adj. 1. (of a derivative) of or involving second derivatives. This is consistent with calling a quadratic term in a polynomial second-order if one considers the polynomial as a Taylor series.
2a. (of an ordinary differential equation) involving the first and second derivatives, but no derivative of a higher order, of the dependent variable with respect to the independent variable. Linear, autonomous and homogeneous second-order equations have standard methods of solution. Equations in which the dependent variable does not explicitly occur can be regarded as first-order equations in the first derivative. See Van der Pol equation.
b. (of a partial differential equation) such that no partial derivative of order greater than 2 occurs in it. See linear differential equations, Monge's methods.
3. metatheoretical.
4. (of a logical theory) admitting quantification over some classes as well as individuals; for example, second-order arithmeticor second-order set theory. Compare first-order. 5. see tensor.