APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5010 Numerical Analysis Spring 3 0 3 8
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: Tr
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ERSİN ÖZUĞURLU
Course Objectives: Scientific computation and simulation require both a theoretical knowledge of the subject and computational experience with it. Understanding these aspects in terms of error analysis, stability and efficiency of the methods plays an important role.

Learning Outputs

The students who have succeeded in this course;
The students who succeeded in this course;
o will be able to solve Linear and Non Linear Equations by using methods.
o will be able to provide logical proofs of important theoratical results.
o will be able to apply the theory of simulation by modeling real life examples.

Course Content

Error analysis, root finding for nonlinear equations, interpolation theory, numerical solution of systems of linear and nonlinear equations, the matrix eigenvalue problem.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Errors, Condition Numbers, Norms
2) Sources and Propagation of Errors
3) General Theory for One-point Iteration Methods
4) Error Analysis of Nonlinear Equations
5) Interpolation
6) Finite Differences and Table-Oriented Interpolation Formulas and Their Error Analysis
7) Further Results on Interpolation Error
8) Approximation of Functions: The Weierstrass Theorem and Taylor’s Theorem
9) Approximation of Functions: The Least Squares Approximation Problem
10) Numerical Solution of Systems of Linear Equations: Direct Methods and Their Error Analysis
11) Numerical Solution of Systems of Linear Equations: Iterative Methods and Their Error Analysis
12) The Matrix Eigenvalue Problem: Error and Stability Results
13) The Matrix Eigenvalue Problem: The Power Method and Eigenvalues of Special Matrices
14) Singular Value Decomposition

Sources

Course Notes: An Introduction to Numerical Analysis (2nd edition), Kendall E. Atkinson, John Wiley and Sons, Inc.
References: .

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance % 0
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes % 0
Homework Assignments 7 % 30
Presentation 1 % 30
Project % 0
Seminar % 0
Midterms % 0
Preliminary Jury % 0
Final 1 % 40
Paper Submission % 0
Jury % 0
Bütünleme % 0
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Laboratory 0 0 0
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 0 0 0
Presentations / Seminar 1 40 40
Project 0 0 0
Homework Assignments 7 14 98
Quizzes 0 0 0
Preliminary Jury 0
Midterms 0 0 0
Paper Submission 0
Jury 0
Final 1 20 20
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.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
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.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
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.
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.
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,