MATHEMATICS (TURKISH, PHD)
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
MAT6021	Selected Topics in Applied Mathematics	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.

Basic information

Language of instruction:	Turkish
Type of course:	Departmental Elective
Course Level:
Mode of Delivery:	Face to face
Course Coordinator :	Prof. Dr. CANAN ÇELİK KARAASLANLI
Recommended Optional Program Components:	There is no optional compnent
Course Objectives:	This course covers the topics which are not covered in the other applied mathematics courses.

Learning Outcomes

The students who have succeeded in this course;
Analyze boundary value problems
Solve differential equations using asymptotic methods underlie numerous applications of physical applied mathematics
Read research papers from journals
Apply methods to interdisciplinary research problems
Develop skills by applying them to specific tasks in tutorials and assessments
Demonstrate mathematical and computational methods
Discuss topics in applied mathematics

Course Content

Asymptotic methods for partial differential equations.
Uniform single-step difference schemes.
Uniform twostep difference schemes.
Asymptotic methods for partial differential equations of mixed types.
Uniform difference schemes for partial differential equations mixed types.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Boundary-value problems for partial differential equations with small parameter multiplying the derivative term.
2)	Boundary-value problems for partial differential equations with small parameter multiplying the derivative term.
3)	Asymptotic methods for partial differential equations.
4)	Asymptotic methods for partial differential equations.
5)	Uniform single-step difference schemes.
6)	Uniform single-step difference schemes.
7)	Uniform single-step difference schemes.
8)	Uniform single-step difference schemes.
9)	Asymptotic methods for partial differential equations of mixed types.
10)	Asymptotic methods for partial differential equations of mixed types.
11)	Asymptotic methods for partial differential equations of mixed types.
12)	Uniform multi-step difference schemes.
13)	Uniform multi-step difference schemes.
14)	Uniform multi-step difference schemes.

Sources

Course Notes / Textbooks:	M.H. Holmes, Introduction to Perturbation Methods, 1995, Springer.
References:	Bender and Orszag, Advanced Mathematical Methods for Scientists and Engineers, 1999, Springer. Michael J. Ward, course notes on Asymptotic methods, http://www.math.ubc.ca/~ward/teaching/math550.html Ferdinand Verhulst. Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, Springer, 2005. ISBN 0-387-22966-3.

Evaluation System

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

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	5	70
Presentations / Seminar	1	40	40
Midterms	2	10	20
Final	1	28	28
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