Course PM

This page includes information about aim and learning outcomes, teachers, literature, examination, examination procedures, old exams and course evaluation. The program for all teaching sessions can be found on a separate page (Course syllabus).

Aim and learning outcomes

The aim and learning outcomes of the course can be found in the course plan Links to an external site..

Problems of numerical linear algebra arise in many different fields of science like computational fluid dynamics, solid mechanics, electrical networks, signal analysis, and optimisation. In this course we study basic linear algebra concepts like matrix algebra, theory for linear systems of equations, spectral theory, and vector- and matrix norms as well as numerical aspects like efficiency, reliability, error analysis and condition numbers. We will study following topics:

For solving linear systems of equations we will present Gaussian elimination with different pivoting strategies and blocking algorithms.
For least-squares problems we study the method of normal equations, QR-factorisation and Singular Value Decomposition (SVD).
The methods for solution of eigenvalue problems which are based on transformation techniques for symmetric and non-symmetric matrices.
The basic iterative methods (Jacobi, Gauss-Seidel and Successive overrelaxation (SOR)) for solution of linear systems.
Introduction to the Krylov subspace methods.
For all topics above we will discuss numerical algorithms with respect to applicability, reliability, and efficiency. By implementing computer exercises in MATLAB and C++/PETSc the students will get experience in implementation and evaluation of numerical algorithms for problems of linear algebra.
By the completion of this course the students will be able to:

use numerical linear algebra as building bricks in computation.
make a linear algebra model of problems from the physical reality.
derive and use the numerical techniques 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 and give advice regarding different choices of models, algorithms, and software with respect to efficiency and reliability.
critically analyze the accuracy of the obtained numerical result and to present it in a visualized way.
The course code for engineering schools and students registered at Chalmers is TMA265. The course code for students registered in GU is MMA600.

Teachers

Examiner: L. Beilina

Lecturer: L. Beilina

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Course literature

Beilina, E. Karchevskii, M. Karchevskii, Numerical Linear Algebra: Theory and Applications, Springer, 2017. Links to an external site.

English-Swedish mathematical dictionary. Links to an external site.

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Examination

Final exam is compulsory, written.

Grades: to pass (get G) requires 15 points together with points from homework
assignments and computer exercises. Grades are set according to the table on the
course homepage.
• Solutions will be announced at the end of exam and placed on the course homepage.
• Aids: you can use written by hand notes (list of formulas/formelblad: formulas, theorems, definitions, algorithms but not proofs or solutions) on the one side of A4 sheet or you can use list of formulas provided for this exam (see the course page). The list of of formulas will be provided at examination together with questions to exam.

This means that you should choose: or write your own list of formulas on the one side of A4 sheet

or take already provided list of formulas for this exam which is available for download at the course page.

In the case if you want to be sure - you also can print our this list of formulas and bring with you to exam.

If you want to write your own list of formulas - I need to see it and sign such that you can bring it to exam.

Easy (not advanced) calculators are also allowed to use.

No AI tools are allowed at exam.

Bring ID and receipt for your student union fee (this is requirement only for Chalmers students. GU students can come on the exam without receipt).
Solutions to the exam will be published at the link which will be written at this homepage. You will be notified the result of your exam by email from LADOK (This is done automatically as soon as the exams have been marked an the results are registered.)
The exams will then be kept at the students office in the Mathematical Sciences building.
Check that the number of points and your grade given on the exam and registered in LADOK coincide.
Complaints of the marking should be written and handed in at the office. There is a form you can use, ask the person in the office.).

List of questions for examination Download List of questions for examination

The dates, times and places for the exams are in the student portal Links to an external site..

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Examination procedures

In Chalmers Student Portal Links to an external site. you can read about when exams are given and what rules apply to exams at Chalmers. In addition to that, there is a schedule Links to an external site. when exams are given for courses at the University of Gothenburg.

Before the exam, it is important that you sign up for the examination. You sign up through Ladok Links to an external site..

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office Links to an external site.. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office Links to an external site.. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

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Course evaluation

At the beginning of the course, at least two student representatives should have been appointed to carry out the course evaluation together with the teachers. The evaluation takes place through conversations between teachers and student representatives during the course and at a meeting after the end of the course when the survey result is discussed and a report is written.

Guidelines for Course evaluation Links to an external site. in Chalmers student portal.

Student representatives

The following students have been appointed:

MPALG johanna.edh1@gmail.com Johanna Edh
MPENM holger.johansson@hotmail.se Holger Johansson
MPENM rosin.lovisa@gmail.com Lovisa Rosin
MPENM albert.vesterlund@gmail.com Albert Vesterlund

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