2. First-Order Equations

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MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014
Instructor: Gilbert Strang

In this lecture, Prof. Strang explains first-order equations.

License: Creative Commons BY-NC-SA

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Good guy Hilbert Strang. He sent me his book on linear álgebra for free because I needed it in Caracas Venezuela

profesorciencias

Actually, I'm really moved by Prof. Gilbert. Since the first time I saw his video, Highlight of Calculus, I thought he was very old and may retire soon. But how could he still teach a lecture! He's over 80 now. Please cherish what he brings us.

masonmu

It’s only later that you realize what a pivotal, primal lecture this is and how important it is to everything you ever want to do.

jimlbeaver

Professor Strang, thank you for a fantastic lecture on First-Order Equations, which is an important part of Ordinary Differential Equations. In order for me to understand this lecture, I took notes from start to finish.

georgesadler

This way of teaching is magic. It tells what the math really is. I love him.

butianxiong

Gilbert Strang. Excelent teacher and friendly person

profesorciencias

Thanks for sharing this lecture video. I was having hard time with this class, and it helps a lot. One thing I want to point out is, the camera moving is very good, but it zooms in too much. I can't see more than three lines of equation. It was good to zoom in when the video quality was bad like old lecture video of Dr. Walter Lewin. But now you guys support 1080p, and I can see everything clear with good amount of zoom out at 17:56

tbpom

I have learned much from 18.06, and I'm really happy to see professor Strang

siriusxie

Thank you for this. The absolute best explanation of how first order differential equations work. This lecture put so much in perspective for me Thank you !

cherylann

Just my two cents: on 57:29, (when the source function is delta(t), the particular function(case 4)=exp[a(t-T)] when t>=T. Compare to the earlier case 3 situation, when the source function is step function, H(t), the particular function(case 3)=(1/a)[exp(at-aT)-1] when t>=T. Since dH(t)/dt=delta(t), so the derivative of particular function at case 3 = the particular function at case 4.

xsli

Great teacher, so cool he is still teaching

lenz

When the math professor is so good that he can even make an English teacher understand the value of tangents and digressions.

berksteraydo

Gil Strang + Prof. Jerrison = 2×(World's Best Math Professor) !!

americanborn

Strang has to be one of the most advanced smartest in the world.have a very good

bettymontoya

Regarding the modelling of the bank account- he showed that in the case of a step function the solution is given by y(t) = y(0)exp(at) + 1/a (exp(a(t-T)) -1). All the modelling at and after time T makes sense, but if we take a time t smaller than T, then our initial deposit y(0) has grown as usual, but the second term is negative since exp(a(t-T)) is smaller then 1 for t smaller than T and hence exp(a(t-T)) - 1 is negative, which would mean that in total, our initial deposit would not be growing as usual, but have a sort of pull-down by the second term in the solution function y(t). Can someone explain why that is reasonable?

vladislavgotsev

Why he can do ayp + ayn = a(yp + yn) and not ayp^2 + ayn^2 = a(yp^2 + yn^2)??? He says that he can yp + yn by linearity, and that it could not be possible with y^2

dunga

May God bless MIT for all these mathematics teaching videos! Anybody help me here please: delta(0) is said to be infinity. However, on 54:30, delta(t-T), how come Professor Strang was saying "you deposit $1 at time t=T to the bank"? I was thinking "depositing infinity amount of money to the bank at time t=T".

xsli

the best lecture on first-order equations :D

hathuytu

okay hear me out highest Math ive ever done is Alg. 2 i now want to go to school for engineering at 28. Just jumped into Engineering MIT courses. How do you guys do this?

cryptochofo

Very good class, but this camera guy moving it all the time is horrible

jonathanperilla

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