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A second-order partial differential equation arising in physics, del ^2psi=-4pirho. If rho=0, it reduces to Laplace's equation. It is also related to the Helmholtz ...

y^('')-mu(1-1/3y^('2))y^'+y=0, where mu>0. Differentiating and setting y=y^' gives the van der Pol equation. The equation y^('')-mu(1-y^('2))y^'+y=0 with the 1/3 replaced by ...

An integral equation of the form f(x)=int_a^xK(x,t)phi(t)dt, where K(x,t) is the integral kernel, f(x) is a specified function, and phi(t) is the function to be solved for.

An integral equation of the form phi(x)=f(x)+int_a^xK(x,t)phi(t)dt, where K(x,t) is the integral kernel, f(x) is a specified function, and phi(t) is the function to be solved ...

The wave equation is the important partial differential equation del ^2psi=1/(v^2)(partial^2psi)/(partialt^2) (1) that describes propagation of waves with speed v. The form ...

An expression is called "well-defined" (or "unambiguous") if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be ...

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 most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

A matrix, also called a canonical box matrix, having zeros everywhere except along the diagonal and superdiagonal, with each element of the diagonal consisting of a single ...

A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff ...