# Mathematics 20 - Electrical Engineering Mathematics 2012-2013 - REA2051 - 10 ECTS

## On the basis of

The courses REA1042 Matematikk 10 and REA1051 Matematikk 15

## Expected learning outcomes

The student shall gain familiarity with some basic concepts, types of problems and methods of solution needed for technical applications.

## Topic(s)

The Laplace transform:
Definition and properties of the Laplace transform, inverse Laplace transforms, solving linear differential equations, transfer functions and block diagrams, dynamic modelling, poles and zeros in the s plane, frequency response.

Difference equations:
Sequences, definitions, general and numeric solutions, block diagrams.

The z transform:
Definition and properties, sampling, inversion of z transforms, solving difference equations.

Series:
Geometric series, power series, Taylor series, series convergence, convergence tests

Fourier series:
Periodic functions, trigonometric functions, Fourier series, odd and even functions, half-range periodic extension

Functions of several variables:
Graphs, partial derivatives, finding maximum and minimum points, total differential.

Lectures
Exercises

## Form(s) of Assessment

Written exam, 4 hours

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

## External/internal examiner

All student works is 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

Approved calculator.

Haugan, J. Tabeller og formelsamling. NKI-forlaget. ISBN 82-562-2483-5

None

## Teaching Materials

Croft, Davison, Hargreaves: Engineering Mathematics. Prentice Hall. ISBN 0 130 26858 5

Lorentzen, Hole, Lindstrøm: Kalkulus med en og flere variable, Universitetsforlaget. ISBN 82-00-42433-2

Hans Engenes: "Om periodiske funksjoner og Fourierrekker" (free paper)

All written material published on the homepage of the course. ( http://www2.hig.no/at/realfag/matematikk/Ma20-Elektro/ )