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Use the search function to find more information about the study programmes and courses available at Chalmers. When there is a course homepage, a house symbol is shown that leads to this page.

Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA672 - Linear algebra and numerical analysis  
Linjär algebra och numerisk analys
 
Syllabus adopted 2019-06-13 by Head of Programme (or corresponding)
Owner: TKTFY
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mathematics, Engineering Physics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 57150
Open for exchange students: No
Maximum participants: 180
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Laboratory 1,5 c Grading: UG   1,5 c    
0219 Examination 6,0 c Grading: TH   6,0 c   01 Jun 2020 pm J,  12 Oct 2019 am SB_MU   27 Aug 2020 am J

In programs

TKAUT AUTOMATION AND MECHATRONICS ENGINEERING, Year 3 (elective)
TKTFY ENGINEERING PHYSICS, Year 1 (compulsory)
TKTEM ENGINEERING MATHEMATICS, Year 1 (compulsory)

Examiner:

Thomas Bäckdahl

  Go to Course Homepage


Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

Course specific prerequisites

A first course in Linear algebra and geometry

Aim

To present an introduction to linear spaces concepts such as linear dependence/independence, basis, dimension, orthogonality and spectral theory.
To give the basics in numerical analysis and computational mathematics.

Learning outcomes (after completion of the course the student should be able to)

- Use linear algebra concepts for solving problems in engineering and science.

- Use mathematical models for numerical solution of real world problems.

- Find and use appropriate mathematical software for the current application.

- Critically analyze and give advice regarding different models, algorithms, and software with respect to efficiency and reliability.

Content

Basics in Linear Algebra; Vector Spaces, Basis, Dimension, Linear Dependence/Independence, Inner Product, Orthogonality.
Linear mappings.
Eigenvalues and eigenvectors, Spectral theory,
Quadratic forms, Applications in Analysis; Systems of Ordinary Differential Equations.
Introduction to Computational Mathematics and Scientific Computing, Mathematical Software.
Numerical Techniques and Numerical Methods.
Numerical Solution of Linear Systems, Least Squares Problems and Eigen Problems.
QR-factorization and SVD.
Numerical Methods for Solving Equations, Interpolation and Splines, Numerical Integration and Differentiation.
Numerical Solution of Ordinary Differential Equations, Explicit and Implicit Methods, Stability and Order of Approximation.

Organisation

Lectures, lessons, and computer exercises.

Literature

- Kjell Holmåker och Ivar Gustafsson, Linjär Algebra: fortsättningskurs, 1st ed., Liber
- Ivar Gustafsson och Kjell Holmåker, Numerisk Analys, 1st ed., Liber

Examination including compulsory elements

Written examination with problems of theoretical and applied nature.
Computer exercises.
Homework assignments giving credit points for the examiantion may exist.


Page manager Published: Thu 04 Feb 2021.