Calculus of Variation

 

    The calculus of variations is a branch of mathematics that employs variations, or small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to real numbers. It was first developed by Johann Bernoulli (one of the famously mathematical Bernoulli family from Switzerland) in 1696. Today, the calculus of variations is an important mathematical tool for optimisation problems. It is a powerful technique for solving some dynamic problems that are otherwise difficult to solve. In the pictures above, you can see that there is an example of the Brachistochrone problem to help you understand the concept of the calculus of variations.