PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these. Hard to say what's the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you shoul…
The Black Scholes equation is present though, which is used in pricing securities in financial markets. Perhaps this page is aimed at physicists who intend on jumping ship to become a quant!