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The magnitude of the output voltage is proportional to the distance moved by the core (up to its limit of travel), which is why the device is described as having a "linear" response to displacement. The coils are connected in reverse series, so that the output voltage is the difference (hence "differential") between the two secondary voltages.
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
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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.
It is a field of math that uses calculus, specifically, differential calc, to study geometry. Some of the commonly studied topics in differential geometry are the study of curves and surfaces in 3d