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| MAK5350 | Variational Calculus and Applications | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MECHANICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To give the students fundamental concepts about variational calculus and fundamental mathematical preliminaries, and their applications in mechanics (Hamiltonian principle) and to inform direct methods in variational calculus. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn the concept of variational calculus, the formulation of extermal problems and their applications in engineering. | 1 | 1,3 | | PO - 2 : | solve various variational problems. | 1,4,5 | 1,3 | | PO - 3 : | inform variational principles and their applications in mechanical engineering. | 1,4,5 | 1,3 | | PO - 4 : | introduce direct methods such as Euler's finite difference methods, the Ritz method and finite element method in variational calculus | 1,5,9 | 1,3 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Definitions and fundamental concepts. Extremum of a functional. Euler-Lagrange equations and its particular forms. Variational principles. The applications of variational calculus to mechanics (Hamiltonian principle) . Variational principle corresponds to a differential equation. Direct methods in variational calculus (Euler's finite difference method, Kantorovich's method, the Ritz method, finite element method) |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Variational calculus and firs examples of variational problems. | | | Week 2 | definitions and fundamental concepts. | | | Week 3 | Extremum of a functional. | | | Week 4 | Euler-Lagrange equation. | | | Week 5 | Particular forms of Euler-Lagrange equation. | | | Week 6 | Various variational calculus problems and their solutions. | | | Week 7 | variational principles. | | | Week 8 | Mid-term exam | | | Week 9 | Application of variational calculus to mechanics and Hamiltonian principle. | | | Week 10 | Variational principle corresponds to a differential equation. | | | Week 11 | Direct methods in variational calculus. | | | Week 12 | Euler's finite-difference method. | | | Week 13 | Rayleigh-Ritz method. | | | Week 14 | Kantorovich's method. | | | Week 15 | Finite element method. | | | Week 16 | End-of-term exam | | | |
| 1 | Durgun, O. Ders Notları, Yayınlanmamış | | | |
| 1 | Finlayson, BA. 1972; The Method of Weighted residuals and variational Principles, Academic Press. | | | 2 | Brebbia, CA. 1978; The Boundary Element methods for Engineers, John Wiley and Sons. | | | 3 | Elsgolts, L. 1977; Diffferential Equations and the Calculus of Variations, MIR Publishers. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 21/11/2012 | 2 | 30 | | In-term studies (second mid-term exam) | 12 | 12/12/2012 | 2 | 20 | | End-of-term exam | 17 | 11/01/2011 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Arasınav için hazırlık | 3 | 5 | 15 | | Arasınav | 2 | 1 | 2 | | Uygulama | 1 | 7 | 7 | | Ödev | 4 | 7 | 28 | | Dönem sonu sınavı için hazırlık | 3 | 5 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 3 | 5 | 15 | | Diğer 2 | 3 | 5 | 15 | | Total work load | | | 197 |
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