Available online
Description
This programme looks at the logarithmic function and its inverse the exponential function. This leads to the ability to express all power functions in the form E(x) and simplifies many operations i...n the calculus.
This programme looks at the logarithmic function and its inverse the exponential function. This leads to the ability to express all power functions in the form E(x) and simplifies many operations i...n the calculus.
| Module code and title: | MS283, An introduction to calculus |
|---|---|
| Item code: | MS283; 12 |
| First transmission date: | 01-08-1979 |
| Published: | 1979 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:04 |
| + Show more... | |
| Producer: | John Jaworski |
| Contributors: | A. Daniel Lunn; Anne Walton |
| Publisher: | BBC Open University |
| Keyword(s): | Computer animation; Power series |
| Footage description: | Daniel Lunn introduces the programme. Pointing to a graph of the area function, he explains that he suspects that this is in fact a log function. He labels it as a mystery function L(x). With the aid of computer animations, Lunn looks at the graph of the function L(x) and its derivative. Anne Walton plots the graph for the inverse of L(x) by reflecting the L(x) graph along the line y = x. She labels this inverse function E(x). With the aid of a computer animation, Walton then looks at the graph of the derivative of E(x) and points out that it is the same as the graph of E(x). She writes on a board the proof that E(x) is its own derivative. Daniel Lunn looks back at the function L(x) and points out its various log-like properties. He goes on to show these properties graphically with the aid of a computer animation. Anne Walton writing on a drawing board and pointing to graphs, relates the log-like properties of L(x) to those of E(x). She points out, particularly, that E(x) is the power function of e. Daniel Lunn and Anne Walton demonstrate, with the aid of still and computer animated graphics, that all power functions are represented in the form E(x). Daniel Lunn sums up the programme. |
| Master spool number: | 6HT/72941 |
| Production number: | 00525_4307 |
| Videofinder number: | 498 |
| Available to public: | no |
