Prerequisite Courses:
Course Language:
English
Course Objectives:
To understand the problems of Physics and Engineering better and find their solutions
Course Content:
Euler-Lagrange equations and generalizations.Hamiltonian functions. Invariant integrals. Noether theorem. Second variation and Jacobi fields. Constraint variational problems. Isoperimetric problems. Non-holonomic systems.
Course Methodology:
1: Lecture, 2: Problem Solving, 3:Question-answer, 4: Homework
Course Evaluation Methods:
A: Written examination, B: Homework
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Program Learning Outcomes | Teaching Methods | Assessment Methods |
| 1) Knows variations and their properties | 3,4,5,7,8,9 | 1,2 | A |
| 2) Derives Euler equation | 3,4,5,7,8,9 | 1,2 | A |
| 3) Can perform generalizations | 3,4,5,7,8,9 | 1,2 | A |
| 4) Investigates moving boundary value problems | 3,4,5,7,8,9 | 1,2 | A |
| 5) Knows the direct method and Ritz method | 3,4,5,7,8,9 | 1,2 | A |
| 6) Can investigate the multiple independent variables case | 3,4,5,7,8,9 | 1,2 | A |
Course Flow
| Week | Topics | Study Materials |
| 1 | Minima and maxima of differentiable functions | |
| 2 | Variations and its properties | |
| 3 | Euler equation | |
| 4 | Some generalizations | |
| 5 | Parametric representations of variation problems | |
| 6 | Variation problems with moving boundaries | |
| 7 | Variation problems with moving boundaries (continued) | |
| 8 | Sufficiency for an extremum | |
| 9 | Problems with constrained extrema | |
| 10 | Problems with constrained extrema (continued) | |
| 11 | Direct methods | |
| 12 | Ritz’s method | |
| 13 | Generalizations to more than one independent variables | |
| 14 | Generalizations to more than one independent variables |
Recommended Sources
| Textbook | L. E. Elsgolc; Calculus of Variations |
| Additional Resources | F. B. Hildebrand; Methods of Applied Mathematics |
Material Sharing
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Documents |
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Assignments |
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Exams |
Assessment
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 2 | 100 |
| Quizzes | - | |
| Assignments | - | |
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 40 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 60 | |
| Total | 100 |
| COURSE CATEGORY | Expertise/Field Courses |
Course’s Contribution to Program
| No | Program Learning Outcomes | Contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | X | ||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | X | ||||
| 3 | Ability form and interpret the relations between research topics in mathematics | X | ||||
| 4 | Ability to define, formulate and solve mathematical problems | X | ||||
| 5 | Consciousness of professional ethics and responsibilty | X | ||||
| 6 | Ability to communicate actively | X | ||||
| 7 | Ability of self-development in fields of interest | X | ||||
| 8 | Ability to learn, choose and use necessary information technologies | X | ||||
| 9 | Lifelong education | X | ||||
ECTS
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 3 | 42 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 5 | 70 |
| Mid-terms (Including self study) | 2 | 15 | 30 |
| Quizzes | 0 | 0 | 0 |
| Assignments | 0 | 0 | 0 |
| Final examination (Including self study) | 1 | 30 | 30 |
| Total Work Load | 172 | ||
| Total Work Load / 25 (h) | 6.88 | ||
| ECTS Credit of the Course | 7 |