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  2. Area under the curve (pharmacokinetics) - Wikipedia

    en.wikipedia.org/wiki/Area_under_the_curve...

    In the field of pharmacokinetics, the area under the curve ( AUC) is the definite integral of the concentration of a drug in blood plasma as a function of time (this can be done using liquid chromatography–mass spectrometry [ 1] ). In practice, the drug concentration is measured at certain discrete points in time and the trapezoidal rule is ...

  3. Receiver operating characteristic - Wikipedia

    en.wikipedia.org/wiki/Receiver_operating...

    A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the performance of a binary classifier model (can be used for multi class classification as well) at varying threshold values. The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR) at each threshold setting.

  4. Toughness - Wikipedia

    en.wikipedia.org/wiki/Toughness

    Toughness as defined by the area under the stress–strain curve. In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. [ 1] Toughness is the strength with which the material opposes rupture. One definition of material toughness is the amount of energy per unit ...

  5. Probability density function - Wikipedia

    en.wikipedia.org/wiki/Probability_density_function

    This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1.

  6. Simpson's rules (ship stability) - Wikipedia

    en.wikipedia.org/wiki/Simpson's_rules_(ship...

    Rules used in ship stability and naval architecture. Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures. [ 1] This is an application of Simpson's rule for finding the values of an integral, here interpreted as the area under a curve. Simpson's First Rule.

  7. Stress–strain curve - Wikipedia

    en.wikipedia.org/wiki/Stress–strain_curve

    Definition. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves. The stress and strain can be normal, shear, or mixture, and can also can be uniaxial, biaxial, or multiaxial, even change with time. The form of deformation can be compression ...

  8. Arc length - Wikipedia

    en.wikipedia.org/wiki/Arc_length

    When rectified, the curve gives a straight line segment with the same length as the curve's arc length. Arc length sof a logarithmic spiralas a function of its parameter θ. Arc lengthis the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected ...

  9. Line integral - Wikipedia

    en.wikipedia.org/wiki/Line_integral

    In qualitative terms, a line integral in vector calculus can be thought of as a measure of the total effect of a given tensor field along a given curve. For example, the line integral over a scalar field (rank 0 tensor) can be interpreted as the area under the field carved out by a particular curve. This can be visualized as the surface created ...