KURSPLAN
Linjär algebra och optimering, 7,5 högskolepoäng
Linear Algebra and Optimization, 7.5 credits
Kursplan för studenter höst 2020
 Kurskod: TAOG19 Fastställd av: VD 2019-06-01 Gäller fr.o.m.: 2019-01-01 Version: 1
 Utbildningsnivå: Grundnivå Utbildningsområde: Naturvetenskapliga området Ämnesgrupp: MA1 Fördjupning: G1N

## Lärandemål

After a successful course, the student shall

### Kunskap och förståelse

- display knowledge of vectors, matrices and the basic operations, defined for these objects
- display knowledge of systems of linear equations, their possible solution sets, as well as how can these be formulated as matrix equations
- display knowledge of what constitutes a linear programming problem

### Färdighet och förmåga

- demonstrate the ability to use Gauss elimination and basic matrix algebra to solve systems of linear equations
- demonstrate the ability to use vector operations and linear systems to solve geometrical problems in two or three dimensions
- demonstrate the ability to calculate determinants, eigenvalues of square matrices, draw conclusions about unique solvability of square linear systems, matrix singularity and linear dependence of vectors
- demonstrate the ability to formulate a real world problem as a linear programming problem
- demonstrate the ability to use graphs and the Simplex algorithm to solve limited-sized linear programming problems and to draw sensitivity conclusions from the solutions
- demonstrate the ability to formulate the dual of a linear programming problem and to draw conclusions from its solution
- demonstrate the ability to use computer software to solve linear algebraic and optimization problems

## Innehåll

The course introduces several elements from the linear algebra as well as techniques for linear optimization.

The course includes the following elements:
- Systems of simultaneous linear equations and Gauss elimination
- Vectors, basic operations and some vector geometry
- Matrices and matrix algebra
- Eigenvectors and eigenvalues
- Linear programming
- Graphical solutions to two-dimensional linear programming problems
- The Simplex method and sensitivity analysis
- Duality in linear programming
- Examples of computer software for optimization.

## Undervisningsformer

Lectures, seminars and computer exercises.

Undervisningen bedrivs på engelska.

## Förkunskapskrav

Grundläggande behörighet samt Engelska 6, Fysik 1, Kemi 1, Matematik 3c. Eller: Engelska B, Fysik A, Kemi A, Matematik D (eller motsvarande kunskaper).

## Examination och betyg

Kursen bedöms med betygen 5, 4, 3 eller Underkänd .

The final grade will only be issued after satisfactory completion of all assessments.

Poängregistrering av examinationen för kursen sker enligt följande system:
ExaminationsmomentOmfattningBetyg
Skriftlig tentamen7,5 hp5/4/3/U

## Kurslitteratur

The literature list for the course will be provided one month before the course starts.

Hardy: Linear algebra for engineers and scientists using Matlab, Pearson,
ISBN 0-13-010988-6