Search results
Results from the WOW.Com Content Network
Principal value. In mathematics, specifically complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued. A simple case arises in taking the square root of a positive real number. For example, 4 has two square roots: 2 and −2; of these the positive root ...
Mohr's circles for a three-dimensional state of stress. Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor . Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural ...
Cauchy principal value. In mathematics, the Cauchy principal value, named after Augustin-Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined. In this method, a singularity on an integral interval is avoided by limiting the integral interval to the non singular domain.
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend ...
The trigonometric function are periodic functions, and their primitive period is 2π for the sine and the cosine, and π for the tangent, which is increasing in each open interval (π/2 + kπ, π/2 + (k + 1)π). At each end point of these intervals, the tangent function has a vertical asymptote .
Electric quantities Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Definitions. For real non-zero values of x, the exponential integral Ei ( x) is defined as. The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero. For ...
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.