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
1)	Ability to assimilate mathematic related concepts and associate these concepts with each other.	4
2)	Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.	5
3)	Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.	5
4)	Ability to make individual and team work on issues related to working and social life.
5)	Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.	3
6)	Ability to use mathematical knowledge in technology.	5
7)	To apply mathematical principles to real world problems.	5
8)	Ability to use the approaches and knowledge of other disciplines in Mathematics.	5
9)	Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.	5
10)	To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data.	5
11)	To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12)	To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.	5