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The ordinary differential equation (1) (Byerly 1959, p. 255). The solution is denoted E_m^p(x) and is known as an ellipsoidal harmonic of the first kind, or Lamé function. ...

In conical coordinates, Laplace's equation can be written ...

Partial differential equation boundary conditions which, for an elliptic partial differential equation in a region Omega, specify that the sum of alphau and the normal ...

In three dimensions, the spherical harmonic differential equation is given by ...

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...

A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

The Euclidean algorithm, also called Euclid's algorithm, is an algorithm for finding the greatest common divisor of two numbers a and b. The algorithm can also be defined for ...