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A Fredholm integral equation of the second kind phi(x)=f(x)+lambdaint_a^bK(x,t)phi(t)dt (1) may be solved as follows. Take phi_0(x) = f(x) (2) phi_1(x) = ...

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.

The symbol int used to denote an integral intf(x)dx. The symbol was invented by Leibniz and chosen to be a stylized script "S" to stand for "summation."

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

The quantity being integrated, also called the integral kernel. For example, in intf(x)dx, f(x) is the integrand.

A discrete subset of R^s which is closed under addition and subtraction and which contains Z^s as a subset.

The intercept form of a line in the Cartesian plane with x-intercept a and y-intercept b is given by x/a+y/b=1.

Interest is a fee (or payment) made for the borrowing (or lending) of money. The two most common types of interest are simple interest, for which interest is paid only on the ...

The interior of a set is the union of all its open subsets. More informally, the interior of geometric structure is that portion of a region lying "inside" a specified ...

Lines that intersect in a point are called intersecting lines. Lines that do not intersect are called parallel lines in the plane, and either parallel or skew lines in ...