Sergey Kryzhevich, Gdańsk University of Technology, Poland
We would like to explain the basic methods of the Calculus of Variations (CV). In a nutshell, this is how multiple differential equations of classical Mechanics and Physics can be deduced from the principal Physical laws. We formulate the main results of the CV and prove them rigorously for the simplest case of the so-called quadratic functional (this results in linear differential equations and does not require the deep knowledge in nonlinear ODEs or Functional Analysis). We also discuss some classical problems of CV, equation of the chain line, brachistochrone, Dido's problem and some others.
Some more advanced results will be provided in supplementary materials for further reading.
Poster