Ciro Santilli @cirosantilli  40

Some light YouTube channels, good for the first view, but which don't go into enough detail to truly show the subject's beauty:

The finite element method is one of the most common ways to solve PDEs in practice.

The majority likely comes from physics:

If you have a PDE that models physical phenomena, it is fundamental that:

Unlike for ordinary differential equations which have the Picard–Lindelöf theorem, the existence and uniqueness of solution is not well solved for PDEs.

For example, Navier-Stokes existence and smoothness was one of the Millennium Prize Problems.

In many important applications, what you have to solve is not just a single partial differential equation, but multiple partial differential equations coupled to each other. This is the case for many key PDEs including:

One major application of this classification is that different boundary conditions are suitable for different types of partial differential equations as explained at: which boundary conditions lead to existence and uniqueness of a second order PDE.

Bibliography:

ourbigbook.com is a website created by Ciro Santilli.

The website is the reference instance of OurBigBook Web, which is part of the OurBigBook Project, the other main part of the project are software that users can run locally to publish their content such as the OurBigBook CLI.

The source code for ourbigbook.com is present at: github.com/ourbigbook/ourbigbook/tree/master/web

The project documentation is present at: docs.ourbigbook.com#ourbigbook-web-user-manual

This page contains further information about the project's rationale, motivation and planning.

The reason public relations is evil in modern society is because, like discrimination, public relations works by dumb association and not logic or fairness.

If you're the son of the killer, you're fucked.

This is unlike our ideal for law which attempts, though sometimes fails, at isolating cause and effect.

iubmb.onlinelibrary.wiley.com/doi/full/10.1002/bmb.2002.494030030067 Surprises and revelations in biochemistry: 1950-2000 by Perry A. Frey (2006). This should be worth a read.