More Examples of Second Order Differential Equations

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This video gives more examples of second-order Ordinary Differential Equations and their solutions. We review the characteristic polynomial and how to use initial conditions. We also show that eigenvalues of the matrix system are roots of the characteristic polynomial.
Playlist: • Engineering Math: Diff...
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This video was produced at the University of Washington
%%% CHAPTERS %%%
0:21 First Example
11:23 Writing as a Matrix System of Equations
16:11 Matlab Code Example: Plotting and Integrating the Solution
23:14 Matlab Code Example: Plotting and Integrating the Solution
25:23 Second Example (Unstable System)
28:33 Third Example

Опубликовано:

29 сен 2024

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Комментарии : 19

@RainierVerschuren 20 дней назад

You make differential equations a fun subject to study. Thanks!

@ahmedbassam9587 Год назад

The quality and the preparation is just amazing. Thanks a lot for giving this for free on RU-vid

@lioneloddo 2 года назад

I don't remenber very well, but I believe that we can use two other constants which have a more physical meaning. Instead of using two exponentials, we can use : A.cos(wt+phi) where the two equivalent unknown are A and phi (the amplitude and the phase). We can also use A.cos(wt) + Bsin(wt) where the 2 unknown are A and B (just two ampltitudes without phase). It's less beautiful (from a mathematical point of view) but sometimes it's more practical ...

@hoseinzahedifar1562 2 года назад

You are right... However, your idea is good when we have full imaginary values for \lambda1 and \lambda2 (\labmda = a +ib or a-ib, with a=0)... If we got real values for these two \lambdas (or complex values with real part not equal to zero), the best way to get the true solution is using the expression of c1*exp(\lambda1*t)+c2*exp(\lambda2*t)... don't you think so?

@lioneloddo 2 года назад

@@hoseinzahedifar1562 That's a good point, sir.

@danhvo2702 2 месяца назад

I hope the "like button" will be effective for multiple clicks. Great lecture.

@starriet Год назад

for future ref) I haven't investigated how the ODE45(or 'solve_ivp' in Python code) works, but the parameter 't' of the lambda function @(t,y)A*y seems like "dummy", just for making the ODE45 work.

@curtpiazza1688 6 месяцев назад

Great preview of eigenvalues! 😂

@RodgerRabbit-k5k 5 месяцев назад

Thankyou Steven, you are a very good teacher.

@Amitpatel-fn6bf 7 месяцев назад

❤

@drscott1 7 месяцев назад

👍🏼

@steadyfield 2 года назад

Great video. But what if the right hand side of the differential equation in 9:00 is a non-zero constant (i.e. the system is non-autonomous and has an external control input), how to solve the equation by assuming x(t) = exp(λ*t)?

@ТимурГубаев-ж8ы Год назад

Probably you already watched this video but still: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-wCeDUbZQ_zA.html

@danilomoura4387 Год назад

great lecture!! I am learning a lot! thx!

@manfredbogner9799 9 месяцев назад

very good

@manfredbogner9799 9 месяцев назад

thanks a lot

@declanwk1 Год назад

thank you so much for these videos

@Eigensteve Год назад

Thank you for watching!

@davidmurphy563 2 года назад

I paused the video at 1:39 and did the sum no problem. I've also done a lot of linear algebra, built a 3d graphics engine from scratch, make a neural net, games, etc. Wouldn't call myself an expert by a long shot but this is all stuff I'm reasonably familiar with. 20 mins into the video I was completely lost. On maths that I can do. Wow. Maybe this isn't the right channel for me...