Calculus of variations

The calculus of variations is one of the classic subjects of mathematics. It has attracted many famous mathematicians. Before presenting the most important model case, we'll start with an informal discussion. In mathematics, physics, engineering or even economics or ecology, models are often expressed in terms of a minimality or maximality principle. This is precisely the central issue in calculating variations. For example, in mathematics, we may be interested in finding, under certain constraints, a curve of minimum length or a surface of minimum area. In physics, a typical example is the principle of least action; other examples will be given in more detail in this presentation. Conservation laws, which correspond mathematically to differential equations, are often derived from a variational principle. The solutions of the variational problem are then solutions of associated differential equations.