Suppose you start from partial differential equations and functional analysis (on $\mathbb R^n$ and on real manifolds$manifolds, which prominent example problems lead you to work with Pseudo-differential operators? I would appreciate any good examples, as well as some historical outlines on the topics development (Shubins classical book spends a few lines on history and motivation in the preface, but no "natural" examples. I am not aware of any historical outlines in literature.). 2 added 1 characters in body Suppose you start from partial differential equations and functional analysis (on$\mathbb R^n R^n$and on real manifolds$, which prominent example problems lead you to work with Pseudo-differential operators?