Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameNumerisk linjär algebra
- CodeTMA265
- Credits7.5 Credits
- OwnerMPENM
- Education cycleSecond-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language English
- Application code 20120
- Open for exchange studentsYes
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0101 Examination 7.5 c Grading: TH | 7.5 c |
|
In programmes
- MPDSC - DATA SCIENCE AND AI, MSC PROGR, Year 1 (elective)
- MPDSC - DATA SCIENCE AND AI, MSC PROGR, Year 2 (elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
Examiner
Larisa Beilina- Full Professor, Applied Mathematics and Statistics, Mathematical Sciences
Eligibility
General entry requirements for Master's level (second cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Basic knowledge of numerical analysis and linear algebra.
Aim
To give the students knowledge and skill in using algorithms and numerical software for linear algebra problems.
Learning outcomes (after completion of the course the student should be able to)
- use numerical linear algebra as building bricks in computation - make a linear algebra model of a problem from the physical reallity - derive and use the numerical tecniques needed for a professional solution of a given linear algebra problem - use computer algorithms, programs and software packages to compute solutions to current problems - critically analyze anf give advice regarding different choices of models, algorithms, and software with respect to efficience and reliability - critically analyze the accuracy of the obtained numerical result and to present it in a visualized way.
Content
Numerical linear algebra problems arise in many different fields of science like solid mechanics, electrical networks, signal analysis and optimisation. In this course we study basic linear algebra concepts like matrix algebra, vector- and matrix norms, error analysis and condition numbers. For solving linear systems of equations we consider Gaussian elimination with different pivoting strategies. For least-squares problems we study QR-factorisation and singular value decomposition. The metods for eigenvalue problems are based on transformation techniques for symmetric and nonsymmetric matrices. We discuss the numerical algorithms with respect to computing time and memory requirements. By homework assignments and project work the students get experiences in implementation and evaluation of numerical algorithms for linear algebra problems.
Organisation
Lectures, supervising of hand-ins and computer exercises
Literature
Numerical Linear Algebra: Theory and Applications, Larisa Beilina, Evgenii Karchevskii, and Mikhail Karchevskii, Springer 2016.
Examination including compulsory elements
Experimental and homework assignments(hand-ins) and written examination.
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.