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Used to prove uniqueness of solutions in ODE problems
Z tranform can be used to solve the differential equations occurring in electrical problems.
Partial differential equations are great in calculus for making multi-variable equations simpler to solve. Some problems do not have known derivatives or at least in certain levels in your studies, you don't possess the tools needed to find the derivative. So, using partial differential equations, you can break the problem up, and find the partial derivatives and integrals.
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.