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In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem. Change of variables is an operation that is related ...
Relative change. In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. [1] The comparison is expressed as a ratio and is a unitless number.
The result, div F, is a scalar function of x. Since this definition is coordinate-free, it shows that the divergence is the same in any coordinate system. However it is not often used practically to calculate divergence; when the vector field is given in a coordinate system the coordinate definitions below are much simpler to use.
Calculus. In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. [1]
A plot of hours of daylight as a function of the date for changing latitudes. This plot was created using the simple sunrise equation, approximating the sun as a single point and does not take into account effects caused by the atmosphere or the diameter of the Sun. The sunrise equation or sunset equation can be used to derive the time of ...
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation. Integration was initially used to solve problems in mathematics and ...
Fold change. Fold change is a measure describing how much a quantity changes between an original and a subsequent measurement. It is defined as the ratio between the two quantities; for quantities A and B the fold change of B with respect to A is B / A. In other words, a change from 30 to 60 is defined as a fold-change of 2.
v. t. e. The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.