Systems of linear first-order odes | Lecture 39 | Differential Equations for Engineers

Matrix methods to solve a system of linear first-order differential equations.
Join me on Coursera: imp.i384100.net/mathematics-f...
Lecture notes at www.math.ust.hk/~machas/differ...
Paperback book at www.amazon.com/dp/B0BL9X4QWN/
Subscribe to my channel: ua-cam.com/users/jchasnov?...

[@esscate]

Thank you Jeff Bezos

[@lukaskrause6022]

When he’s looking down and to the right he looks like Mike from breaking bad

[@healthlife2372]

Are you bro. Of Jeff Bezoss

[@aashsyed1277]

Lol

[@Mrsingh-mn4bt]

XD 🤣🤣

[@ggg17ggg17]

hahahaqhahhhaahahahhahahhahahaha

[@RBB.]

thank you Mike Ehrmantraut

[@foldandfray4859]

I thought the squeaking was a rat in my wall and paused the video many times to go look 😂

[@ProfJeffreyChasnov]

Haha! I know it was there but my producer/editor said he eliminated it post-production. I can't hear it now. Old ears, I guess. I'll ask my daughter.

[@harrytaylor4360]

I like the way that you emphasise that we're using an assumption here- the anzatz that y=ve^At- that it isn't something obvious implied by the previous step. Sometimes that little fact gets skipped over along the way...

[@garrettweil3464]

THANK YOU SO MUCH! Your's are the only videos I've found which explain this and work through an example in a way I can understand!

[@moise6792]

You sound so much like my last HS math teacher. I fell in love with your courses before I even try to understand😍 😍

[@ProfJeffreyChasnov]

Find other Differential Equations videos in my playlist ua-cam.com/play/PLkZjai-2JcxlvaV9EUgtHj1KV7THMPw1w.html

[@amaleranga5637]

this one helped! Thank you Sir

[@sofiyavyshnya6723]

So clearly explained in under 10 minutes!! Amazing video! Thank you so much

[@alwaleed1414]

Thanks Mike!

[@bhavinmoondra6492]

Amazing explanation😊🙌

[@RefinerSimilitude]

This is essentially a summary and overview of three consecutive one and ahalf hour lectures in differential equations.

[@AJ-et3vf]

Thank you so much for this sir! Very helpful! Love revisiting my differential equations knowledge!

[@bendustin7609]

I totally remember the linear algebra class that I never took.

[@user-ox6zu4ce5g]

why do we try to substitute x(t) to ve^{lambda*t}?? Is it just trying one form of a solution? or is there any logical reason to do so?

[@ProfJeffreyChasnov]

There is logic to it because of the behavior of the exponential function on differentiation.

[@pawpatrol55]

what do we do if there are varible coefficients for one of the ODEs? so like for instance if (x2)' = 0x1 +0x2 + 2x1/x2

[@ProfJeffreyChasnov]

That would be a nonlinear system. May or may not be able to analytically solve it.

[@pawpatrol55]

@@ProfJeffreyChasnov Understood. thanks. so there is no direct method for this?

[@vivekbajpai6637]

Thanks a lot sir ❤️ love from India ❣️

[@GoldenTiger01]

Can someone explain to me the term "on sots" that he uses? Just trying to understand more math terms and it's the first time I hear it being used.

[@ProfJeffreyChasnov]

ansatz. It is a guess for the form of solution that contains at lease one free parameter that you will try and solve for.

[@monsieurLDN]

Anzatz is just an educated guess

[@mohanprasad6373]

Good explanation

[@TheWP120]

Omg ’ansats’ is a swedish word. That’s so cool, english rarely lacks good words for things.

[@danieljensen2626]

Came trying to remember how to solve a system of ODEs, left wondering if this man is a wizard or if he's just the worlds foremost expert on writing backwards on the cleanest piece of glass in the universe

[@latticepoint5245]

Probably reverses the video in post, still pretty neat though

[@pauld8747]

What’s more likely, he spent years mastering writing backwards, or he wrote normally and flipped the video horizontally post recording?

[@kaursingh637]

excellent

[@industrialdonut7681]

What can this be a physical model for?

[@riccardodellorto4267]

An electric circuit with 2 capacitors that charges with different speed.
If you want a clear schematic: R1 // C1 // (C2 + C3 // R2)
This is what I am trying to solve and I ended up with a system like the one in this video

[@thenewstyle8704]

What if there is more than x1 and x2?

[@ProfJeffreyChasnov]

Then you deal with a bigger matrix.

[@staphenW77]

BIG THANK

[@samirelzein1978]

nice!

[@jyotirohila7190]

Sir, I'm confused in case of repeated roots

[@kim15742]

The word ansatz is so funny, I thought my German professors made that up

[@sinaabedini7487]

Bless you

[@vickerszhu2621]

How that guy can write in a mirror symmetry way???

[@protoxpire0]

He cant. The video is just flipped horizontally when editing

[@toshi2252]

@@protoxpire0 No wonder he is writing using his left, which is in fact his right

[@mettataurr]

@@toshi2252 imagine meeting him irl after watching his lectures online

[@vinithadaniel7752]

@@protoxpire0 When the video flipped, why didn't the contents on the board flip?

[@garrettweil3464]

@@vinithadaniel7752 they do! Keep in mind, from our perspective, they would originally have appeared backward (Like looking at someone's writing with the page flipped over) but then when the video is flipped, the words go back to being readable from our perspective!

[@industrialdonut7681]

SQUEARK~!K!K!

[@markoalex8819]

kid named finger

[@stanleyzhang5058]

thanks for ur teaching, but i have one question. how did u record this video, did u just write everything reversely?

[@giantatom]

Waltuh we have to solve the ode waltuh

[@jasonthomas2908]

This man has a pink lid on a purple texture, and I'm confused.

[@thehmsp7304]

AYYO FINGER....AIN'T NO WAYYY 💀💀💀💀

[@rgaurii]

kid named finger:

[@koka1571]

waltuh

[@sukruciris]

you look like megamind

[@friedrichwilhelmhufnagel3577]

@06m50s let me Samurais