Kocaeli University / European Credit Transfer System (ECTS)

Name of Lecturer(s)

Prof. Dr. Aydın ÜSTÜN
Associate Prof. Dr. Orhan KURT
Assistant Prof. Dr. Erman ŞENTÜRK

Learning Outcomes of the Course Unit
Program Competencies-Learning Outcomes Relation

Learning Outcomes of the Course Unit

1) Understand the interrelationship between norm, error and approximation concepts Recognize various norm types Learn the theorem of best approximation Know the properties of Chebyshev and Legendre polynomials and apply to problems of approximation Use Least Squares in functional and numerical analysis Learn parameter estimation, signal prediction and noise filtering Apply Least Squares Collocation for solving various geodetic problems
2) Recognizes various norm types
3) Learns the theorem of best approximationKnow the properties of Chebyshev and Legendre polynomials and apply to problems of approximationUse Least Squares in functional and numerical analysisLearn parameter estimation, signal prediction and noise filteringApply Least Squares Collocation for solving various geodetic problems
4) Know the properties of Chebyshev and Legendre polynomials and apply to problems of approximationUse Least Squares in functional and numerical analysisLearn parameter estimation, signal prediction and noise filteringApply Least Squares Collocation for solving various geodetic problems
5) Uses Least Squares in functional and numerical analysisLearn parameter estimation, signal prediction and noise filteringApply Least Squares Collocation for solving various geodetic problems
6) Learn parameter estimation, signal prediction and noise filteringApply Least Squares Collocation for solving various geodetic problems
7) Applies least squares collocation for solving various geodetic problems

Program Competencies-Learning Outcomes Relation

		Program Competencies
		1	2	3	4	5	6	7
Learning Outcomes
	1	No relation	High	Middle	Middle	Middle	Low	Low
	2	High	High	Middle	Middle	Middle	Low	Low
	3	High	High	Middle	Middle	Low	Low	Low
	4	High	High	Middle	Low	Low	No relation	No relation
	5	High	High	Middle	Middle	High	Low	No relation
	6	High	High	Middle	Middle	High	No relation	No relation
	7	High	High	Middle	Middle	Middle	No relation	Low

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Probability and statistics, Numerical Analysis, Adjustment Theory

Course Contents

Introduction and background, Norm spaces and best approxiamtion, Chebyshev and Legendre polynomials, Least Squares Approximation,, Polynomial and spline interpolation, Prediction, Covariance function, Collocation, Solving geodetic problems using LS collocation.

Weekly Schedule

1) Introduction: Key concepts in approximation theory
2) Geodetic approximation theory: Real world-observation-model-error
3) Norm space on errors and best approximation
4) Uniform approximation: Weiestrass theorem
5) Chebyshev norm, equi-oscillation theorm and Remez algorithm
6) Examples
7) Chebyshev and Legendre polynomials and least square approximation
8) Midterm
9) Interpolation: Curve and surface fitting
10) Spline functions
11) Collocation
12) Covariance Function
13) Least Squares Collocation
14) Examples
15) Presentation of midterm projects and discussion
16) Final

Planned Learning Activities and Teaching Methods

1) Lecture
2) Lecture
3) Question-Answer
4) Question-Answer
5) Drill and Practice
6) Drill and Practice
7) Self Study
8) Self Study

Assessment Methods and Criteria

Contribution of Quiz to Course Grade	20%
Contribution of Final Examination to Course Grade	80%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required

Course Unit Title	Course Unit Code	Type of Course Unit	Level of Course Unit	Year of Study	Semester	ECTS Credits
Approximation Methods In Geodesy: Interpolation and Collocation	JJM519	Elective	Master's degree	1	Fall	8