ECTS - Numerical Linear Algebra
Numerical Linear Algebra (MDES621) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Linear Algebra | MDES621 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to give engineering students in graduate level the expertise necessary to understand and use computational methods for the approximate/numerical solution of linear algebra problems that arise in many different fields of science like electrical networks, solid mechanics, signal analysis and optimisation. The emphasis is on methods for linear algebra problems such as solutions of linear systems, least squares problems and eigenvalue-eigenvector problems, the effect of roundoff on algorithms and the citeria for choosing the best algorithm for the mathematical structure of the problem under consideration. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Floating point computations, vector and matrix norms, direct methods for the solution of linear systems, least squares problems, eigenvalue problems, singular value decomposition, iterative methods for linear systems. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Introduction to numerical computations. Vector and matrix norms | Read related sections in references |
| 2 | Condition numbers and conditioning, Stability, Propogation of roundoff errors | Read related sections in references |
| 3 | Direct methods for linear systems, Gaussian elimination, Pivoting, Stability. LU and Cholesky decompositions | Read related sections in references |
| 4 | LU and Cholesky decompositions (cont.) Operation counts, Error analysis, Perturbation theory, Special linear systems | Read related sections in references |
| 5 | Least Squares. Orthogonal matrices, Normal equations, QR factorization | Read related sections in references |
| 6 | Gram-Schmidt orthogonalization, Householder triangularization, Least Squares problems | Read related sections in references |
| 7 | Eigenproblem. Eigenvalues and eigenvectors, Gersgorin’s circle theorem, Iterative methods for eigenvalue problems | Read related sections in references |
| 8 | Power, Inverse Power and Shifted Power methods, Rayleigh quotients, Similarity transformations, Reduction to Hessenberg and tridiagonal forms | Read related sections in references |
| 9 | QR algorithm for eigenvalues and eigenvectors, Other eigenvalue algorithms. Singular Value Decomposition | Read related sections in references |
| 10 | SVD(cont.) and connection with Lesat Squares problem, Computing the SVD using the QR algorithm | Read related sections in references |
| 11 | Iterative Methods for Linear Systems. Basic iterative methods, Jacobi, and Gauss-Seidel methods | Read related sections in references |
| 12 | Richardson and SOR methods, Convergence analysis of the iterative methods | Read related sections in references |
| 13 | Krylov subspace Methods, Preconditioning and preconditioners | Read related sections in references |
| 14 | General Review | - |
| 15 | General Review | - |
| 16 | Final exam | - |
Sources
| Course Book | 1. L.N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997. |
|---|---|
| 2. J.W.Demmel, Applied Numerical Linear Algebra, SIAM, 1997 | |
| Other Sources | 3. G.H. Golub and C.F. van Loan. Matrix Computations, John Hopkin’s University Press, 3rd edition, 1996. |
| 4. A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM, 1997. | |
| 5. C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000. | |
| 6. O. Axelsson, Iterative Solution Methods, Cambridge University Press, 1996. | |
| 7. D.S. Watkins, Fundamentals on Matrix Computations, John Wiley and Sons, 1991. | |
| 8. K.E.Atkinson, An Introduction to Numericall Analysis, John Wiley and Sons, 1999. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | 5 | 10 |
| Homework Assignments | 7 | 9 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 46 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 15 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Gains accumulated knowledge on mathematics, science and mechatronics engineering; develops an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. | X | ||||
| 2 | Develops ability to differentiate, identify, formulate, and solve complex engineering problems; develops ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. | X | ||||
| 3 | Develops ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; develops ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions includes economics, environment, sustainability, producibility, ethics, human health, social and political problems.) | X | ||||
| 4 | Gains ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; develops ability to use information and communications technologies effectively. | X | ||||
| 5 | Develops ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. | |||||
| 6 | Develops ability to work effectively on single disciplinary and multi-disciplinary teams; gains ability for individual work; develops ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. | |||||
| 7 | Develops ability to express creative and original concepts and ideas orally or written effectively, in Turkish and English language. | |||||
| 8 | Develops ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; gains consciousness on the necessity of improvement and sustainability as a result of life-long learning; gains ability for monitoring the developments on science and technology; develops awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation. | |||||
| 9 | Gains ability to be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself. | |||||
| 10 | Gains 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 | Gains 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; develops consciousness on these issues and develops awareness of legal results of engineering solutions. | |||||
| 12 | Gains the competence 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 | Gains conciousness on the environmental and social responsibility and develops conciousness to be an individual in society. Gains ability to develop and implement projects and asses them with a critical view for their social implications and gains ability to change the related norms if necessary. | |||||
| 14 | Gains the competence on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of quality standarts. | |||||
ECTS/Workload Table
| 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 | 16 | 2 | 32 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 7 | 3 | 21 |
| Quizzes/Studio Critics | 5 | 1 | 5 |
| Prepration of Midterm Exams/Midterm Jury | 2 | 8 | 16 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 132 | ||