculations. i love this teacher's lectures

funny and useful

Se Deus quiser, eu vou estudar aí.

Beautiful conclusion to the lesson.

12:15 fckn t-series

I was lost from the beginning.

This is excellent! What a simply amazing teacher – makes my university (UNSW) look like shit. Pathetic really by comparison.

At minute 41 he made a mistake and forgot to write that the (-sin(x)) term was multiplied by y, sad confusing some students