Mathematics for Economists

Calculus of variations

As it is true for any variationyone has that

q(t)p^0 (t)= 0 ,

that is

Fx^0



t,x(t),x(t)



d

dt

Fx^0 



t,x(t),x(t)



= 0 ,

whereFx^0 andFx^0 are the partial derivative ofF

DeÖnition

This is the so-called the EulerñLagrange di§erential equation.