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If you are a scientist, engineer or mathematician, there are too many examples to list. If you aren't, then there are basically none, except in finance.
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.