Available online
Description
This programme examines the iteration process, giving graphical explanantions of why a result is sometimes obtained and why the sequence sometimes diverges froma result.
This programme examines the iteration process, giving graphical explanantions of why a result is sometimes obtained and why the sequence sometimes diverges froma result.
| 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 |
| + Show more... | |
| 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 |
