Complements of Higher Mathematics by Marin Marin & Andreas Öchsner

Author:Marin Marin & Andreas Öchsner
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(2)if then , that is ;

(3)we can compute the derivative of as follows

For , as such, , the representative of the vicinity reduces to the curve y(x) that extremizes the functional I. That means that is the extremal of the function , and, according to the classical condition of the extremum, we have

(5.5.1)

Integrating by parts, we obtain

and, since , it results

Similarly,

and, since , it results

Taking into account these estimations, the conditions of extremum (5.5.1) become

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