# Mathematics 10 - Functions with One Variable. 2010-2011 - REA1042 - 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)

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.

## 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.

Lectures
Exercises

Maple

## Form(s) of Assessment

Portfolio Assessment
Written exam, 4 hours

## Form(s) of Assessment (additional text)

Portfolio assessment (counts 50%)
Written Exam, 4 hours (counts 50%)
Each part must be individually approved of.
Portfolio assessment is based on results of the exercises.