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Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

There are several types of integrals which go under the name of a "Dirichlet integral." The integral D[u]=int_Omega|del u|^2dV (1) appears in Dirichlet's principle. The ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

A series which is not convergent. Series may diverge by marching off to infinity or by oscillating. Divergent series have some curious properties. For example, rearranging ...

_3F_2[n,-x,-y; x+n+1,y+n+1] =Gamma(x+n+1)Gamma(y+n+1)Gamma(1/2n+1)Gamma(x+y+1/2n+1) ×Gamma(n+1)Gamma(x+y+n+1)Gamma(x+1/2n+1)Gamma(y+1/2n+1), (1) where _3F_2(a,b,c;d,e;z) is a ...