Available online
Description
This summer school film, comprising animation and models, is presented in five sections. Each section assumes that ideas have been introduced by a tutor. The film provides a visual introduction and... insight into the problems the students most solve with the help of the tutor.
This summer school film, comprising animation and models, is presented in five sections. Each section assumes that ideas have been introduced by a tutor. The film provides a visual introduction and... insight into the problems the students most solve with the help of the tutor.
| Module code and title: | M101, Mathematics: a foundation course |
|---|---|
| Item code: | M101; SS |
| First transmission date: | 1978 |
| Published: | 1978 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:33:03 |
| + Show more... | |
| Producer: | John Richmond |
| Contributor: | Graham Read |
| Publisher: | BBC Open University |
| Keyword(s): | Area; Integral; Segments; Summation; Volume |
| Footage description: | This summer school film is designed as a major component of a half-day tutorial exercise for students at the Mathematics Foundation Course summer school. The film, comprising animation and models, is presented in five sections. Each section assumes that ideas have been introduced by a tutor. The film provides a visual introduction and insight into the problems. Each sequence ends by posing the problems the students must solve with the help of the tutor. Section 1. This poses the problem of the volume of water contained in a cylinder tilted at an angle of 30°. Solid model animation introduces the idea of calculating the volume by slicing it up and adding the volumes of the segments. With thinner slices the summation could be achieved by evaluating an integral. A second model shows an alternative way of cutting up the volume. The question remains - which method will lead to the simplest integral? To start the film poses two specific problems to highlight the difference between areas and integrals. Section 2. This starts with a graphical model of finding the area between two curves. It demonstrates two ways of cutting up this area and selects vertical cuts to start with. It introduces five steps to the solution: First sketch the graphs, then Select a method of cutting up the area. Select a rectangle for the summation. The limits for integration must be found. The integral must then be evaluated. Section 3. This section explores cutting the area into horizontal strips. A visual argument is used to establish an alternative approach. The student is left to compare the two methods - horizontal and vertical strips for the example posed in section 2. Section 4. This introduces the theme of volumes. A solid animation of a cone is used to establish that volumes of revolution can be found by cutting them into circular discs. The general form (...) is introduced and various volumes of revolution depicted. The section finishes by setting the student a problem of the volume formed by rotating the area between two curves around the axis. Section 5. This returns to the problem of cutting up volumes so that an integral can be used to calculate it. The example chosen is to find the volume of intersection of two equal circular cylinders. Solid models depict the volume in question and then slices are taken to provide hints for the student how to proceed. The calculations of the volume are left for the remainder of the tutorial. |
| Production number: | FOUM051Y |
| Available to public: | no |
