Interval (mathematics)In mathematics, an interval is the set of all real numbers lying between two fixed lower or upper bounds ("endpoints") with no "gaps". For example, the set of real numbers consisting of 0, 1, and all numbers in between is an interval, denoted [0, 1] and called the unit interval. An interval may contain neither endpoint (called an open interval), both endpoints (called a closed interval), or either endpoint (called a semi-open or semi-closed interval).
Domain of a functionIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom(f){\displaystyle \operatorname {dom} (f)} or domf{\displaystyle \operatorname {dom} f}, where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".
Multivariable calculusCalculus of functions of several variables Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to functions of several variables: the differentiation and integration of functions involving multiple variables (multivariate), rather than just one. Multivariable calculus may be thought of as an elementary part of calculus on Euclidean space.
AverageNumber taken as representative of a list of numbersIn mathematics, an average of a collection or group is a value that is most central, common, or typical in some sense, and represents its overall position. In mathematics, it most commonly refers to the arithmetic mean, but may also refer to other measures such as other types of mean, the median, or the mode.
IntegralOperation in calculusA definite integral of a function can be represented as the signed area of the region bounded by its graph and the horizontal axis; in the above graph as an example, the integral of f(x){\displaystyle f(x)} between a{\displaystyle a} and b{\displaystyle b} is the yellow (−) area subtracted from the blue (+) areaDomain (mathematical analysis)In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space. In particular, it is any non-empty connected open subset of the real coordinate spaceR or the complex coordinate spaceC. A connected open subset of coordinate space is frequently used for the domain of a function.Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
Continuous functionMathematical function with no sudden changesCalculusCalculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies instantaneous rates of change and slopes of curves; integral calculus studies accumulation of quantities and areas under or between curves.
One-dimensional spaceSpace with one dimension A one-dimensional (1D) space is a mathematical space in which location can be specified with a single coordinate. An example is the number line, each point of which is described by a single real number. Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples include the circle on a plane, or a parametric space curve.
DimensionProperty of a mathematical space From left to right: a square, a cube and a tesseract. The square is two-dimensional (2D) and bounded by one-dimensional line segments; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes. The first four spatial dimensions, represented in a two-dimensional picture.Relatively compact subspaceIn mathematics, a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological spaceX is a subset whose closure is compact. PropertiesEvery subset of a compact topological space is relatively compact (since a closed subset of a compact space is compact). In an arbitrary topological space every subset of a relatively compact set is relatively compact. Every compact subset of a Hausdorff space is relatively compact.*As an Amazon Associate I earn from qualifying purchases.