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A point x_0 at which the derivative of a function f(x) vanishes, f^'(x_0)=0. A stationary point may be a minimum, maximum, or inflection point.

Stochastic optimization refers to the minimization (or maximization) of a function in the presence of randomness in the optimization process. The randomness may be present as ...

Integrals of the form intf(costheta,sintheta)dtheta (1) can be solved by making the substitution z=e^(itheta) so that dz=ie^(itheta)dtheta and expressing costheta = ...

The integral of 1/r over the unit disk U is given by intint_(U)(dA)/r = intint_(U)(dxdy)/(sqrt(x^2+y^2)) (1) = int_0^(2pi)int_0^1(rdrdtheta)/r (2) = 2piint_0^1dr (3) = 2pi. ...

The limit of an upper sum, when it exists, as the mesh size approaches 0.

Let the greatest term H of a sequence be a term which is greater than all but a finite number of the terms which are equal to H. Then H is called the upper limit of the ...

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

The vercosine, written vercos(z) and also known as the "versed cosine," is a little-used trigonometric function defined by vercos(z) = 2cos^2(1/2z) (1) = 1+cosz, (2) where ...

A triple integral over three coordinates giving the volume within some region G, V=intintint_(G)dxdydz.