I know a bit about how integral transformations can be applied to differential equations. ODEs can be transformed under some circumstances to algebraic equations and PDEs can be transformed under some circumstances to ordinary differential equations. My question is very fundamental and so unfortunately not very precise... What is this sort of mathematics which is transforming "more complicated objects" to "easier objects", especially via those transforms? Is there a "transform mathematic" behind it? Thanks for hints and sorry for strange wording, I am not a mathematician.
Best, Jens