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A calibration curve plot showing limit of detection (LOD), limit of quantification (LOQ), dynamic range, and limit of linearity (LOL).. In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. [1]
The characteristic S-shaped sigmoid curve is obtained with only for integers n ≥ 1. The order of the polynomial in the general smoothstep is 2 n + 1. With n = 1, the slopes or first derivatives of the smoothstep are equal to zero at the left and right edge ( x = 0 and x = 1), where the curve is appended to the constant or saturated levels.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function , which is defined by the formula: [ 1 ]
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time . FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of ...
SO has a MATLAB example that demonstrates the algorithm and recreates the first image in this article; Lagrange Method of Interpolation — Notes, PPT, Mathcad, Mathematica, MATLAB, Maple; Lagrange interpolation polynomial on www.math-linux.com; Weisstein, Eric W. "Lagrange Interpolating Polynomial". MathWorld.
GNU Octave is an open source high level programming language and library, including a command line interface and GUI, analogous to commercial alternatives such as Maple, MATLAB, Mathematica, etc. APIs, functions and libraries can be called from many platforms, including high level engineering programs, where functions are, in many cases ...
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...