Calculus of Variations (MAE849): Διαφορά μεταξύ των αναθεωρήσεων
Γραμμή 37: | Γραμμή 37: | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
| | | | ||
Classical Mechanics | Classical Mechanics | ||
|- | |- |
Αναθεώρηση της 17:22, 23 Ιουλίου 2022
Undergraduate Courses Outlines - Department of Mathematics
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE849 |
Semester |
8 |
Course Title |
Calculus of Variations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses |
Classical Mechanics |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | - |
Learning Outcomes
Learning outcomes |
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:
|
---|---|
General Competences |
|
Syllabus
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
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See Eudoxus. Additionally:
- 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.