Solving System of differential equation by diagonalizing a matrix, Dr. Peyam's Show

Solving System of differential equation by diagonalizing a matrix,
by Dr. Peyam Tabrizian,
system of equations and linear algebra,

blackpenredpen

[elf]

I love this guys voice.From now on when ether I do a differentiate I can just hear his voice in my head.

[Gold]

He has broken his chalk at least once in every single video I've seen of him. Very impressive

[Shlungoidwungus]

Maybe it's just me, but I honestly don't find his voice annoying.
Combine that with his enthusiasm for an interesting method for solving differential equations and it makes a better teacher than most.

[DarkRedZane]

Not even 5 seconds in and I'm already hyped by his voice. 😂

[hgaclark]

THANK YOU, I've been trying to find a decent tutorial on this topic for
Edit: It's much better than decent XD

[mattgillespie]

Being only through calculus 1 so far, this looks super cool, but I have literally no idea what's going on lol

[emlmm]

I love linear algebra... so much fun. Even better in Functional Analysis.

[lmmartinez]

It still feels weird to me that many of you Americans don't study Linear Algebra at the same time you study calculus. In my former engineering degree, we had a subject of the first semester called Mathematics I, which divided in single-var calculus and linear algebra, and Mathematics II in the second semester that focuses in applying many linear algebra stuff related to multi-var calculus

[PackSciences]

I got a second order differential system that gave a 3x3 matrix at the Math oral of the Concours Commun Polytechniques, this technique is fairly useful.

[dr.rahulgupta]

Excellent presentation of the topics. DrRahul Rohtak India

[kwinvdv]

It is worth mentioning that not all matrices can be diagonalized in that way. Namely you can have Jordan blocks of size bigger then one. Next step would also be to calculate e^(A t), which has the nice property that you do not need to solve for the initial conditions coefficients: x(t)=e^(A t) x(0).

[Agreedtodisagree]

Having recently taken both diff q and linear alg, I can confirm to people confused about the two distinct topics, this is one hell of a trick to solve at least one kind of pretty challenging differential equation questions.

[xsli]

Dear Dr. Peyam: I love your teaching! Thank you very much! For this type of question, I found that the technique you are teaching is not useful: on 4:30, you already know the two eigenvalues(lamda1=5, lamda2=3), and you also know their associated eigenvectors. So the answer of the problem is already known at that moment: C1*eigenvector1*exp(5t) + C2*eigenvector2*exp(3t). This is the same answer you have derived at the end. I guess this technique is useful in some other situations.

[Jinx-iwzb]

Thats too much energy to handle very distracting

[vendettaanonimous]

Weo, I am very excited about math specially with differential equations, but I was wondering if this could be solved:

x'(t) + y'(t) + z(t) = 0
x(t) + y'(t) + z'(t) = 1
x'(t) + y(t) + z'(t) = 2

Where the initial conditions would be x(0) = y(0) = z(0) = 0.

I don't know if it makes any sense or if it has some physical interpretation, however I would like to know if is possible to solve or if there are some material or paper that relate those kinds of differential equation system.

Greetings from Dominican Republic 😊😊😊

[swamitagupta]

Amazing content! Finally cleared my doubts in the topic. Thank you sir! Also, love your enthusiasm :)

[danielborrero]

This semester I'm starting differential equations not sure if they teach this method but surely I will use it, in which books can I find this? I just started to study Tom Apostol's book, is this method there?

[piupiuhafner]

Excellent explanation. Congratulations...

[muhammadasimsarwar]

Sir I have problem to solve one question related to linear algebra.

[amanmahendroo]

dr peyam is scary... im effing scared of this guy