Applying the optimal control systems of the calculus of variations

The aim of this thesis is to introduce optimal control and calculus of variation which are used in various branches of applied mathematics and engineering. In accordance with this, first it also manifests all the basic informations about calculus of variations and optimal control systems. In this thesis, information concerning optimal control, optimization and calculus of variations is explained in basic terms. Furthermore, for optimal control, basic informations about calculus of variations and applied to optimal control systems are explained. While calculating the optimum of the function, Langrange multiplier method was being utilized. While applying the Optimal Control Systems of the Calculus of Variations, optimization of the function, equation of Lagrange and eguation of Hamilton are used.