What are PDE's? And how can we solve the Heat Equation Numerically?

Nature can be very complicated, but knowledge seeking creatures we are, we always tried our best to model certain natural events with mathematical equations, these equations often are partial differential equations, and solving them helps us understanding our world better, doing it analytically is almost always very complicated, but luckily there is a way to do it numerically.

In this video, you will understand what PDE's are and how to solve them with the finite difference method and the logic behind it, Enjoy ~.

A huge shoutout to Grant Sanderson (3Blue1Brown) for providing and sharing his python math animation engine (Manim), and for his inspirational videos, As well as everyone contributing to the Manim project.

[ilyestoumi]

PDE‘s make finally sense to me ! Thank you for this amazing work 💪💪💪

[nourhamsho]

Thanks very much for your helpful explanation. How can do like this presentation ? Which App do yo used to write in this way ?

[cylinder_down]

This was a very good explanation, thank you :)

[powerofwisdom]

Great job! It was very interesting even though i was familiar with the subject...

[themathics-yt]

Nice! I have always wondered how to use analytical methods on partial differential equations but its always hard to find good sources

[jaimeduncan]

I will say that if possible, between the finite difference method and the finite element method take the second if you don't have the time, the knowledge about the problem (for example the problem is Nobel) or the experience to peek carefully.