Inverse hyperbolic functionsIn mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols for the hyperbolic functions, prefixed with arc- or ar-.
Mean value theoremIn mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.
Wirtinger derivativesIn complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives with respect to one real variable, when applied to holomorphic functions, antiholomorphic functions or simply differentiabl
Inverse function theoremIn mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point. The theorem also gives a formula for the derivative of the inverse function. In multivariable calculus, this theorem can be generalized to any continuously differentiable, vector-valued function whose Jacobian determinant is nonzero at a point in its domain, giving a formula for the Jacobian matrix of the inverse.
Leibniz's notationIn calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively. Consider y as a function of a variable x, or y = f(x).
FloodA flood is an overflow of water (or rarely other fluids) that submerges land that is usually dry. In the sense of "flowing water", the word may also be applied to the inflow of the tide. Floods are an area of study of the discipline hydrology and are of significant concern in agriculture, civil engineering and public health. Human changes to the environment often increase the intensity and frequency of flooding, for example land use changes such as deforestation and removal of wetlands, changes in waterway course or flood controls such as with levees, and larger environmental issues such as climate change and sea level rise.
100-year floodA 100-year flood is a flood event that has on average a 1 in 100 chance (1% probability) of being equaled or exceeded in any given year. The 100-year flood is also referred to as the 1% flood. For coastal or lake flooding, the 100-year flood is generally expressed as a flood elevation or depth, and may include wave effects. For river systems, the 100-year flood is generally expressed as a flowrate. Based on the expected 100-year flood flow rate, the flood water level can be mapped as an area of inundation.
Flood mythA flood myth or a deluge myth is a myth in which a great flood, usually sent by a deity or deities, destroys civilization, often in an act of divine retribution. Parallels are often drawn between the flood waters of these myths and the primaeval waters which appear in certain creation myths, as the flood waters are described as a measure for the cleansing of humanity, in preparation for rebirth. Most flood myths also contain a culture hero, who "represents the human craving for life".
Flood controlFlood control (or flood mitigation or flood protection or flood alleviation) methods are used to reduce or prevent the detrimental effects of flood waters. Flood relief methods are used to reduce the effects of flood waters or high water levels. Flooding can be caused by a mix of both natural processes, such as extreme weather upstream, and human changes to waterbodies and runoff. A distinction is made between structural and non-structural flood control measures.
Flood warningA flood warning is closely linked to the task of flood forecasting. The distinction between the two is that the outcome of flood forecasting is a set of forecast time-profiles of channel flows or river levels at various locations, while "flood warning" is the task of making use of these forecasts to make decisions about whether warnings of floods should be issued to the general public or whether previous warnings should be rescinded or retracted.
Atan2In computing and mathematics, the function atan2 is the 2-argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument (also called phase or angle) of the complex number The function first appeared in the programming language Fortran in 1961. It was originally intended to return a correct and unambiguous value for the angle θ in converting from Cartesian coordinates (x, y) to polar coordinates (r, θ).
SinIn a religious context, 'sin' is a transgression against divine law or a law of God. Each culture has its own interpretation of what it means to commit a sin. While sins are generally considered actions, any thought, word, or act considered immoral, selfish, shameful, harmful, or alienating might be termed "sinful".
