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Description
This programme explores the need for a directional derivative, a quantity which is the rate of change of some function but dependent on the direction in which it is taken.
Module code and title: MS283, An introduction to calculus MS283; 15 12-09-1979 1979 00:22:18 + Show more... Ted Smith Alan Durrant; A. D.(A. Daniel) Lunn BBC Open University Aluminium plate; Beeston castle; Electrical flow; Heat flow Alan Durrant introduces the programme. He points out the contour lines on an Ordnance Survey map of the Beeston Castle area in Cheshire and then shows a plaster cast model of the same area with contour lines marked. Durrant goes on to look at a mathematical perspex model of the area. He points out that scalar and vector fields occur together in this model, Durrant rolls a ball bearing down the model to illustrate the vector fields. Daniel Lunn looks at another physical example where scalar and vector fields occur together - an aluminium plate which is heated at one end and cooled at the other. He points out the flow of heat from high to low temperatures (vectors) and the lines of constant temperatures (scalars). Lunn goes on to conduct another experiment, physically different but mathematically similar to the one above. He applies an electric current to a current conducting plate and points out that the current flows from areas of high voltage to areas of low voltage in the plate. Lines of constant voltage (scalars) are sketched on the plate. Using captions and a diagram, Alan Durrant demonstrates that the process of differentiation is the link between the scalar and the vector fields. Durrant labels the derivatives obtained the directional derivatives and points out that the directional derivative at 90° to the scalar is the derivative of maximum magnitude. Daniel Lunn carries out an experiment, on the electric current carrying plate to demonstrate that the conclusions drawn on the directional derivative above work in practise. Alan Durrant sums up the programme. 6HT/73103 00525_4321 467 no