Elements of Calculus of Variations


In the summer semester 2023, the Institute of Applied Analysis offers an introductory course on the Calculus of Variations (2 + 1 SWS).  

  • Lecture: Tuesday, 10am - 12pm in N24 - 131
  • Exercises: Monday, 2pm - 4pm in N24 - 226

For further information, please enroll in Moodle!



The calculus of variations is the study of (real-valued) functions of functions known as functionals, and in particular the search for minima and maxima of these functionals, so-called extremal functions.

Many classical problems in mathematics and physics can be solved using the calculus of variations, by exploiting the fact that a solution of the problem, typically given by a differential equation, must be a minimiser or maximiser of a functional. Examples include the principle of least action, the theory of minimal surfaces (such as the description of soap bubbles), the problem of determining the shortest path between two points on a surface or manifold (geodesics), or brachistochrone curves (curves of fastest descent).

Historically, the calculus of variations accompanied the development of other areas of analysis such as functional analysis and the theory of partial differential equations. It continues to find use as an important tool in these areas of mathematics, as well as in differential geometry (Morse theory), control theory, and of course in physics.