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A phase curve is a plot of the solution to a set of equations of motion in a phase plane (or more generally, a phase space) as a function of time (Tabor 1989, p. 14). Phase ...

Consider the expression 3×7+2^2. This expression has value (3×7)+(2^2)=25 due to what is called operator precedence (or "order of operations"). Precedence of common operators ...

The unsorted union of a list S is a list containing the same elements as S but with the second and subsequent occurrence of any given element removed. For example, the ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

A plot of equipotential curves. If desired, the regions between contours can be shaded or colored to indicate their magnitude. Contour plots are implemented in the Wolfram ...

Ai(z) and Ai^'(z) have zeros on the negative real axis only. Bi(z) and Bi^'(z) have zeros on the negative real axis and in the sector pi/3<|argz|<pi/2. The nth (real) roots ...

The term "gradient" has several meanings in mathematics. The simplest is as a synonym for slope. The more general gradient, called simply "the" gradient in vector analysis, ...

A function for which all critical points are nondegenerate and all critical levels are different.

Sample size is the number of observations in a sample (Evans et al. 2000, p. 16). It is commonly denoted n or N.