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Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...

A method of determining coefficients alpha_l in an expansion y(x)=y_0(x)+sum_(l=1)^qalpha_ly_l(x) so as to nullify the values of an ordinary differential equation L[y(x)]=0 ...

Newton's term for a variable in his method of fluxions (differential calculus).

A formula for numerical solution of differential equations, (1) where k_1 = hf(x_n,y_n) (2) k_2 = hf(x_n+1/2h,y_n+1/2k_1) (3) k_3 = ...

The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is del _mu=[1/cpartial/(partialt); partial/(partialx); ...

A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Rosenbrock methods.

A generalization of the product rule for expressing arbitrary-order derivatives of products of functions, where (n; k) is a binomial coefficient. This can also be written ...