Mathematics 15  Linear Algebra and Discrete Mathematics

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
Teaching Methods
Lectures
Exercises
Form(s) of Assessment
Written exam, 4 hours
Grading Scale
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).
Resit examination
A resit 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 9780132391443
 Lorentzen, Hole, Lindstrøm: Kalkulus med en og flere variable, Universitetsforlaget. ISBN 8200424332
All written material published at the homepage of the course (http://www2.hig.no/at/realfag/matematikk/Ma15/)