Euler's Method for Approximating Differential Equations [ +Python Insights ]

Get yourself a 2 MONTH FREE PREMIUM TRIAL by using Daddy's special link skl.sh/flammablemaths4 :)
The worked Example: • Video
DE Playlist: • Separable Differential...
This Video has been sponsored by Skillshare! =D
Today we are going to introduce euler's method for solvig first degree DE's! Using the difference quotient and interpreting as the discrete h-derivative is going to be a very useful tool here in deriving this recursive algorithm!
Source Code #1: www.pastiebin.com/5da1985b1113f
Source Code #2: www.pastiebin.com/5da198bab78cb
Help me create more free content! =)
/ mathable
Merch :v - teespring.com/de/stores/papaf...
www.amazon.com/shop/flammable...
shop.spreadshirt.de/papaflammy
2nd Channel: / @rockhardwooddaddy
--------------------------------------------------------------------------------
Wanna send me some stuff? lel:
Postfach 60 06 03
14406 Potsdam
Brandenburg
Germany
--------------------------------------------------------------------------------
My Website: www.papaflammy.engineer/
Instagram: / flammablemaths
Flammy's subreddit: / flammybois
Twitter: / flammablemaths
Facebook: / flammablemaths
Got some time to spare? Make sure to add captions to my videos! =) kzbin.info_cs_p...
Want to know more about me? Watch my QnA! =D • Question and Answer Ti...

[@non-inertialobserver946]

When your code works after only the 58th try: "Sometimes my genius is... it's almost frightening"

[@jackcarr45]

"Oh boi papi is going to love this :v" - Wheeler, 1755

[@Blox117]

who is this "wheeler" you speak of? are you perhaps referring to the famous mathematician Yooler?

[@ffggddss]

@@Blox117 Yule log? Fred

[@allaincumming6313]

Now engineers and physicists can congratulate, not only constants and functions can be approximated.

[@Blox117]

whut do ya meen, theres nothin wrong with approximatin my spellin or muh mathuhmatics *plane wings fall off and buildings collapse in background*

[@allaincumming6313]

@@Blox117 _What? Error term? I don't understand that mathematician shit_ *continues using only the first Taylor term*

[@duncanw9901]

*laughs ass off in runge-kutta*

[@mrandersonpw53]

You know Jens, this channel turned into an Engineering channel so gradually, I didn't even notice.

[@benjaminbrady2385]

Only real g's know that it was actually archimedes who invented differential calculus but then a monk destroyed the document describing it

[@sw3aterCS_]

Given some Medieval scholars’ adverse reaction to infinitesimals, this makes a lotta sense.

[@duncanw9901]

@@sw3aterCS_ in their defence it took ol' wierstrau🅱️ to make the things rigorous

[@yonatanh8722]

15:25 The error is actually getting bigger with every iteration

[@ramon1930]

Bruh i love you. It's incredible when i'm trouble you simply come out with the keeeeeey insight.

[@non-inertialobserver946]

It wouldn't be a papa Flammy episode without the "who would win" poll

[@hambonesmithsonian8085]

We did this exact thing in my physics seminar class!

[@Vincentsgm]

this is exactly what im doing those last days in class python odeint, euler implicit/explicit, rk2, rk4

[@Vincentsgm]

if you know how to use jupyter notebook, i could send u those algorithms, with graphs using matplotlib etc

[@sergey7375]

Loved the video, my boi. Any chance for a video about Runge-Kutta Method?

[@damiandassen7763]

I learned this last week in university, but I'll watch it anyways. :)

[@SpaghettiToaster]

Looking forward to 100k subscriber special lit method for solving high-order nonlinear PDEs analytically!

[@July-gj1st]

Hey papa, what’s the simplest chaotic system you can think of, I need to use one to create a key for an encryption (for computer mathematics).

[@starship1701]

At 15:28 you said the error is first quite big, but then gets smaller. It has an "e-05" at the end of that number though. If you look closely the error in that case gets larger.

[@davide467]

A serious question: does this method also work for stochastic differential equations?

[@dgrandlapinblanc]

Cool. Thanks.

[@musa4539]

got my tea. I'm ready for some maths

[@kwirny]

Pogramming stuff is always fun, and you can always challenge yourself. C/C++ is also great for pogramming algorithms.

[@kwirny]

@Daniel G It's an old language, what do you expect. You can do everything you want but it just takes more time and knowledge. But the Performance is better.

[@kwirny]

@Daniel G Cause when you know c++, you know more than just pogramming and you get a deeper understanding of how a computer calculates.

[@MuitaMerdaAoVivo]

@@kwirny That's was what a professor i had always said to the class. If you understand C, you get way better at programing anything.

[@kwirny]

@@MuitaMerdaAoVivo Yeah :). It's not efficient to always use c/c++. But you can benefit from knowing it. It's cool that we came to an consens.

[@cestpasmoices3550]

Thanks

[@wompastompa3692]

Python? Nah son, just pull up a spreadsheet, define a few cells, and have fun dragging the formulae for thousands of lines.

[@trololollolololololl]

Thx for 2nd theorem of engineering

[@tbar7290]

Thanks bro What is your specialization and your university level?

[@tatjanagobold2810]

Yeeh infinite boi Wearing this shirt every Analysis lecture now haha

[@IsmaelAlvesBr]

How do I make this with zeros in the Transfer Function ?

