Diferansiyel

Diferansiyel is a term used in mathematics, physics, and engineering to denote the idea of a differential—the infinitesimal change in a quantity. In calculus, the differential of a function y = f(x) is written as dy = f′(x) dx, where dx represents a small change in x. Differentials generalize to functions of several variables, with expressions like dy = ∂f/∂x dx + ∂f/∂y dy, providing a linear approximation of how output changes with input. In differential geometry, differentials form differential forms such as dx and dy, which are used to define integrals over curves, surfaces, and manifolds. Differentials underpin the chain rule, Taylor expansions, and many formulations of physical laws as rate laws or conservation statements.

In applied contexts, diferansiyel concepts appear in differential equations that model systems evolving in time or space, including motion, population dynamics, and electrical circuits. They also support small-signal analysis, where changes around an operating point are approximated linearly.

In mechanical engineering, a diferansiyel (differential gear) is a device within a vehicle’s drivetrain that splits torque between two wheels, allowing them to rotate at different speeds. An open differential provides normalization of torque but accommodates wheel speed differences; limited-slip and locking differentials adjust traction under challenging conditions. Most automobiles use some form of differential, typically integrated with other transmission components, to enable smooth turning and stable handling.