Euler's Method for Approximating Differential Equations [ +Python Insights ]
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- Опубликовано: 30 сен 2024
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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!
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"Oh boi papi is going to love this :v"
- Wheeler, 1755
who is this "wheeler" you speak of? are you perhaps referring to the famous mathematician Yooler?
@@Blox117 Yule log?
Fred
When your code works after only the 58th try:
"Sometimes my genius is... it's almost frightening"
Now engineers and physicists can congratulate, not only constants and functions can be approximated.
whut do ya meen, theres nothin wrong with approximatin my spellin or muh mathuhmatics *plane wings fall off and buildings collapse in background*
@@Blox117 _What? Error term? I don't understand that mathematician shit_ *continues using only the first Taylor term*
*laughs ass off in runge-kutta*
Only real g's know that it was actually archimedes who invented differential calculus but then a monk destroyed the document describing it
Given some Medieval scholars’ adverse reaction to infinitesimals, this makes a lotta sense.
@@sw3aterCS_ in their defence it took ol' wierstrau🅱️ to make the things rigorous
15:25
The error is actually getting bigger with every iteration
Python? Nah son, just pull up a spreadsheet, define a few cells, and have fun dragging the formulae for thousands of lines.
Sorry, I don't use that virgin python shit. I only use C or certain assemblys
If you didn't bootstrap the compiler yourself, is it really C?
@@duncanw9901 I prefer to use a magnet to write processor instructions myself actually
@@benjaminbrady2385 You're not a real programmer unless you create your own processor.
@@PeterJavi absolute fact
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?
You know Jens, this channel turned into an Engineering channel so gradually, I didn't even notice.
It wouldn't be a papa Flammy episode without the "who would win" poll
Looking forward to 100k subscriber special lit method for solving high-order nonlinear PDEs analytically!
this is exactly what im doing those last days in class
python odeint, euler implicit/explicit, rk2, rk4
if you know how to use jupyter notebook, i could send u those algorithms, with graphs using matplotlib etc
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........
IGNORED
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.
Komm du aus Deutschland weil du eine ln deutschen Akzent hast
Approximating engineer papa at it again.
"If the greatest number x then x+1>x and can we deal without knowing one of its solutions?"
Pogramming stuff is always fun, and you can always challenge yourself. C/C++ is also great for pogramming algorithms.
@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.
@Daniel G Cause when you know c++, you know more than just pogramming and you get a deeper understanding of how a computer calculates.
@@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.
@@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.
Boi in portuguese means ox... Infinity 🐮
this guy is the hottest guy i have ever seen in my entire life
seriously? xD
His mature way of speaking mixed with the german accent just puts him way above everyone else
Who would win? An almost impossible equation or a math boi?
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!
Bullshit, there is always a person who is first, who gets the gold medal! 🤯🤯🤯🤯🤯🤯🤡🤡🤡🤡🌍🌍🌍🌍
Something to think about. I watched ruclips.net/video/oS4MaZKdfE0/видео.html 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?
Virgin Python vs Chad MatLab
Jk, MatLab is a plague on the science community
Loved the video, my boi. Any chance for a video about Runge-Kutta Method?
The smell... That smelly smell...
Smells like Numerical Approxilation
Yeeh infinite boi
Wearing this shirt every Analysis lecture now haha
Bruh i love you. It's incredible when i'm trouble you simply come out with the keeeeeey insight.
4:19 Pre-emptively calming down the maths fanboys
A serious question: does this method also work for stochastic differential equations?
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 :))
@@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.
got my tea. I'm ready for some maths
Yeah that CoMa. I am sure to go to CoMa after taking Maths :(
your introduction is more like an overacting
I got 3 ads for Brilliant in this video
Why would anyone dislike this? I don’t understand 😭
:(
im a pro in python
I love that shirt 😀😀😀
Please, reply.
Thanks bro
What is your specialization and your university level?
Naisu. I think you could have shown some graphs with your examples at the end of the video
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.
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).
Cool. Thanks.
I learned this last week in university, but I'll watch it anyways. :)
3:47 Why not
very nice
How do I make this with zeros in the Transfer Function ?
Thanks
Gettin close to 2^2^2^2^2 subscribers tho. :/
ok real boi question flammable man
gauss
or euler
bro.
So there are other integrators than Velocity Verlet?
We did this exact thing in my physics seminar class!
They were skillshare 😂😂😂🙌🏼🙌🏼
Mach bitte ein video uber dans intégral mit den grenzen 0 und ♾ von cos(ln(x))
Thx for 2nd theorem of engineering
Oh boi
Everyone knows real Chads do it in J A V A S C R I P T
Real bros make their graphs in assembly language.
Котята круто, я считаю.
Papa covering another class I failed.
@@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.