norsk norsk&engelsk / norwegian&english

Course Description REA1042 - Mathematics 10 - Functions with One Variable. (2005/2006)

LevelUndergraduate
ECTS Credits5
DurationAutumn
Three-term students: summer, autumn and spring
LanguageNorwegian
Prerequisite(s) 
Aim

The students shall
- be able to show skill in algebraic manipulations, transforming of function expressions, differentiation and integration.
- be able to show a good understanding of central concepts in the subjects of the course. The students shall be able to apply functions, differentiation and integration on simple pravtical problems (modelling).
- have knowlede on plotting of function graphs, numerical solving of equations and numerical integration with calculator and computer programmes (Maple)

There will also be an extra part covering fundamental subjects for the "three term students", following a programme mot requiring maximum amount of mathematics and physics from upper secondary school.

Content

Numbers:
Integers, rational, real and complex numbers.
Functions:
Explicitly and implicitly defined functions, inverse functions, limits, continuity. Parametrised curves, vector valued functions, position, velocity and acceleration. Trigonometric and inverse trigonometric functions, exponential and logaritmic functions.
Differentiation:
Definition and differentiation rules, differential and linear approximation, implicit differentiation. Modelling.
The integral:
Riemann sums, integration by substitution and by parts, partial fraction, arc length, area, volumes, mass centre, momentum.

Basic use of the Computer Algebra Programme Maple.

Study MethodsLectures, Mandatory Assignments, Exercises
AssessmentPortfolio Assessment (counts 50%)
Written Exam, 4 hours (counts 50%)
.
Grading SystemAlphabetical Scale, A (best) - F (fail)
Course RequirementsNone