>>14119194For one, the heat equation, especially in one dimension is typically the first or 2nd PDE one is thought how to solve because it's solution has a relatively simple series solution in terms of trig functions.
Most PDE's you'll encounter in a first class on PDE's (I'e a class that doesn't explicitly use methods from functional analysis) have more exotic functions that you'll have to expand in terms of, Bessel functions being one example.
https://en.wikipedia.org/wiki/Bessel_function>how much more advanced in calculus can you get than PDE's?Assuming you mean basic PDE's, then there are plenty, real analysis isn't exactly more advanced than PDE's, least not at the begining, but it's more technical, and towards the end of a first class you should study some interesting results like the implicit function theorem and the inverse function theorem.
Other than that, differential forms, meassure theory, functional analysis, differrential geometry and differential topology are a few examples.