[@pawehoowicki7940]

very nice

[@empireempire3545]

So there are other integrators than Velocity Verlet?

[@Xrelent]

Could you do a video on Euler's technique for holding chopsticks? Pascal's fork method is elegant in it's approach, sure, but I'm tired of being made fun of.

[@Ricocossa1]

Naisu. I think you could have shown some graphs with your examples at the end of the video

[@IshaaqNewton]

Flammy, I want to know about The shapes which look like Ellipse but not the same and their functions. Please, it's a big request. Please........

[@matron9936]

IGNORED

[@frozenmoon998]

Approximating engineer papa at it again.

[@absolutelymath3399]

They were skillshare 😂😂😂🙌🏼🙌🏼

[@benjaminbrady2385]

Sorry, I don't use that virgin python shit. I only use C or certain assemblys

[@duncanw9901]

If you didn't bootstrap the compiler yourself, is it really C?

[@benjaminbrady2385]

@@duncanw9901 I prefer to use a magnet to write processor instructions myself actually

[@PeterJavi]

@@benjaminbrady2385 You're not a real programmer unless you create your own processor.

[@benjaminbrady2385]

@@PeterJavi absolute fact

[@mastershooter64]

wait WTF? are you like 2 weeks old or something? you don't even create a universe and create a star and wait for a rocky planet to form around that star and mine silicon, gold, copper, iron, and aluminium and make your own processor?

[@minhaj283]

Us engineers use these numerical integration techniques all the time! Who cares about rigour... Side note: Could you do the Verlet method as well and compare it to Euler's method :))

[@starship1701]

@@PapaFlammy69 We are learning about all these numerical methods right now in my computational physics class. Super cool to see you do a video about euler's method. We derived it in class with taylor expansions so seeing you do it a different way is awesome! Verlet is something we are learning too, it's for second order ODEs instead of first order like Euler's. We have only really used it to start the first step of more accurate methods like Numerov's algorithm (because y-1 needs to be estimated to estimate y1). I could send you my professor's notes about verlet if you are curious about it because tbh it's hard to find this information quickly in some other sources.

[@duncanw9901]

"If the greatest number x then x+1>x and can we deal without knowing one of its solutions?"

[@epicmorphism2240]

Mach bitte ein video uber dans intégral mit den grenzen 0 und ♾ von cos(ln(x))

[@klei7263]

ok real boi question flammable man gauss or euler bro.

[@521Undertaker]

3:33 Your solution curves that differ only by “a constant” seem to all pass through the origin but have different slopes. A small but nontrivial flammy error!

[@luisramrod9121]

I love that shirt 😀😀😀

[@tszhanglau5747]

Who would win? An almost impossible equation or a math boi?

[@micayahritchie7158]

I got 3 ads for Brilliant in this video

[@davidepascu3026]

Oh boi

[@pendulousphallus]

Papa covering another class I failed.

[@pendulousphallus]

​@@PapaFlammy69 I think most science, math and engineering students are willing to accept the risk of failing a class. It happens, it just means you're being appropriately challenged. I just wish I had that money back is all. Please only be crying over my bank account and not my transcript.

[@ozzyfromspace]

Why would anyone dislike this? I don’t understand 😭

[@PapaFlammy69]

:(

[@morbidmanatee5550]

Something to think about. I watched kzbin.info/www/bejne/pYSXfpSQgMmZe5I and realized.... This is a very interesting question. I think that matter and anti-matter probably exist in equal numbers. Just that they ended up existing in different "universes". Due to Heisenberg, the anti-matter likely formed its own universe, likely in a slightly offset time frame due to the uncertainty principle. But due to a miniscule but non-zero time frame (Plank scale?) between the balance of particles and anti-particles, there are two universes offset by a non-zero time difference, but occupying the same space, but can't interact (not "there" at the same "time") via electrodynamics. But maybe there is gravitational interaction between them that is what we see as "dark matter" (the two universes pushing against each other internally?). Thoughts?

[@georgian_thoughts]

Котята круто, я считаю.

[@girishtripathy3354]

Yeah that CoMa. I am sure to go to CoMa after taking Maths :(

[@The_Professor123]

3:47 Why not

[@ge3neva]

4:19 Pre-emptively calming down the maths fanboys

[@jeffersonbezerra6107]

Boi in portuguese means ox... Infinity 🐮

[@x15cyberrush9]

im a pro in python

[@cassiel5150]

Gettin close to 2^2^2^2^2 subscribers tho. :/

[@BrandonSLockey]

this guy is the hottest guy i have ever seen in my entire life

[@PapaFlammy69]

seriously? xD

[@nirash8018]

His mature way of speaking mixed with the german accent just puts him way above everyone else

[@kilisaas2536]

Komm du aus Deutschland weil du eine ln deutschen Akzent hast

[@YitzharVered]

Everyone knows real Chads do it in J A V A S C R I P T

[@Ricocossa1]

Real bros make their graphs in assembly language.

[@IshaaqNewton]

Please, reply.

[@hanniffydinn6019]

Bullshit, there is always a person who is first, who gets the gold medal! 🤯🤯🤯🤯🤯🤯🤡🤡🤡🤡🌍🌍🌍🌍

[@oleksiishekhovtsov1564]

Virgin Python vs Chad MatLab Jk, MatLab is a plague on the science community

[@MathematicsOptimization]

The smell... That smelly smell... Smells like Numerical Approxilation

[@amruthmandappat.s4337]

your introduction is more like an overacting