MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT6013 | Advanced Calculus of Variations | Fall Spring |
3 | 0 | 3 | 8 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | Turkish |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
Recommended Optional Program Components: | None |
Course Objectives: | The aim of this course is to give the students basic information about variation analysis, to understand variational approximation methods, to apply algebraic equations that include unspecified parameters, and also, to have any opinion about the errors and convergency of the variational method. |
The students who have succeeded in this course; The ability to reveal the importance of concepts about the approximate and variational solution concepts. The ability to use the technics in the solutions of the problems which based on variational techniques. be able to improve to understanding of the asymptotic behavior of solutions of difference equations by various examples The ability to improve analytical thinking about the characterization and the solution of the problems |
The basic conceps about functional analysis, Variational formulation of boundary value problems, Existence and Uniqueness of Solutions,Variational methods of approximation, The Ritz Method,The Method of Weighted Residuals. |
Week | Subject | Related Preparation |
1) | Definition and properties of variation, variational problems and their applications | |
2) | The basic conceps about functional analysis linear vector spaces,linear transformations and functionals, normed spaces, iner product spaces | |
3) | Variational formulation of boundary value problems, some integral relations | |
4) | Sobolev Spaces and consept or generalized solution | |
5) | Weak(or Generalized) solutions | |
6) | Concepts from Variational Calculus | |
7) | Linear operator equations | |
8) | Linear operator equations (continued) | |
9) | Variational boundary value problems | |
10) | Variational problem and the existence of weak solution | |
11) | Rayleigh-Ritz method | |
12) | Convergence and stability | |
13) | The Weighted Residual method(Collocation, least square, Galerkin,Subdomain methods) | |
14) | The Kantorovich and Trefftz Methods |
Course Notes / Textbooks: | 1.Alemdar Hasanoğlu(Hasanov), “Varyasyonel problemler ve sonlu elemanlar yöntemi”,Literatür yayıncılık, 2001. |
References: | 1. J.N.Reddy, “An introduction to the finite element method”, McGraw –Hill Inc., 1993. 2. J.N.Reddy, Applied Functional Analysis and Varyasyonel Methods in engineering, McGraw-Hill Inc.,1986. 3. Rao.L. 1982. The finite element method in engineering: Pergamon Pres 4. I.M. Gelfand, S.V. Fomin and R.A. Silverman, Calculus of Variations, Dover Pub., 2000. |
Semester Requirements | Number of Activities | Level of Contribution |
Presentation | 1 | % 20 |
Midterms | 1 | % 30 |
Final | 1 | % 50 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 3 | 42 |
Presentations / Seminar | 1 | 50 | 50 |
Midterms | 1 | 31 | 31 |
Final | 1 | 35 | 35 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |