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q. -derivative. In mathematics, in the area of combinatorics and quantum calculus, the q-derivative, or Jackson derivative, is a q -analog of the ordinary derivative, introduced by Frank Hilton Jackson. It is the inverse of Jackson's q -integration.
The cokernel of a linear operator T : V → W is defined to be the quotient space W/im(T). Quotient of a Banach space by a subspace. If X is a Banach space and M is a closed subspace of X, then the quotient X/M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section.
Lie derivative. In differential geometry, the Lie derivative ( / liː / LEE ), named after Sophus Lie by Władysław Ślebodziński, [1] [2] evaluates the change of a tensor field (including scalar functions, vector fields and one-forms ), along the flow defined by another vector field. This change is coordinate invariant and therefore the Lie ...
Covariant derivative. In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal ...
e. In calculus, the differential represents the principal part of the change in a function with respect to changes in the independent variable. The differential is defined by. where is the derivative of f with respect to , and is an additional real variable (so that is a function of and ). The notation is such that the equation.
Quotient ring. In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring [1] or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. [2] [3] It is a specific example of a quotient, as viewed from the general setting ...
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets and is . The symmetric difference of the sets A and B is commonly denoted by (traditionally, ), , or .
In calculus, the general Leibniz rule, [1] named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if and are n -times differentiable functions, then the product is also n -times differentiable and its n -th derivative is given by. where is the binomial coefficient and ...