Miscellaneous tricks with functions. The purer side of the functional wrangling which gets you, e.g. variational approximation.
Dan Piponi's functional logarithms
Nice hack, Dan Piponi -- Logarithms and exponentials of functions:
A popular question in mathematics is this: given a function , what is its “square root” in the sense that . […] I want to approach the problem indirectly. When working with real numbers we can find square roots, say, by using . I want to use an analogue of this for functions. So my goal is to make sense of the idea of the logarithm and exponential of a formal power series as composable functions.
Tom Leinster's course
Tom Leinster, is teaching a course on functional equations (course notes here):
Today was a warm-up, focusing on Cauchy’s functional equation: which functions satisfy
He goes on to talk about Shannon entropy from a functional equation perspective, which is a refreshing derivation.