differensiell

Differensiell is an adjective used in Norwegian to describe something related to the differential, particularly in mathematics, physics and engineering. The term stems from the concept of a differential, an infinitesimal change in a quantity, and is closely tied to differential calculus and related ideas.

In mathematical calculus, the differential of a function expresses how the function changes for a small change in its input. For a single-variable function y = f(x), the differential is dy = f′(x) dx, where dx represents an infinitesimal change in x. For functions of several variables, f(x1, x2, …), the total differential is df = ∑ (∂f/∂xi) dxi. Differentials provide linear approximations to changes and underpin rules such as the chain rule. In differential geometry, differentials appear as basis 1-forms (dx, dy, …) used to define integrals and curvature, and they combine into higher-order objects known as differential forms.

Differensial or differensiell contexts also appear in differential equations, where relationships involve differentials such as dy/dx or df = g(x) dx. These equations describe how quantities evolve and are solved through methods like separation of variables or integrating factors.

In engineering and mechanics, a differential (differensial) refers to the device in a vehicle that allows wheels to rotate at different speeds, enabling smooth turns. It comprises gears that distribute torque between wheels, with variations such as open, limited-slip, or locking differentials.

Overall, differensiell encompasses core mathematical ideas about infinitesimal changes and their applications across science and engineering.