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5.2 Summary of Section 5

  1. The structural formulae of organic molecules can be divided into the carbon-hydrogen framework or skeleton, and the functional group(s). In the first approximation, the functional groups are the sites where reaction occurs, the framework remaining unreactive.

  2. This approximation works best when the framework consists of saturated carbon atoms.

Author(s): The Open University

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Learning outcomes

After studying this unit you should be able to:

  • create simple models, given a clear statement of the problem;

  • write down the simplifying assumptions that underpin a model;

  • identify the key variables and the parameters of a model;

  • apply the input–output principle to obtain a mathematical model, where appropriate;

  • obtain mathematical relationships between variables, based on or linking back to the simplifying assumption
    Author(s): The Open University

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5.1 Arithmetic with real numbers

At the end of Section 1, we discussed the decimals and asked whether it is possible to add and multiply these numbers to obtain another real number. We now explain how this can be done using the Least Upper Bound Property of Author(s): The Open University

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Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Learning outcomes

After studying this unit you should:

  • be able to solve homogeneous second-order equations;

  • know a general method for constructing solutions to inhomogeneous linear constant-coefficient second-order equations;

  • know about initial and boundary conditions to obtain particular values of constants in the general solution of second-order differential equations.


Author(s): The Open University

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1 Modelling with Fourier series

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 0.6 MB).

1.3 Designing alternative programmes and curricula

Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
Author(s): The Open University

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