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The equations defined by q^. = (partialH)/(partialp) (1) p^. = -(partialH)/(partialq), (2) where p^.=dp/dt and q^.=dq/dt is fluxion notation and H is the so-called ...

A finite set of equations in the same unknowns of which the common solutions have to be determined. Solution of simultaneous equations in implemented in the Wolfram Language ...

Maxwell's equations are the system of partial differential equations describing classical electromagnetism and therefore of central importance in physics. In the so-called ...

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, ...

If x is a regular patch on a regular surface in R^3 with normal N^^, then x_(uu) = Gamma_(11)^1x_u+Gamma_(11)^2x_v+eN^^ (1) x_(uv) = Gamma_(12)^1x_u+Gamma_(12)^2x_v+fN^^ (2) ...

For a connection A and a positive spinor phi in Gamma(V_+), Witten's equations (also called the Seiberg-Witten invariants) are given by D_Aphi = 0 (1) F_+^A = ...

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...

The conjugate gradient method can be applied on the normal equations. The CGNE and CGNR methods are variants of this approach that are the simplest methods for nonsymmetric ...

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.