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A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the ...

The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I=max_(W in S)(dimW) where ...

The solutions to the Riemann P-differential equation are known as the Riemann P-series, or sometimes the Riemann P-function, given by u(z)=P{a b c; alpha beta gamma; alpha^' ...

A smooth manifold M=(M,g) is said to be semi-Riemannian if the indexMetric Tensor Index of g is nonzero. Alternatively, a smooth manifold is semi-Riemannian provided that it ...

The metric tensor g on a smooth manifold M=(M,g) is said to be semi-Riemannian if the index of g is nonzero. In nearly all literature, the term semi-Riemannian is used ...

The vector Laplacian can be generalized to yield the tensor Laplacian A_(munu;lambda)^(;lambda) = (g^(lambdakappa)A_(munu;lambda))_(;kappa) (1) = ...

In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...