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Let I be a set, and let U be an ultrafilter on I, let phi be a formula of a given language L, and let {A_i:i in I} be any collection of structures which is indexed by the set ...

There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...

A method of numerically integrating ordinary differential equations by using a trial step at the midpoint of an interval to cancel out lower-order error terms. The ...

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x)=a_3x^3+a_2x^2+a_1x+a_0. An equation involving a cubic polynomial is called a ...

The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

Let L(x) denote the Rogers L-function defined in terms of the usual dilogarithm by L(x) = 6/(pi^2)[Li_2(x)+1/2lnxln(1-x)] (1) = ...