Response to Oscillating Input

[@PeteZam]

I would really like to tank MIT and Dr. Strang for uploading these videos to the public. Although my university is not as prestigious as MIT, and I will never receive a degree from a school such as MIT. It is amazing that i can just go online and learn from the brilliant minds that teach at MIT. This will probably be the closest thing to free education in my lifetime, and I cannot thank MIT enough for not locking these beautiful videos behind some sort of pay wall. My school often glosses over or completely skips many things that I have watched in MIT OpenCourseWare videos(especially Calc 3 and now ODEs), and I thoroughly enjoy how the math classes at MIT do not gloss over the theory and just say, "Use this formula for this and do this when you see that, ect." It is very frustrating to me when my teachers never take the time to explain why a formula works, or what is the underlying reason that you do this when you see that. I like to understand the inner workings of mathematics, and I just want to thank you one more time for posting these videos. They are very insightful, helpful and informative.

[@boxxer221]

Yes MIT lecturers have a really unique way of making you appreciate the value and purpose of maths, they don't hide you from the real applications of maths which is the key to understanding. It gives you a real way to think through problems intuitively instead of being completely stuck because you don't understand what you are actually solving and why. Without context differential equations are just completely alien and most educators don't address this.

[@MrAngryCucaracha]

Yingdi Xu Probably there is no Honors classes in his school. I know there wasn't in mine

[@wagsman9999]

Prof. Strang's course on Linear Algebra is really good as well.

[@ihbarddx]

Yes! I found him when I wanted to review singular value decomposition. He was so lucid and entertaining that I went through the whole course!

[@vanu71]

I wish I had a professor like him when I went to college

[@stumbling]

Not many like him. I found out he has a method for solving differential equations named after him.

[@pubgplayer1720]

Zero dislikes. Gilbert Strang is one of the best MIT lecturers.

[@taofiknassan2016]

This is how they teach math and this is why they are leading the world

[@companymen42]

Transient solutions are actually important because they represent the ringing in a system and you want to minimize that as much as possible.

[@atomskyjahid1533]

As energetic as ever!

[@dhruvkachhiya9897]

Sir, You are just simply great. thanks for public this wonderful classes.

[@CatsBirds2010]

Thanks youtube for giving me this wonderful teacher.

[@stevenk113]

More math instructors need to point out applications when they introduce each new topic as Dr. Strang does. It really drives home the importance.

[@markus-sagen]

Such an amazing series! Thanks professor!!

[@l1mmg0t]

don't know how I got my EE degree. with you were there then.

[@MrFanius]

Thank you Prof and MIT for the video. I don't think the y_p (t) catch with the initial condition y(0) = 0. So I guess the e^{at} term does count.

[@rakhimovv]

y = e^{at}y(0) - e^{at}*M + Mcos(wt) + Nsin(wt). The terms involving e^{at} will die out if a < 0.

[@wahidamiri7233]

It was very informative, such a great professor as i have ever seen.

[@jeremyboyle4274]

The only question I have is where on earth are these particular solutions coming from in the first place!

[@zacharythatcher7328]

I’m very confused about why he is able to just solve the equations for the coefficients. Is he trying to get them to sum to zero, since that is the only way for sint=cost for all t? That seems like the justification, which really would have helped me with my homework last night...

[@zoro_719]

Thank you

[@Hobbit183]

wow so clear explanation

[@tigerwuli2760]

hope my teacher is as one tenth awesome as Gil

[@omprakasharya9020]

M should b in terms of sin,N in cos ??

[@companymen42]

3:18 I dont understand what he means by matching?

[@marouaniAymen]

Why we didn't add the impulse free solution to the sinusoidal one like in the previous lecture ?

[@youchuanwang1738]

I'm confused when he solves for the m and n with cos and sine. Since cos and sine are interchangeable, is it safe to write the pair of function "-aM+omegaN = 1 ..." to find the solution? I don't think so. It could be that they sum to 1.5 and a -0.5 from sine part cancel out to be a 1 on the right.

[@luanau]

I think he just rearrange and then compare terms, -wMsin(wt) -aNsin(wt) -aMcos(wt) + wNcos(wt) = cos(wt)

[@ege5383]

In 'another form' part we say y(t)=Gcos(wt-alpha), is it just a particular solution so => do we have to add Ce^at as a null/homogenous solution?

[@jcl_c]

Yeah, but we're here not interested in the null/homogenous solution, coz a is usually negative, therefore Ce^at will eventually be zero.

[@tedchirvasiu]

Let's find Eminem

[@evgeniystepankevich7964]

It's my favorite form

[@apocalypt0723]

LMAO

[@leoxu9673]

The results for M & N seem suspiciously similar to the Laplace Transforms of sin(at) and cos(at). Is this just a coincidence or is there some underlying meaning behind this?

[@Amine-gz7gq]

I dunno

[@stearin1978]

5:30 The system may be nicely solved in 3 steps by Cramer's formula. det = w^2+a^2)

[@GC00001]

So.. You do it substituting a column of the coefficients matrix [-a w; -w -a] by the independents terms matrix [1; 0], and then you divide the determinant of that one by the determinant of the original coefficients matrix.. In this case, M = det( [1 w; 0 -a] ) / det( [-a w; -w -a] ) N = det( [-a 1; -w 0] ) / det( [-a w; -w -a] ) *I just wrote that because even I dind't remember Cramer's formula

[@hathuytu]

hahah, the exponential grow only exists in heaven places :D

[@sachinIITD23]

My bike sounds like 03:23 - 03:25 when I try to press the shelf on.

[@bd_harold7752]

I would really like to tank MIT and Dr. Strang for uploading these videos to the public. Although my university is not as prestigious as MIT, and I will never receive a degree from a school such as MIT. It is amazing that i can just go online and learn from the brilliant minds that teach at MIT. This will probably be the closest thing to free education in my lifetime, and I cannot thank MIT enough for not locking these beautiful videos behind some sort of pay wall. My school often glosses over or completely skips many things that I have watched in MIT OpenCourseWare videos(especially Calc 3 and now ODEs), and I thoroughly enjoy how the math classes at MIT do not gloss over the theory and just say, "Use this formula for this and do this when you see that, ect." It is very frustrating to me when my teachers never take the time to explain why a formula works, or what is the underlying reason that you do this when you see that. I like to understand the inner workings of mathematics, and I just want to thank you one more time for posting these videos. They are very insightful, helpful and informative.