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The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states e^(ix)=cosx+isinx, (1) where i is the imaginary unit. Note that Euler's ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...