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Description
Part 1 : Eigenvectors and diagonalisation -- Part 2 : Symmetries of the octahedron -- Part 3 : Images of functions ... Part 1 looks at linear transformation and how changing the basis for R2 it will change the matrix Part 2 looks at the eight faces of this octahedron are congruent isosceles triangles. In other words it's made up of two equal square pyramids. What we're going to do in this video programme is to look at the group of symmetries of this object and to investigate the group's conjugacy classes and its subgroups. Part 3, the final part of the video cassette looks at the problems of finding the image of the domain of functions. It shows how a graphical analysis of the properties of any given function can readily lead to the image set corresponding to the original domain. Having obtained a sketch of the graph within the given domain, it is possiole to identify the maximum, minimum and turning points of the function, and hence to split the domain up into the union of disjoint sub-intervals on which the function is monotonic, i.e. either increasing or decreasing but not both. Finding the in ages of each sub-interval is a straight-forward task, and then the image of the entire domain is just the union of each sub-interval image. Students are involved in the processes of sketching, finding subintervals, finding images of these and hence the image of the domain by a series of questions posed during the programme. Two different functions are considered, a continuous one, and one which is given by two formulae and hence has a discontinuity within the given domain. In addition, there are notes accompanying the cassette which contain both pre and post programme work and which form an integral part of the package.
Part 1 : Eigenvectors and diagonalisation -- Part 2 : Symmetries of the octahedron -- Part 3 : Images of functions ... Part 1 looks at linear transformation and how changing the basis for R2 it will change the matrix Part 2 looks at the eight faces of this octahedron are congruent isosceles triangles. In other words it's made up of two equal square pyramids. What we're going to do in this video programme is to look at the group of symmetries of this object and to investigate the group's conjugacy classes and its subgroups. Part 3, the final part of the video cassette looks at the problems of finding the image of the domain of functions. It shows how a graphical analysis of the properties of any given function can readily lead to the image set corresponding to the original domain. Having obtained a sketch of the graph within the given domain, it is possiole to identify the maximum, minimum and turning points of the function, and hence to split the domain up into the union of disjoint sub-intervals on which the function is monotonic, i.e. either increasing or decreasing but not both. Finding the in ages of each sub-interval is a straight-forward task, and then the image of the entire domain is just the union of each sub-interval image. Students are involved in the processes of sketching, finding subintervals, finding images of these and hence the image of the domain by a series of questions posed during the programme. Two different functions are considered, a continuous one, and one which is given by two formulae and hence has a discontinuity within the given domain. In addition, there are notes accompanying the cassette which contain both pre and post programme work and which form an integral part of the package.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; SS |
| Recording date: | 1983-07-04: 1983-07-05: 1974-02-28 |
| Recording location: | Milton Keynes |
| First transmission date: | NXT |
| Published: | 1984 |
| Rights Statement: | Rights owned or controlled by The Open University |
| Restrictions on use: | This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all OUDA web pages. |
| Duration: | 00:40:12 |
| + Show more... | |
| Producers: | Jack Koumi; Colin Robinson; Pip Surgey |
| Contributors: | Ian Harrison; Alan Best; Peter strain |
| Keyword(s): | Co-domain; Diagonalisation; Domain; Eigenvectors; Summer school |
| Master spool number: | HAP1997: HOU4533 |
| Production number: | FOUM203J |
| Videofinder number: | 2378 |
| Available to public: | no |
