Available online
Description
The programme shows with the aid of computer graphics, how Taylor Polynomials give an approximation to the sine curve. A general formula providing polynomials for any function is proved.
The programme shows with the aid of computer graphics, how Taylor Polynomials give an approximation to the sine curve. A general formula providing polynomials for any function is proved.
| Module code and title: | M101, Mathematics: a foundation course |
|---|---|
| Item code: | M101; 14 |
| First transmission date: | 27-05-1978 |
| Published: | 1978 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:30 |
| + Show more... | |
| Producer: | John Richmond |
| Contributors: | Louis Leithold; Graham Read |
| Publisher: | BBC Open University |
| Keyword(s): | Approximation; Calculus; Computer animations; Function-synthesising-machine; Illustration; Sine |
| Footage description: | Graham Read introduces the programme and works through some pre-set problems which involve the use of a formula used to calculate the sine of an angle. This formula is a set of polynomials called the Taylor polynomials. With the aid of computer graphics, Louis Leithold demonstrates how the Taylor polynomials give an increasingly better approximation to the sine curve. Graham Read shows how the formula for sine is derived. This formula is true also for any arbitrary function. Using computer graphics, he shows how the Taylor polynomials give different curves as different values are given to the derivation. Louis Leithold sets Graham the task of matching the derivatives of sin X + cos X with the Taylor Polynomials. Graham does this using the computer graphics. Louis then sets a further problem when the Taylor polynomials do not get closer to the function. Graham, again with the computer display, works through the problem, reaching the conclusion that the recipe for Taylor Polynomials will not always work for all values of X. |
| Master spool number: | 6HT/72529 |
| Production number: | 00525_4251 |
| Videofinder number: | 4344 |
| Available to public: | no |
