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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.
Metadata describing this Open University video programme
Module code and title: MS283, An introduction to calculus
Item code: MS283; 08
First transmission date: 30-05-1979
Published: 1979
Rights Statement:
Restrictions on use:
Duration: 00:24:01
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Producer: Jean Nunn
Contributors: Graham Read; Colin Rourke; Allan I.,1936-2013 Solomon
Publisher: BBC Open University
Keyword(s): Computer animation; Convergence; Tangent; Chord; Slope
Footage description: 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.
Master spool number: 6HT/73039
Production number: 00525_4317
Videofinder number: 484
Available to public: no