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Let a function h:U->R be continuous on an open set U subset= C. Then h is said to have the epsilon_(z_0)-property if, for each z_0 in U, there exists an epsilon_(z_0)>0 such ...

If a matrix A has a matrix of eigenvectors P that is not invertible (for example, the matrix [1 1; 0 1] has the noninvertible system of eigenvectors [1 0; 0 0]), then A does ...

A boundary value problem is a problem, typically an ordinary differential equation or a partial differential equation, which has values assigned on the physical boundary of ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

A standard normal distribution is a normal distribution with zero mean (mu=0) and unit variance (sigma^2=1), given by the probability density function and distribution ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

A method of displaying simple statistical parameters including hinges, the statistical median, and upper and lower values.

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], ...