Flashcards: Differential calculus

In mathematics, a differential operator is an operator defined as a function of the differentiation operator.

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable.

In mathematics, Fermat's theorem (also known as Interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function derivative is zero in that point).

In mathematics, the gradient is a generalization of the usual concept of derivative to functions of several variables.

In mathematics, the mean value theorem states, roughly, that given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function.

In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v.

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

In mathematics, the Fréchet derivative is a derivative defined on Banach spaces.

In calculus, Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, states that for an integral of the form then for x in (x0, x1) the derivative of this integral is thus expressible as provided that f and its partial derivative fx are both continuous over a region in the form [x0, x1] × [y0, y1].

In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point of the domain of the function where the derivative is zero (equivalently, the slope of the graph at that point is zero).