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Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.
Differential equations were invented separately by Isaac Newton and Gottfried Leibniz. This debate on who was the first one to invent it was argued by both Isaac and Gottfried until their death.
Calc 2, then Calc 3, then usually Differential Equations
Some partial differential equations do not have analytical solutions. These can only be solved numerically.