ECTS - Numerical Linear Algebra
Numerical Linear Algebra (MDES621) Course Detail
Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
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Numerical Linear Algebra | MDES621 | 3 | 0 | 0 | 3 | 5 |
Pre-requisite Course(s) |
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MATH 275 Linear Algebra or equivalent |
Course Language | English |
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Course Type | N/A |
Course Level | Natural & Applied Sciences Master's Degree |
Mode of Delivery | Face To Face |
Learning and Teaching Strategies | Lecture. |
Course Lecturer(s) |
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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;
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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 |
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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. |
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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 |
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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 |
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Percentage of Final Work | 35 |
Total | 100 |
Course Category
Core Courses | X |
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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 | ||||
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1 | 2 | 3 | 4 | 5 | ||
1 | Ability to expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement. | |||||
2 | Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering. | |||||
3 | To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines. | |||||
4 | Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed. | |||||
5 | Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions. | |||||
6 | Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs. | |||||
7 | Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process. | |||||
8 | Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility. | |||||
9 | To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level. | |||||
10 | Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments. | |||||
11 | To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications. | |||||
12 | Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities. |
ECTS/Workload Table
Activities | Number | Duration (Hours) | Total Workload |
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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 |