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A method for solving ordinary differential equations using the formula y_(n+1)=y_n+hf(x_n,y_n), which advances a solution from x_n to x_(n+1)=x_n+h. Note that the method ...

An implicit method for solving an ordinary differential equation that uses f(x_n,y_n) in y_(n+1). In the case of a heat equation, for example, this means that a linear system ...

_2F_1(a,b;c;z)=int_0^1(t^(b-1)(1-t)^(c-b-1))/((1-tz)^a)dt, (1) where _2F_1(a,b;c;z) is a hypergeometric function. The solution can be written using the Euler's ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a ...

Euler integration was defined by Schanuel and subsequently explored by Rota, Chen, and Klain. The Euler integral of a function f:R->R (assumed to be piecewise-constant with ...

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number ...

A 3-cusped hypocycloid, also called a tricuspoid. The deltoid was first considered by Euler in 1745 in connection with an optical problem. It was also investigated by Steiner ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...