Základy variačního počtu a některé jeho aplikace

Abstract

In this Master thesis at first some parts of functional analysis are mentioned which will be used in the following chapters. Afterwards, the fundamental problem of calculus of variations and whole theory which is necessary in order to find stationary points of explored functional. Thereafter, a way how to prove an existence of extrema will be shown correctly. The rest of the thesis deals with the most common problems of calculus variations which are, namely, the brachistochrone problem, and the minimal surface problem. Both of them are completely solved analytically. Consequently, there are introduced two suitable numerical methods supplemented by results. Photographs of several practical experiments commited for illustration and videos are integral parts of the thesis.