Available online
Description
This programme looks at a few of the many interesting functions that are neither discontinuous, or nowhere differentiable or both.
This programme looks at a few of the many interesting functions that are neither discontinuous, or nowhere differentiable or both.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 05B; 1995 |
| First transmission date: | 1994 |
| Published: | 1995 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:35 |
| + Show more... | |
| Producer: | Pip Surgey |
| Contributors: | David H. Brannon; Phil Rippon; Robin Wilson |
| Publisher: | BBC Open University |
| Keyword(s): | Continuous; Differentiable; Function; Modulus; Space-filling Curve |
| Subject terms: | Mathematics |
| Footage description: | Mostly students only meet well-behaved functions, ones that were continuous, if not differentiable, at all but a few well-chosen points. This programme considers the vast majority of functions which are not so well-behaved. The examples chosen are easily constructed from simple functions, and are either nowhere continuous, or continuous but nowhere differentiable. The two nowhere continuous functions discussed are the Dirichlet and Riemann functions. One nowhere differentiable function can be constructed by forming the infinite sum of a series of sawtooth functions. It's the so-called "blancmange" function. The programme proves both its continuity, and its non-differentiability. Other nowhere-differentiable functions can simulate natural phenomena, such as Mandelbrot's mountain ranges. Finally, this leads to the properties of curves of infinite length, snowflake curves, and the idea of a space-filling curve. |
| Master spool number: | DOU8162 |
| Production number: | FOUM503N |
| Videofinder number: | 1141 |
| Available to public: | no |
