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

Matrix methods to solve a system of linear first-order differential equations.
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Lecture notes at www.math.ust.hk...
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[@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...

[@garrett-weil]

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!

[@bendustin7609]

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

[@sofiyavyshnya6723]

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

[@alwaleed1414]

Thanks Mike!

[@RefinerSimilitude]

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

[@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?

[@moise6792]

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

[@TheWP120]

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

[@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

[@markoalex8819]

kid named finger

[@amaleranga5637]

this one helped! Thank you Sir

[@maxtian6096]

the scrachy noise made by marker pen writing on the glass scared the s**t out of me.... I thought there's sth going wrong with my laptop

[@ProfJeffreyChasnov]

We tried our best to minimize the scratch noise. Sorry.

[@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?

[@ProfJeffreyChasnov]

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

[@김민우-z3j]

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.

[@vivekbajpai6637]

Thanks a lot sir ❤️ love from India ❣️

[@thenewstyle8704]

What if there is more than x1 and x2?

[@ProfJeffreyChasnov]

Then you deal with a bigger matrix.

[@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?

[@garrett-weil]

@@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]

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

[@bhavinmoondra6492]

Amazing explanation😊🙌

[@stanleyzhang5058]

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

[@mohanprasad6373]

Good explanation

[@AJ-et3vf]

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

[@kim15742]

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

[@jyotirohila7190]

Sir, I'm confused in case of repeated roots

[@kaursingh637]

excellent

[@staphenW77]

BIG THANK

[@samirelzein1978]

nice!

[@frederikhansen9636]

This guy says homogeneous like he is talking about Alan Turing.

[@saltybreadstick]

Thank you Lord Voldemort

[@industrialdonut7681]

SQUEARK~!K!K!

[@thehmsp7304]

AYYO FINGER....AIN'T NO WAYYY 💀💀💀💀

[@giantatom]

Waltuh we have to solve the ode waltuh

[@koka1571]

waltuh

[@rgaurii]

kid named finger:

[@sinaabedini7487]

Bless you

[@jasonthomas2908]

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

[@sukruciris]

you look like megamind

[@friedrichwilhelmhufnagel3577]

@06m50s let me Samurais