While I am working on some physical/mathematical problems, I feel strongly that these three areas are almost the identical thing, except that they have different methods/from different aspects to solve the problem.
For example, I remembered that wave equation can be derived from probability approach(maybe random walk and detailed balance. Excuse me I forget the book name.).
Based on that, some cell automatons can be used to solve PDE.
And an example for optimization problem and DE problems: it seems that Lagrange-Euler equation uses DE approach to model a optimization problem(minimize the action).
I have only undergraduate level mathematical/physical education(and almost all about engineering. I come from a Computer Science background actually). I want to self learn these three areas, and make use of powers of various areas to solve a problem.
Can you direct me to some books/papers on the relations between DE, Probability/Statistic, and Optimization?