COURSE UNIT TITLE

: ELLIPTIC BOUNDARY VALUE PROBLEMS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6024 ELLIPTIC BOUNDARY VALUE PROBLEMS ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics
Mathematics

Course Objective

This course gives an account of elements of the boundary value problems for the general elliptic equations and their properties. Eigenvalue-eigenfunction problems for the elliptic operators and their properties. Theory of the harmonic functions and their application to study the elliptic boundary value problems.

Learning Outcomes of the Course Unit

1   Ability to understand the modern theory of the boundary value problems for the general elliptic equations and their applications.
2   Ability to express the fundamental concepts of the boundary value problems for the general elliptic equations.
3   Ability to use the main methods for soling the eigenvalue-eigenfunction problems for the elliptic operators.
4   Ability to understand the modern theory of the harmonic functions.
5   Ability to use the theory of the harmonic functions to study the elliptic boundary value problems.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Linear operators, continuous operators, bounded operators. Eigenvalues and eigenfunctions of the operator; multiplicity of eigenvalues. Hermitian operators; bilinear and quadratic forms. Positive operator.
2 Greens formulas for an elliptic operator: first and second Greens formulas. Properties of the elliptic operator.
3 Boundary value problem for an elliptic type. Eigenvalue problem for an elliptic equation. The uniqueness theorem.
4 Method of separation of variables.
5 Laplace equation in polar, spherical and cylindrical coordinates. Eigenvalue problem for Laplace equation in the circle.
6 Eigenvalue problem for Laplace equation in the cylinder, in the sphere.
7 Midterm
8 Solving initial boundary value problems for the wave, heat equations in circle, sphere and cylinder by the Fourier series expansion methods.
9 Interior and Exterior Dirichlet problem for the Laplace equation in the circle.
10 Interior and Exterior Dirichlet problem for the Laplace equation in the sphere.
11 Harmonic functions; Greens formula; extension of Greens formulas.
12 Mean Value Theorem.
13 Maximum Principle. Corollaries of the Maximum Principle.
14 Uniqueness Theorems on Interior and Exterior Dirichlet and Neumann Problems.

Recomended or Required Reading

1.EVANS L. C., Partial Differential Equations, Graduate Studies in Mathematics, vol 19, American Mathematical Society, Institute for
Advance Study, Providence, Rhode Island, 1998.
2. A.N. Tikhonov, A.A. Samarskii, Equations of Mathematical Physics, Pergamon Press, 1963.
3.Vladimirov V. S. Equations of mathematical Physics, Pergamon Press, 1963

Planned Learning Activities and Teaching Methods

Lectures
Homeworks
Examinations
Assignments

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Examinations

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

valery.yakhno@deu.edu.tr

Office Hours

Will be determined in the beginning of the term.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 1 15 15
Preparation for final exam 1 25 25
Preparing assignments 10 8 80
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 204

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155555
LO.25555555
LO.3555555
LO.4555555
LO.5555555555

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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