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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA671 - Linear algebra and numerical analysis  
 
Syllabus adopted 2016-02-15 by Head of Programme (or corresponding)
Owner: TKTFY
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics, Engineering Physics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0199 Examination 7,5c Grading: TH   7,5c   29 May 2017 pm M,  08 Oct 2016 am SB,  19 Aug 2017 am SB

In programs

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

Examiner:

Doktor  Geir Bogfjellmo



  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

- Ivar Gustafsson och Kjell Holmåker, Linjär Algebra och Numerisk Analys, kompendium, Cremona
OR
- David C. Lay: Linear Algebra and its Applications, Addison Wesley, 2003.
- Michael T. Heath: Scientific Computing: An Introductory Survey. McGraw Hill, 2002.

Examination

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.