Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
DMB0008		Approximation Techniques	3/0/0	DE	Turkish	8

Course Goals	To Introduce some approximation methods to apply to some problem.
Prerequisite(s)	-
Corequisite(s)	-
Special Requisite(s)	The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)	Assist. Prof. Dr. Hikmet Çağlar
Course Assistant(s)
Schedule	Day, hours, XXX Campus, classroom number.
Office Hour(s)	Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques	Lecture and laboratory recitation
Principle Sources	Approximation Theory and Methods, M.J.D. Powell, Cambridge University, 1996.
Other Sources	-

Course Schedules
Week	Contents	Learning Methods
1. Week	The approximation problem and existence of best approximations	Lecture and laboratory recitation
2. Week	The uniqueness of best approximations	Lecture and laboratory recitation
3. Week	Approximation operators and some approximating functions	Lecture and laboratory recitation
4. Week	Polynomial interpolation	Lecture and laboratory recitation
5. Week	Divided differences	Lecture and laboratory recitation
6. Week	The uniform convergence of polynomial approximations	Lecture and laboratory recitation
7. Week	The theory of minimax approximation	Lecture and laboratory recitation
8. Week	Least squares approximation	Lecture and laboratory recitation
9. Week	Properties of orthogonal polynomials	Lecture and laboratory recitation
10. Week	Approximation of periodic functions	Lecture and laboratory recitation
11. Week	The order of convergence of polynomial approximations	Lecture and laboratory recitation
12. Week	The uniform boundedness theorem	Lecture and laboratory recitation
13. Week	Interpolation by piecewise polynomials	Lecture and laboratory recitation
14. Week	Uniform Approximation	Lecture and laboratory recitation
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	1	30
Homework / Term Projects / Presentations	2	20
Final Exam	1	50

Program Outcomes PO-1 Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making. PO-2 Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas. PO-3 Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process. PO-4 Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written. PO-5 Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals. PO-6 Use computer software to solve problems effectively by following the developments in information and communication technologies. PO-7 Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values. PO-8 To solve problems related to the field, establish functional interacts by using strategic decision making processes. PO-9 Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.

Learning Outcomes LO-1 I. Use approximation operators and some approximating functions. LO-2 II. Apply polynomial and spline interpolation to suitable problems. LO-3 III. Approximates functions at some point using divided differences. LO-4 IV. Construct modal of datas using least squares.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9