Variations of calculation methods of the solution of the problem

In this thesis, normed spaces defined in the valuable real unconditional and conditional functional problems of extreme (maximum and minimum values of no problems) were analyzed taken up solution methods. Specifically discussed Euler and Lagrange methods. Applications were evaluated in the following functional solution methods of frequently encountered problems with extreme connected: F(y)=∫_a^b▒f(x,y,y^' )dx F(y)=∫_a^b▒f(x,y,y^',...,y^((n) ) )dx F(y_1,y_2...,y_n )=∫_a^b▒f(x,y_1,y_2,...,y_n,y_1^',y_2^',...,y_n^' ) dx This functional at f ( ...) functions are given functions . But y ( x) ... and u ( x, y) function are the appropriate functional argument . The thesis also mathematics direct method termed the methods were also discussed . These methods are resolved over the solution of the equation in operator -shaped variation about solving problems. Euler discussed here especially Poisson and Ostrogradski equations. The implementation of these methods are displayed in the appropriate examples. Keywords: Calculus of Variations , Euler equation, affine manifolds , Functional