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School of Science
Department of Mathematics
|Level of Studies||
Calculus of Variations
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
Yes (in English)
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
Calculus of Variations deals with optimisation problems where the variables, instead of being finite dimensional as in ordinary calculus, are functions. This course treats the foundations of calculus of variations and gives examples on some (classical and modern) physical applications. After successfully completing the course, the students should be able to:
The Euler-Lagrange equation. The brachistochrone problem. Minimal surfaces of revolution. The isoperimetric problem. Fermat's principle (geometric optics). Hamilton's principle. The principle of least action. The Euler-Lagrange equation for several independent variables. Applications: Minimal surfaces, vibrating strings and membranes, eigenfunction expansions, Quantum mechanics: the Schrödinger equation, Noether's theorem, Ritz optimization, the maximum principle.
Teaching and Learning Methods - Evaluation
Face to face
|Use of Information and Communications Technology||Yes|
|Student Performance Evaluation||
- Calculus of Variations, I. M. Gelfand and S. V. Fomin, Dover Publications, 2000.
- Εφαρμοσμένα Μαθηματικά, D. J. Logan, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010.
- Θεωρητική Μηχανική, Π. Ιωάννου και Θ. Αποστολάτος, ΕΚΠΑ, 2007.