Mathematics. Dictionary

A diagonal matrix all of whose diagonal elements are equal to 1.

A number of the form bi, where b is any real number and i denotes the imaginary unit.

A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially where said equation is such that the value is not directly calculable from the other variables.

An integral where at least one of the endpoints is taken as a limit, either to a specific number or to infinity.

Any function of a real variable whose value increases (or is constant) as the variable increases.

The set of all functions whose derivative is a given function; the set of all antiderivatives of a given function.

A statement which might be true for any natural number. In mathematical induction, such a statement is proven true for all natural numbers by first proving it for the base case and then proving that each case implies the next.

Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers.

The problem of solving an ordinary differential equation together with an initial condition (a set of specified values for the unknown function or its derivatives at some point).

A vector space which is additionally equipped with an inner product.

Any function that possesses a finite integral

A method of integration directly related to the rule for differentiation of products; can be written as \int u\ dv = uv - \int v\ du.

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 a corresponding point in its domain that the function maps to that value.

The process of estimating the value of a function at a point from its values at nearby points.

The branch of algebra concerned with actions of groups on algebraic varieties from the point of view of their effect on functions.

For a given function f, another function, denoted f−1, that reverses the mapping action of f; given a function f: X\rightarrow Y, a function g: Y\rightarrow X such that, \forall x\in X,\ f(x) = y \implies g(y)=x.

Of a matrix A, another matrix B such that A multiplied by B and B multiplied by A both equal the identity matrix.

A morphism which has a two-sided inverse; the composition of the morphism and such an inverse yields either one of two identity morphisms (depending on the order of composition).

In multivariable calculus, the result of applying integrals to a function of more than one variable in such a way that each of the integrals considers some of the variables as given constants.