This page gathers the 46 dictionary entries belonging to the domain “Calculus”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples.
- boxcar function noun Any function whose value is zero except for a finite part of its argument for which it has a constant non-zero value.
- calculus of variations noun The form of calculus that deals with the maxima and minima of definite integrals of functions of many variables.
- codifferentiation noun The act or process of obtaining the codifferential of a function, or a function which obtains the codifferential
- conservative adj That is the gradient of a function.
- constant of integration noun An unspecified constant term added to a particular antiderivative to make it represent its whole family of antiderivatives, usually denoted…
- curl noun The vector field denoting the rotationality of a given vector field.
- delay differential equation noun a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the…
- derivable adj Differentiable.
- derivation noun The process of application of the derivative operator to a function, yielding another function called the derived function of the first.
- derivative noun The derived function of f(x): the function giving the instantaneous rate of change of f; equivalently, the function giving the slope of the…
- derived function noun Of a function, another function, the value of which for any value of the independent variable is the instantaneous rate of change of the…
- difference quotient noun The average rate of change of the function f(x) over the interval [a,,a+h]. As h approaches zero, the value of (f(a+h)-f(a))/h approaches…
- differentiability noun The existence of the derivative.
- differentiable adj Having a derivative, said of a function whose domain and codomain are manifolds.
- differential noun A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but…
- differentiation noun The process of applying the derivative operator to a function; of calculating a function's derivative.
- directional derivative noun A function which measures the rate of change of some other function at any point in a particular direction; formally, the directional…
- divergence noun The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- exterior derivative noun A differential operator which acts on a differential k-form to yield a differential (k+1)-form, unless the k-form is a pseudoscalar, in…
- gradient noun The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.
- improper integral noun An integral where at least one of the endpoints is taken as a limit, either to a specific number or to infinity.
- incompressible adj Having a divergence equal to zero.
- infinitesimal analysis noun calculus
- initial value problem noun The problem of solving an ordinary differential equation together with an initial condition (a set of specified values for the unknown…
- integral calculus noun The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying…
- integration noun The operation of finding the integral of a function.
- intermediate value theorem noun A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is…
- inviscid adj having a gradient of zero
- irrotational adj Having zero curl.
- irrotational field noun A vector field that has a irrotational vector value at any point, i.e. one that has zero curl everywhere in the domain.
- irrotational flow noun A flow that at any point in time is a irrotational field, i.e. one that has zero curl everywhere in the domain.
- Jacobian noun A Jacobian matrix or its associated operator.
- kernel noun A function used to define an integral transform.
- logarithmic derivative noun Given a real or complex function f, the ratio of the value of the derivative to the value of the function, (f')/f, regarded as a function.
- Maclaurin series noun Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated…
- monotone function noun A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent…
- rotational adj Having non-zero curl somewhere, i.e. not irrotational
- saddle point noun A point in the range of a smooth function, every neighbourhood of which contains points on each side of its tangent plane.
- stochastic differential equation noun a type of differential equation in which one or more of the terms is a stochastic process resulting in a solution which is itself a…
- superconstructive adj In which the constructive propositional calculus can be simulated or is reducible; at least as powerful for proofs as the constructive…
- Taylor series noun A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order…
- time derivative noun A derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function.
- time integration noun A numerical method for solving differential equations that describes the manner in which a system changes over time.
- turning point noun A maximum or minimum on a graph.
- u-substitution noun A method of integration in which a function of a variable is replaced with a new variable, conventionally called u.
- vector calculus noun The branch of mathematics that covers the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space.