| GENERAL INFORMATION: | Instructors: Papadopoulos Christos-Filelis Semester: 8th |
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| CREDITS: | ECTS Units: 3 Teaching Units: 3 Theory Hours: 2 Exercises Hours: 1 Lab Hours: 0 |
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| COURSE PAGE: | https://eclass.duth.gr/courses/TMA531/ | |
Course Description |
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| The brachystochrone problem. The minimal surfaces problem. The simple isoperimetric problem. The Navigation problem. Simple optimal control problem. Functionals. Gateux variation or first variation. Function Spaces. The first necessary condition for a local minimum. Euler-Lagrange equation. Lagrange method. Special cases of the Euler-Lagrange equation. Normal and abnormal components of the Εuler-Lagrange equation. High order functionals. Generalization for several dependent variables. The canonical form of the Euler-Lagrange differential equations system. Generalization for several independent variables. Variational problems with constraints. A sufficient condition. Isoperimetric problems. A sufficient condition for a weak extemum. Direct variational methods. | ||
