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Solving a problem about a goat leads to a powerful formula iteration method which makes use of differentiation.
Module code and title: M101, Mathematics: a foundation course M101; 11; 1983 1984 1983 00:24:30 Also used for MST204/Summer School programme. + Show more... John Jaworski Bob Margolis; Anne Walton BBC Open University Bisection; Calculus; Iteration formulae; Newton-Raphson method; Polynomial expressions; Trigonometry In this programme, which is associated with Unit 1 of block III (the Calculus Block), students are involved in the process of finding a method of obtaining a rearrangement which will almost always work, and which will normally give any desired root, provided a reasonable first approximation is chosen. It is revealed as the Newton-Raphson method for formula iteration. Students are first presented with the problem of determining the length of tether required for a goat to graze half the area of a circular field. Use is made of the problem-solving strategy introduced in block 1 of the course (see TV M101/1) although it would not be essential for a viewer to be familiar with that material. The resulting equation is only soluble by numerical methods. Using a micro computer the problem is solved initially by bisection (Block I Unit 1), and then for contrast by an unknown rearrangement (the Newton-Raphson formula). The rest of the programme is devoted to showing how the Newton-Raphson formula can be used to find more than one root, to applying the method to the solution of a cubic equation, and to an investigation of occasions when the method breaks down. The programme should be useful to anyone who has some knowledge of numerical techniques, who has just begun to study differentiation and who is interested in the application of calculus to a "real" problem. HOU4223 FOUM169T 2465 no