Időpont: 2014.09.04 10:00 - 2014.09.04 16:00

Helyszín: Bolyai Institute, Szeged

Programme

10.00-12.00   Workshop (Bolyai Library)

Topics:

• Teaching programmes at Beuth FachochSchule

• Didactic problems of computer-aided teaching of Mathematic 

Guests:

Prof. Dr. Norbert Kalus and Prof.  Dr. Angela Schwenk-Schellschmidt, Beuth HochSchule für Technik Berlin

Seminar lectures at Bolyai Institute (Irinyi courtyard-room)

14.00-14.50  Norbert Kalus: Computer-Aided Exploring the Mathematics behind Technical Problems - Examples of Classroom Practices

Abstract: The mathematics in technical problems can be discovered by computer-aided experiments. Examples are presented from four different courses in the areas of statics, elasticity, finite elements and partial differential equations. One focus is on linking the notion of Technical Mechanics and Linear Algebra. It will be reported on the implementation within the curriculum at Beuth University of Applied Sciences, the classroom experiments and the teacher’s role.

15.00-15.50  Angela Schwenk-Schellschmidt: The Common Idea behind all Roulettes, one Formulae Fits for all - an Application of complex numbers

Abstract: A roulette is the curve traced out by a point that is attached to a curve (wheel) as the curve rolls along another curve (street) without slippage. Mostly the wheels are circles and the streets are straight lines or other circles. Normally the parameterisation of a roulette is derived by a special solution that fits only for the considered type of wheel and street. Changing the type of the wheel or the type of the street requires new thinking just form the beginning. But there is one common idea behind all roulettes. This idea fits to all situations. One just needs a time depending Euclidean motion that transforms the wheel from its starting position to its current position. A general formula is derived. Just by plugging in the equations of the wheel and the street generates the equations of the roulette or the current equation of the rolling wheel. Complex numbers make the formula very simple.