Mathematics 10 - Functions with One Variable.
2009-2010 - REA1042F - 5 ECTS

Expected learning outcomes

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, integration and differential equations 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)


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.
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.

Differential equations:
Linear and separable ordinary first order differential equations.

Basic use of the Computer Algebra Programme Maple.

Teaching Methods


Teaching Methods (additional text)


Form(s) of Assessment

Written exam, 4 hours

Grading Scale

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

External/internal examiner

Internal examiner

Re-sit examination

Ordinary re-sit examination.

Coursework Requirements

5 coursework requirements

Teaching Materials

Edwards & Penney: Calculus (7e) (Pearson), ISBN 9780136158400