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This programme examines the iteration process, giving graphical explanantions of why a result is sometimes obtained and why the sequence sometimes diverges froma result.
Metadata describing this Open University video programme
Module code and title: M101, Mathematics: a foundation course
Item code: M101; 09
First transmission date: 16-04-1978
Published: 1978
Rights Statement:
Restrictions on use:
Duration: 00:24:16
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Producer: Jack Koumi
Contributors: Colin Rourke; Allan I.,1936-2013 Solomon
Publisher: BBC Open University
Keyword(s): Convergence; Flow diagrams; Scale factors; Staircase/cobweb diagrams
Footage description: Allan Solomon introduces the programme. He discusses the iteration process and why there is sometimes convergence and sometimes divergence using this method. Colin Rourke, using a mapping diagram gives a pictorial view of the iteration process. He explains why a converging sequence will never reach an absolute point, but will always be approximate. He relates this to the Scale factor. Allan Solomon show how the points where a diagonal crosses the graph of the function can give starting points for the iteration process. He and Colin Rourke give demonstrations of how the iteration process works, graphically using staircase diagrams and several different starting values. He and Colin Rourke then work through examples with a negative slope. They obtain the rule that with a scale factor, or slope, greater than 1, there is divergence, with a scale factor less than 1, there is convergence.
Master spool number: 6HT/72453
Production number: 00525_4246
Videofinder number: 2461
Available to public: no