วีดีโอ

Dear Professor Bramburger, Thank you for your thorough explanation. I believe I have found an error in your proof that all eigenfunctions are unique. You plugged in the boundary conditions but then concluded that the expression is zero for all x between [a, b], however, the expression is zero only on the boundaries. Sincerely Mahyar

I briefly studied Poincaré Maps for my final project of my bachelors. My study was more focused on a computational side of it, where I used Poicare Maps to see the periodicity/quasiperiodicity/chaotic behavious of dynamical systems. I used a little trick to view non autonomous systems on a poincare maps (although this dependeds on the vector being within boundaries for such system). The thing that I found incredible is how quasi periodic and periodic look very different in a poincare map. At first I was expecting some clusters of non converging points for the quasiperiodic, but to my surprise the points for a quasic periodic system follow a closed curve in the poincare section.

Thanks again! Are you going to more work on dynamical systems theory or a series on neuronal dynamics/mathematical neuroscience

Thank you, Professor. After I left school, I usually learned math by reading books and doing exercises. I have tried several TH-cam videos before. You are the first to make me think that video lectures on Math can be quite helpful.

Dear Jason, so well done, I studied this 40 years ago, now I'm reviewing for research reasons, and I'm so appreciative for your in depth and intuitive approach. Thanks a ton, an Electrical Engineer before simulations ruled :)

Thanks, a lot!

Thank you for my engineering mathematics ...

you are saving lives out here what a great video

Jason you've clearly put so much into this, thank you for your efforts teaching. Would you consider doing an applied series on neuronal dynamics using "Dynamical systems in neuroscience" by izhikevich 2005?

Thanks for this lecture! I'm struggling to work out if/how this relates to action angle coordinates in Hamiltonian mechanics.

So interesting! Thank you for explaining.

Thank you for these videos!

one of the best yt channel but yet very under rated .

very much helpful

damn , these lectures are so helpful . thanks sir

Sehr gur

Sehr gut

my test is this morning and I am cooked.

impressive video. At time 37:25 the coefficients of the sin and cos term are interchanged -> 48/17 sin(t)+12/17 cos(t)

When we assume v(0) is 0, isn't D = 49 instead of -49? Or is it possible for D to be positive and negative at the same time?

i love mathematical modelling and from today im your student im a civil engineering graduate sir

Thank you for doing God’s work, sir.

I am an electrical engineer...enjoyed your lecture.

will factor 3 appear in @10:30

excuse me, is this for math364?

I passed my PhD Mathematics Qualifying Exams at the first trial last month (August, 2024). Your PDE lecture series were very instrumental to my success. Thank you very much for your great content.

you saved UAB engineering grad students my man

Here to solidify a foundation in D.S. that can help me work with ties between probability theory and fractal geometry for problems in quantum physics. Excited to work through this. Thank you for taking the time to make these!

How is he writing on the blackboard like that?

Good Stuff! You are a great man.

r u nuts? what's the point of using transparent glass. Get a board idiot.

2 years ago I watched your Calculus II video series to help study. This semester I am taking PDEs and am delighted to see you have a new playlist! Keep up the great work :)

OMG! That's all I wanted right now!!!!!!!!!!!!!!!!!!! Thnks!!!!!!!

Thank you for your lectures. It is a well explained series so far and I am really enjoying it. Thank you. However, I do have 1 question: why can't growth and decay happen in a second order linear system? The spring mass damper system has oscillations as well as decay and it is a second order system.

After taking your Dynamical Systems course, it seems that dynamical systems can run forward and backward in time. But the forward (in time) Heat Equation and the backward (in time) Heat Equation are different. Is this true?

Amazing lecture, thanks a lot!

Really cool. Thanks from Brazil

thank you for this! I was looking for this proof for my numerical analysis course but couldn't find a video that made sense to me, until now

Great Series! Fantastic! Thank You for your time, effort, and expertise!

Great job. I jumped into the lecture on poincare maps, as a refresher. Have also watched a few others as well. You are an excellent communicator, and the content is spot on.

Bro you're MY Genie ❤❤

Which book would you recommend , very nice video

I'm up to Lecture 23 and I have to say Fantastic Lecture Series and Thank You!!!

is this direction promising now？

This is gold, thank you for these videos

Gonna do a Linear Algebra series in the future?

17:18 doesn't that sign from 0 to -infinity say y is increasing?

As an electrical engineer I am fascinated by this equation and know for a fact the utility of it. Do you know if there's any material that explains the relationship of this equation properties with the electromagnetic fields?

No precise definition of linearity for DEs is given...

My brain is hamburgered.Amzing job btw