Diferentiaalne

Diferentiaalne is an Estonian adjective meaning relating to a differential, an infinitesimal change in a quantity. It is used in mathematics, physics, and related fields to describe objects, operations, or properties that depend on differential quantities.

In calculus, the differential captures the linear approximation of a change in a function. For a single-variable function f, the differential is dy = f'(x) dx. In several variables, the total differential is df = sum over i of (∂f/∂xi) dxi, representing the first-order change of f with respect to small changes in the variables. Differentials form a foundational language for expressing rates of change and linear approximations.

In differential geometry, the term appears in the concept of differential forms, which are objects that can be integrated along curves or surfaces and generalize functions and differentials. Differential forms, together with tools like the exterior derivative, provide a coordinate-free framework for geometry and topology.

Diferentiaalne is also used in the context of differential equations, where the laws governing a system are expressed through derivatives or differentials. These equations model dynamic processes such as motion, growth, or physical fields, and their study involves methods from analysis and geometry.

The term spans various fields, including analysis, geometry, and mathematical physics, reflecting a common core idea: describing changes to a system through infinitesimal quantities and their linear approximations. Related concepts include diferentiaal (differential), diferentiaalvõrrand (differential equation), and diferentiaalvorm (differential form).