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Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
In time series analysis, a fan chart is a chart that joins a simple line chart for observed past data, by showing ranges for possible values of future data together with a line showing a central estimate or most likely value for the future outcomes. As predictions become increasingly uncertain the further into the future one goes, these ...
graph intersection: G 1 ∩ G 2 = (V 1 ∩ V 2, E 1 ∩ E 2); [1] graph join: . Graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs); [2] graph products based on the cartesian product of the vertex sets:
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.
These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
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For example, time series are usually decomposed into: , the trend component at time t, which reflects the long-term progression of the series (secular variation). A trend exists when there is a persistent increasing or decreasing direction in the data. The trend component does not have to be linear. [1]