Quasilinear

From Wikipedia, the free encyclopedia

The term quasilinear has several meanings, usually meaning something close to almost linear.

The following meanings are related to the field of mathematics and its applications in computer science, game theory and economy.

• In the context of differential equations, quasilinear means that the coefficient of the highest order derivative does not depend on the unknown function (also known as semilinear) or at least not on a highest-order derivative of the unknown functions.
• In the context of complexity analysis, big O notation and related issues, quasilinear means of growth like O( n^a ) for all a>1, or in particular like O( n (log n)^k ) for some k (often k=1).
• In economics and consumer theory, there are quasilinear utility functions, which are generally linear in the numeraire. For example, if the utility function is U(x,y) = u(x) + by, where b is a constant; then, u(x) is increasing in x and the second derivative satisfies d^2u(x) < 0. In this case, the indifference curves are parallel.

[edit] See also

• semilinear