Search Results for ""

Given a Taylor series f(x)=f(x_0)+(x-x_0)f^'(x_0)+((x-x_0)^2)/(2!)f^('')(x_0)+... +((x-x_0)^n)/(n!)f^((n))(x_0)+R_n, (1) the error R_n after n terms is given by ...

The geometric centroid of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as x^_ = ...

Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ...

If f(z) is meromorphic in a region R enclosed by a contour gamma, let N be the number of complex roots of f(z) in gamma, and P be the number of poles in gamma, with each zero ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

The elliptic logarithm is generalization of integrals of the form int_infty^x(dt)/(sqrt(t^2+at)), for a real, which can be expressed in terms of logarithmic and inverse ...

For all integers n and nonnegative integers t, the harmonic logarithms lambda_n^((t))(x) of order t and degree n are defined as the unique functions satisfying 1. ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...