Search Results for ""

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

The ordinary differential equation y^('')+r/zy^'=(Az^m+s/(z^2))y. (1) It has solution y=c_1I_(-nu)((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2) ...

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

The motion along a phase curve as a function of time (Tabor 1989, p. 14).

For a function with 2 degrees of freedom, the 2-dimensional phase space that is accessible to the function or object is called its phase plane.

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

A mathematical relationship expressing f_n as some combination of f_i with i<n. When formulated as an equation to be solved, recurrence relations are known as recurrence ...

Consider a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0. If P(x) and Q(x) remain finite at x=x_0, then x_0 is called an ordinary point. If either P(x) ...