# Numerical Analysis I (MATH521) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Analysis I MATH521 3 0 0 3 5
Pre-requisite Course(s)
Consent of the department
Course Language English N/A Natural & Applied Sciences Master's Degree Face To Face Lecture, Discussion, Question and Answer, Problem Solving. Assoc. Prof. Dr. İnci Erhan This course is designed to give the expertise necessary to understand, construct and use computational methods for the numerical solution of linear algebra problems. The emphasis is on derivation and analysis of iterative methods for linear algebra problems as well as condition number, convergence, stability of algorithms and the criteria for choosing the best algorithm for the problem under consideration. The students who succeeded in this course; Understand the theoretical and practical aspects of the construction and implementation of the numerical methods Establish the advantages, disadvantages and limitations of the numerical methods and select the algorithms that converge to solutions in the most effective way Construct and apply iterative methods for the approximate solution of linear systems and eigenvalue-eigenvector problems, Estimate/determine the condition number of the linear system and condition the linear system whenever necessary Analyze the error and establish the conditions for convergence related to these methods Implement the methods and/or algorithms as computer code and use them to solve applied problems Discuss the numerical methods and/or algorithms with respect to stability, applicability, reliability, conditioning, accuracy, computational complexity and efficiency Matrix and vector norms, error analysis, solution of linear systems: Gaussian elimination and LU decomposition, condition number, stability analysis and computational complexity; least square problems: singular value decomposition, QR algorithm, stability analysis; matrix eigenvalue problems; iterative methods for solving linear systems: Jacobi, Ga

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Matrix and vector norms Atkinson- Sec. 7.3, Kress- Sec. 3.4
2 Error analysis: Absolute and relative error, floating point, round-off errors Atkinson-Sec.1.2-1.5
3 Solutions of linear systems: Gaussian elimination, pivoting and scaling Atkinson-Sec. 8.1,8.2 Kress-Sec. 2.2
4 LU decomposition Kress-Sec. 2.3,2.4
5 Condition numbers, stability, computational complexity Kress- Sec. 5.1
6 QR factorization: Householder transformation, Gram-Schmidt orthogonalization, Givens rotations Atkinson-Sec. 9.3, 9.5
7 Least square problems: Singular value decomposition Atkinson-Sec. 9.7 Kress-Sec. 5.2
8 Midterm Exam
9 Matrix eigenvalue problems: Estimates for eigenvalues, Jacobi method Atkinson-Sec. 9.1 Kress-Sec. 7.2,7.3
10 QR algorithm, Hessenberg Matrices Kress-Sec. 7.4,7.5
11 Schur factorization, Power method, Atkinson-Sec. 9.2, 9.6
12 Inverse Power method Atkinson-Sec. 9.2, 9.6
13 Iterative methods for linear systems: Jacobi Method Gauss-Seidel Method Kress-Sec. 4.1
14 Relaxation Methods Kress-Sec. 4.2
15 Conjugate gradient type methods Atkinson-Sec. 8.9
16 Final Exam

### Sources

Course Book 1. R. Kress, “Numerical Analysis: v. 181 (Graduate Texts in Mathematics)”, Kindle Edition, Springer, 1998. 2. K. E. Atkinson, “An Introduction to Numerical Analysis”, 2nd edition, John Wiley and Sons, 1989 3. G. H. Golub, C.F. Van Loan, “Matrix Computations”, North Oxford Academic, 1983. 4. R. L. Burden, R.J. Faires, “Numerical Analysis”, 9th edition, Brooks/ Cole, 2011.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.) X
4 An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively.
5 An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies.
6 An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines.
7 An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written.
8 An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions.
12 Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism.
14 A competency on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of qualitative processes.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10