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Description
This programme shows how the definition of scale factor together with the idea of a limit of a sequence of values can be used to define the derivative at a point of a function.
Module code and title: MS283, An introduction to calculus MS283; 08 30-05-1979 1979 Rights owned or controlled by The Open University This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all OU Digital Archive web pages. 00:24:01 + Show more... Jean Nunn Graham Read; Colin Rourke; Allan I.,1936-2013 Solomon BBC Open University Computer animation; Convergence; Tangent; Chord; Slope Graham Read introduces the programme. Allan Solomon works out the scale factor for a function which students were asked to calculate before the programme. Solomon goes on to point out that it is often difficult to calculate a scale factor for functions such as f(x) - sin x. Colin Rourke and Allan Solomon explain how the scale factor for sin x at a given point is calculated. An animated diagram and still graph illustrate their points. Rourke arrives at a new way of calculating scale factors which applies to a far wider class of functions than the method used so far in the course. Solomon defines the concept of the derivative with respect to the scale factor calculations above. Using an animated diagram, Solomon illustrates the derivative of a function as the slope of a curve. Graham Read sums up the programme so far. Allan Solomon plots the derivatives for several points of a function and Joins these derivatives together with a curve. This allows him the record the values of derivatives at every point of a curve. An animated diagram recaps the process. Solomon defines this curve as the derived function, Solomon, with the aid of animated diagrams, examines the plots of the derived functions for several functions. Graham Read, also with the aid of animated diagrams explains how one can predict, from a function, what its derived function looks like. He then briefly sums up the programme. 6HT/73039 00525_4317 484 no