# Mathematics 15 - Linear Algebra and Discrete Mathematics 2008-2009 - REA1051 - 5 ECTS

## Expected learning outcomes

Make the students familiar with some basic concepts, problem issues and solving methods regarding linear algebra, linear differential equations and discrete mathematics.

## Topic(s)

Matrices and linear algebra:
Matrix algebra, vector algebra, Gaussian elimination, determinants, inverse matrices, linear transformations, vector spaces, linear independence, basis, rank, dimension, coordinate transformations, eigenvalues and eigenvectors, diagonalisation, orthogonal matrices

Complex numbers:
Complex vectors, addition, multiplication and division, complex conjugate, cartesian and polar form, Euler's and deMoivre's theorems

Differential equations:
2nd order and systems of 1st order linear differential equations with constant coeffisients.

Set theory:
Set, element, inclusion, subset, intersection, union, relative complement, complement, symmetric difference, Venn diagram

Propositional Logic :
Compound proposition, negation, conjunction, disjunction, implication, biimplication, truth table, proof by mathematical induction

Lectures
Exercises

## Form(s) of Assessment

Written exam, 4 hours

Alphabetical Scale, A(best) – F (fail)

## External/internal examiner

The answers will be evaluated by the internal examiner.

An external examiner will be used periodicaly (every 3 to 4 years).

## Re-sit examination

A re-sit examination will be held if necessary

## Examination support

An approved calculator and formula tables

## Coursework Requirements

A number of approved tests (maximum 4) is required but will not influence on the grading scale.

## Teaching Materials

• Glyn James: Modern Engineering Mathematics, 4th edition" , Pearson / Prentice Hall. ISBN 978-0-13-239144-3
• Edwards & Penney: Calculus. ISBN 9780136158400

~All written material published at the homepage of the course (http://www2.hig.no/at/realfag/matematikk/Ma15/)