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.
“Feed a cold, starve a fever” is an adage that’s been around for centuries. The idea most likely originated during the Middle Ages when people believed there were two kinds of illnesses. The illnesses caused by low temperatures, such as a cold, needed to be fueled, so eating was recommended. Illnesses caused by high temperatures, such as a fever, needed to be cooled down, so refraining from eating was thought to deprive the furnace of energy.
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.
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.
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
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
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.
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.
He didnt even try to justify the e ~ c_1h formula. Basically I think the approximation of y_{n + 1} will be off by about 1/2 h^2f(x_n,y_n). We do such an approximation for y_i a total of delta(x)/h times, so the total error will accumulate to delta(x)/h * 1/2 h^2f(x_,y_n) = h * 1/2 * delta(x) * f(x_, y_n) summed over all n. Thus the error indeed is proportional to the step size we choose, and smaller steps are better.
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.
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.
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 :)
If your approximation happens to cross a separatrix, then it's long term behaviour will differ greatly from the long term behaviour of the solution you are trying to approximate
16:50 this is really funny because after doing all these calculations and explaining his method it instantly sounds like hes calling euler high for coming up with this stuff XD
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.
If your approximation happens to cross a separatrix, then it's long term behaviour will differ greatly from the long term behaviour of the solution you are trying to approximate
Ok, I might be starting out with too advanced a lecture, but at around 7:00 - how does he arrive at h*An? Is there some Pythagorean sorcery I'm missing that B = AC?
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!!!!!
"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?
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.
It's impossible to "pull yourself from your bootstraps" but the professor jokes saying, "well it's not impossible since we are doing it" which is comical because they are doing something that's impossible.
![SahBabii - Viking [Official Music Video]](http://i.ytimg.com/vi/D37cL92JX0I/mqdefault.jpg)
holy crap these lectures are so much easier to follow than at my school!
Yes the more knowledge you have the more easy to taught.
17:58 more than a decade and a half later, we still use the terms "concave up" and "concave down" lol
Im a hard aerospace engineer and never liked maths but I swear this teacher is making me love diffrential equations
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....
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.
This is a fantastic explanation of Euler's Numerical Method for y'=f(x,y) and it's Generalizations in Differential Equations.
RIP Professor Arthur Mattuck
Such a great teacher...What a pleasure to learn maths with you. Thanks!!
u getting dopamine lol
“Feed a cold, starve a fever”
is an adage that’s been around for centuries. The idea most likely originated during the Middle Ages when people believed there were two kinds of illnesses. The illnesses caused by low temperatures, such as a cold, needed to be fueled, so eating was recommended. Illnesses caused by high temperatures, such as a fever, needed to be cooled down, so refraining from eating was thought to deprive the furnace of energy.
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.
the Slope=rise/run or as he has it An=RIse/h solve for rise, and you get rise=An*h hope this helps
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.
He might be just a math undergrad who participated in a time travelling experiment some time in the future.
Euler is not the father of number theory.
He is the great great grandfather of Donald trump
@@fitofight8540 this is true! many people are saying this, many fine people are saying this!
Top 3 mathematicians of all time
We meet again 240p.
10 years no comments 💀
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
let's say that I am in LOVE with this old man :)
I clicked on this video to make me sleep and yet I watched the whole video learned something 😂
🤣🤣🤣
nice bro
I can't sleep while watching this video because this lecture makes me simulate something in my brain.
This guys is funny! :D
He makes class quite enjoyable!
I wish I had a professor like him for my differential class!
I found watching PatrickJMT's explanation on Euler's Method helped me better understand this professor's lecture.
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
Check out the 'Runge Kutta 4 method' (I think that's what its called). Uses the first 4 terms of the Taylor expansion, it's this on steroids.
To the people moaning about the quality, which bit are you struggling to read? Thanks.
I wanted to ask the same question. His handwriting is large and clearly visible.
Thank you for your detailed explanation of Euler's Method.
thanks for making mathematics simple prof
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....
"The way you learn to talk in kindergarten is the way you learn to talk rest of your life" is my favourite quote now.
When calculating, multiplications and powers go before addition/subtraction.
0^2 - 1^2 = (0^2) - (1^2) = (0) - (1) = 0 - 1 = -1
He is the man world need .
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.
iSquared
Ok....
Wasteful use of an ellipsis.
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.
29:36 "THAT MEANS YOU, PRETTY BOY"
What was that
@E can you explain what is that
Well, thx, but I think that means us lol
don't be late...
