Available online
Description
This programme investigates the theory and practice of using computers to find the roots of non-linear equations.
This programme investigates the theory and practice of using computers to find the roots of non-linear equations.
| Module code and title: | M351, Numerical computation |
|---|---|
| Item code: | M351; 01 |
| First transmission date: | 09-03-1976 |
| Published: | 1976 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:00 |
| + Show more... | |
| Producer: | John Richmond |
| Contributors: | Bill Arms; Peter Thomas |
| Publisher: | BBC Open University |
| Keyword(s): | Equations; Roots; Secant |
| Footage description: | The programme opens with a short cartoon, which shows a student doing a calculation at high speed and running it through a computer with disastrous results. Bill Arms comments on the folly of hurrying numerical computation and states that the programme deals with finding the roots of non-linear equations. In the studio, Thomas shows how to use the Newton-Raphson method to find the roots of the equation x3 - 5x + 3 = 0. The problem is stated in full in Section 4.4 of Unit 4. Thomas uses a graph to indicate the three roots and calculates one of them on a drawing board. He uses a calculator to demonstrate Newton's method. Thomas uses a computer terminal to find other roots of this equation. He demonstrates the effect of changing the starting value. Arms uses a graph to explain the use of the iteration function. He then applies this to the problem tackled by Thomas, and the results are seen in a computer animation. He emphasises the importance of good starting values. Thomas introduces a second, more difficult non-linear equation, which is dealt with in Unit 2. Thomas discusses the difficulty of finding roots of equations of this complexity. He demonstrates the use of the computer to tabulate the function in the range where roots are likely, and indicate the results on a graph plotter. He explains that Newton's method and the Bisection method are unsuitable for these calculations. Arms explains the Secant method with the help of a graph. He explains that the Secant and Bisection methods can be combined. Thomas demonstrates the use of this root-finding package on the studio VDU, and two roots are located. He concludes by stressing the importance of examining a problem before feeding it into a computer. |
| Master spool number: | 6HT/71885 |
| Production number: | 00525_4220 |
| Videofinder number: | 1216 |
| Available to public: | no |
