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A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. [1][2] It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of ...
Level sets show up in many applications, often under different names. For example, an implicit curve is a level curve, which is considered independently of its neighbor curves, emphasizing that such a curve is defined by an implicit equation. Analogously, a level surface is sometimes called an implicit surface or an isosurface.
The contour integral of a complex function: is a generalization of the integral for real-valued functions. For continuous functions in the complex plane , the contour integral can be defined in analogy to the line integral by first defining the integral along a directed smooth curve in terms of an integral over a real valued parameter.
The name derives from the fact that the prototypical example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a riding saddle. In terms of contour lines, a saddle point in two dimensions gives rise to a contour map with a pair of lines intersecting at the point. Such ...
Formal definitions. Given a relation on pairs of elements of set. and an element of. The upper contour set of is the set of all that are related to : {\displaystyle \left\ {y~\backepsilon ~y\succcurlyeq x\right\}} The lower contour set of is the set of all such that is related to them:
A scalar function whose contour lines define the streamlines is known as the stream function. Dye line may refer either to a streakline: dye released gradually from a fixed location during time; or it may refer to a timeline: a line of dye applied instantaneously at a certain moment in time, and observed at a later instant.
Plot (graphics) A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used.
B) Example of an isoquant map with two inputs that are perfect complements. An isoquant (derived from quantity and the Greek word isos, ίσος, meaning "equal"), in microeconomics, is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. [1][2] The ...