Euler too high
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.
How's life?
@darylicked
using the eqn: y = mx+c
(delta)Y + c = m(delta)X + c
(delta)Y = hAn
He didnt even try to justify the e ~ c_1h formula.
Basically I think the approximation of y_{n + 1} will be off by about 1/2 h^2f(x_n,y_n). We do such an approximation for y_i a total of delta(x)/h times, so the total error will accumulate to delta(x)/h * 1/2 h^2f(x_,y_n) = h * 1/2 * delta(x) * f(x_, y_n) summed over all n. Thus the error indeed is proportional to the step size we choose, and smaller steps are better.
Thank you for the clarity.
One of my favorite subject
22:39 26:53 29:36 LOL, I love this guy. :D
+tokamak Haha he is hilarious isn't he? Loves to get a bit of a laugh in the things he does :D
Mathematicians are humans, just like us. I think.
29:37 lol whaat
dude this guy is awesome.
DON'T BE LATE!!!!!
Does anyone know WHY those people did what they did at 29:40?
2:55 That's exactly what I thought. Then I looked at the Laplace transform and I thought to myself - how the heck could they ever figure this out...
Great lectures!
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.
Great Lecture!, thank You MIT!
these lectures are great!
thx you MIT!
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.
Best part of the 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 :)
Did you discover it?
If your approximation happens to cross a separatrix, then it's long term behaviour will differ greatly from the long term behaviour of the solution you are trying to approximate
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
Sir, commendable job!! 👏🏽
Euler too high made my day :)
对理解微分方程很有用，来自BUPT。
16:50 this is really funny because after doing all these calculations and explaining his method it instantly sounds like hes calling euler high for coming up with this stuff XD
23:28 "UEHEUEHO" love those vocalizations
Just after 28:55 what on earth
Noone literally no-one:
Axe gang from kung fu hustle at 29:36
dont be late！
you pretty boy
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!!
Thank you
MIT is so cool..
we still used the terms concave up/down in my AP Calc class....
Marjorie Buss
Even now
actually, I find these terms are more intuitive
thanks a lot, great lecture.
29:37 What just happened? I'm confused...
a great teacher
this is great. thanks, Prof!
29:40?????
awesome lesson
i love mit
Great lecture
don't be late 29:35
GATE examination tension brings me there,thans prof
Can sum1 tell me how at 6:57 he shows that the 3rd side of the right triangle is h times A n?
the Slope=rise/run or as he has it An=RIse/h solve for rise, and you get rise=An*h
Why thank you dear sir chap.
What's the first pitfall that Prof. Arthur wants us to find out? Is it the 'error accumulation'?
If your approximation happens to cross a separatrix, then it's long term behaviour will differ greatly from the long term behaviour of the solution you are trying to approximate
Ok, I might be starting out with too advanced a lecture, but at around 7:00 - how does he arrive at h*An? Is there some Pythagorean sorcery I'm missing that B = AC?
An(dy/dx) is the slope at that pt. which also equal to tan(theta)
So that side becomes h tan(theta) or hAn
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!!!!!
Please process the videos with a CNN that puts it in HD
Love initial value problems
this is awesome
I love it!
good luck. Math is a strange and special thing
that was great, cheers. I have to ask, what the hell was with those guys in the matrix costumes?
"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?
A quick question. What if there are 2 differential equations? Such as dx1/dt = f(x1,x2) dx2/dt = g(x1,x2). Anyone please...
good stuff...
teachers like him are angels i wish i could have got the same
That's why professors like him teach at MIT :)
Interesting video
Can't we use the second derivative to calculate y_(n+1)?
13:24
Lol yeah, "the way you talk in kindergarten is the way you talk the rest of your life."
I don't think they had HD cameras in 2003.
@euanfoster thats a typical "rook at me, im going to torronto" thing to say
These videos are very helpful!
Oh...and I also would like to know wth happened at 29:39 o_O
Calculous to the rescue!
In calculous we trust
@raydredX It's the first time I hear this has a name. People seem to like to give long names to simple things.
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.
tuncTHEcavo Being high is being under the effect of drugs
can ne1 explain how the 3rd side of the rt Triangle @ 6:57 has come out as hAn???
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.
Eulers method is an approximation. The smaller your step size, the better it gets
22:44 why students are laughing?
It's impossible to "pull yourself from your bootstraps" but the professor jokes saying, "well it's not impossible since we are doing it" which is comical because they are doing something that's impossible.