Mongodb is not actually faster. Postgres still beats it in any benchmark that matters.
Nothing is ever actually schema-less. There is merely explicit and implicit schemas. If you don't want to bother encoding the schema as proper columns and instead want the schema to remain implicitly encoded in JSON, Postgres' jsonb columns do a better job of that than any NoSQL database does.
Many things that work with time series data use calculus all the time. Both derivatives and integrals are very useful in that context: derivatives being the rate of change at some particular time step, and integrals being the sum of the changes across a range of time steps.
There's a pretty wide range of applications.