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Cauchy conditions are initial conditions (time conditions) rather than boundary conditions (space conditions). An initial-value problem is often termed a Cauchy problem. ...

The twistor equation states that del _(A^')^((A)phi^(B...E))=0, where the parentheses denote symmetrization, in a Lorentz transformation, primed spinors transform under the ...

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

Let Q(x) be a real or complex piecewise-continuous function defined for all values of the real variable x and that is periodic with minimum period pi so that Q(x+pi)=Q(x). ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

The Schrödinger equation describes the motion of particles in nonrelativistic quantum mechanics, and was first written down by Erwin Schrödinger. The time-dependent ...