# Mathematics 10 - Functions with One Variable. 2010-2011 - 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)

## Topic(s)

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.

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

Basic use of the Computer Algebra Programme Maple.

Other

Maple

## Form(s) of Assessment

Written exam, 4 hours

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