Calculus Of Variations

Introduction

Functional
function of a function, i.e., some function that takes another function as an argument, and returns a number.

Calculus of Variations is trying to find extrema to functionals.

Which problems can be solved?

  • Find a function that minimizes or maximizes the given functional (sort of optimality criterion).
  • Find the shortest path on some terrain (geodesics).
  • Find the maximal area surrounded by a given length rope.
  • Find the closest to image edges curve that has smoothness constraints.

Learning path

Most of the theory is based on Euler-Lagrange equation.

Map

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