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A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt ...

There are two kinds of Bell polynomials. A Bell polynomial B_n(x), also called an exponential polynomial and denoted phi_n(x) (Bell 1934, Roman 1984, pp. 63-67) is a ...

The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathological continuous function which is nowhere differentiable. Its name ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

The circle map is a one-dimensional map which maps a circle onto itself theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n), (1) where theta_(n+1) is computed mod 1 and K is a ...

The complete elliptic integral of the second kind, illustrated above as a function of k, is defined by E(k) = E(1/2pi,k) (1) = ...

The most common form of cosine integral is Ci(x) = -int_x^infty(costdt)/t (1) = gamma+lnx+int_0^x(cost-1)/tdt (2) = 1/2[Ei(ix)+Ei(-ix)] (3) = -1/2[E_1(ix)+E_1(-ix)], (4) ...

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 ...