MAT6013 Advanced Calculus of VariationsBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6013 Advanced Calculus of Variations Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

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.

Learning Outcomes

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

Course Content

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.

Weekly Detailed Course Contents

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.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Presentation 1 % 20
Midterms 1 % 30
Final 1 % 50
Total % 100
Total % 100

ECTS / Workload Table

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

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution