A Fun Little Differential Equation In Python (Dark Matter)

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Paper Referenced: arxiv.org/pdf/...
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[@astronemir]

One of my favorite classes during my astrophysics career was grad-lvl “computational astrophysics” that I took as an undergrad. We wrote our own solvers for Friedmann equations and lots of other beautiful equations.
We also wrote our own implementations of numerical solver methods but then used the scipy methods as a test.
I had so much fun in that class.

[@CarlosEduardo-pz8ih]

As a suggestion, you could make a partial differential equation (PDE) case and creat 3d graphics

[@lawrencedoliveiro9104]

Pro tip: genuine Jupyter will take only a tiny fraction of the system resources of the hulking behemoth that is VScode.

[@cybernerddante]

Thanks for posting this!! this is awesome. You've got a natural talent for explaining complicated systems.

[@aykutcayir64]

Great video again! Can you prepare a video that teaches us how to solve general relativistic differential equation for mercury perihelion problem using python? This equation confuses my mind :(

[@MrPSolver]

Plz join the discord and send me this equation! Would love to solve

[@PositiveEnergy311]

GUYS !! I FREAKING DID IT !!
I FINISHED THIS ENTIRE SERIE OF 33 VIDEOS THROUGH THAT PAST SEMESTER !
IT HELPED ME A LOT TO GET MY HEAD AROUND PHYSICS PROBLEMS USING PYTHON EVEN IF I DIDN'T ALWAYS UNDERSTAND EVERYTHING. I HAVE TO SAY THAT YOU ARE A BIG TIME BOSS Mr.P ! I THANK YOU VERY MUCH FOR THE KNOWLEDGE YOU GAVE ME ALONG WITH YOUR RAP INTRODUCTIONS. YOU DO A GREAT JOB WITH THIS CHANNEL. I'M GONNA TRY TO DO THE OTHER SERIES NOW.
ANYWAYS, I BECAME A LITTLE MORE SHREGORY...THANK YOU !

[@AstroB7]

woww, you gained a subscriber!
Will look at your content daily, it’s awesome!
Python + Space, can’t ask for more
Keep it up!

[@schrodingersalphacat1862]

This is great! Worked examples are really useful.

[@DaWu76]

beautifully laid out notebook!

[@andrewiglinski148]

Bud you moved into vscode?! I'm proud of you.

[@CoDFOTIS7]

That's amazing! What happens though when we have to deal with PDE's that cannot be solved analytically? I hope in one of the following videos you will provide us with a worked example of a similar type of problem where you will solve PDEs numerically for instance with the newton-raphson approach. Keep up the fantastic content, your channel's a gem!

[@bjmben88]

I'm pretty sure that the solver he's using is solving numerically.

[@weird407]

@@bjmben88 It is, specifically using the Explicit Runge-Kutta method of order 5 (unless you change the method parameter)

[@riccvven2078]

F loving you mate, super cool, one of the best here, will yu do c++ too?
or some cfd?

[@sylwek1177]

Me: Makes sense.
You: How?
Me: Don't know.

[@jakeanderson6081]

When you defined f(x,m) it looks like you used 63 in the denominator but 64 shows up in the denominator of the markdown. Which one is right?

[@benlucke7763]

Great video as always, thanks!

[@carlosfaz2694]

Great video, greetings from México

[@reneticsk]

This is some cool math 😎

[@xderen_xd]

I am literally Billy right now xd

[@lawrencedoliveiro9104]

8:07 What does it decay into?

[@iasonsaganas6795]

Wonderful!

[@henryodonnell2844]

I was wondering, how do you get latex format as output in notebook?

[@banditadas6175]

Hi, I have doubt if we have a vaiable which changes periodically with time how do u pass it and solve the differntial equation, can u please reply , i really need some suggestion

[@BenJohnsonCA925]

Subscribed!

[@kirill_good_job]

hi, from where you took Гh ?

[@HYPERLOG]

Ok I'm a dumdum, can someone please tell me where those unspecified functions came from or how they were derived?

[@chibitoodles5351]

Why cant I join your server even when I click Accept Invite? I feel like 2019 Joker...

[@nextrimus_9618]

Мужик, ты крут

[@lilpuzeen]

How to set up LaTeX in VS code?

[@ahrens1497]

VS code has built in jupyter python notebook support, which includes markdown cells for LaTeX. Just create a .ipynb file

[@sondochannel6740]

This is not a billy video

[@Thanjin_sama]

First

[@Mahmood42978]

First

[@tousifraza1389]

Great work! appreciated.