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Introduction

This unit lays the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit – Modelling static problems – considers why objects stay put.

Please note that this unit assumes you have a good working knowledge of vectors.

This is an adapted extract from the Open University course Author(s): The Open University

Introduction

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

This unit is an adapted extract from the course Mathematical methods and models (MST209
Author(s): The Open University

1.3: Summing vectors given in geometric form

The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

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Acknowledgements

All materials included in this unit are derived from content originated at the Open University.


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Introduction

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

This unit is from our archive and is an adapted extract from Teaching mathematical thinking at Key Stage 3 (ME624) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other cour
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1.3.9 Summary

There is a lot of information available on maths and statistics via the internet. Try the activities below to start exploring what is available.

Activity

1.3.4 Databases

At a basic level, a database is a collection of information which can be searched. It is a way of storing, indexing, organising and retrieving information. You may have created one yourself to keep track of your references – or your friends' names and addresses. They are useful for finding articles on a topic, and can be used to search for many different types of information.

You may find some of the following databases useful for your topic. They contain different types of informatio
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1.3.3 Books and electronic books

Books are a good source of information. The publishing process (where a book is checked by an editor before publishing, and often reviewed by another author) means that books are reliable sources of information, although they may need to be evaluated for bias. A growing number of books can be found online.

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1.2.1 Planning your search

Your approach to searching will depend to a great extent on what kind of person you are. In an ideal world, when searching for information for a specific purpose, we would all find what exactly we were looking for at the first attempt, especially if we are in a hurry. However, it’s always a good idea to have some kind of plan when you are searching for information, if only to help you plan your time and make sure you find the information you need. If I was starting to search for material on
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1.1.4 Evaluating information

How well does the following statement describe your approach to evaluating the information that you use?

When I come across a new piece of information (e.g. a website, newspaper article) I consider the quality of the information, and based on that I decide whether or not to use it.

  • 5 – This is an excellent match; this is exactly what I do


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5 Conclusion – new ways of looking at the world

There is a variety of new approaches or terms that are interlinked, and have been prominent throughout this book. All of them have played a part in this book's journey through the scientific, political, philosophical and social implications of climate change.

Governance of climate change is about: decision making under uncertainty; understanding and representing vulnerability even when vulnerabilities are difficult to assess or unknowable; and making every aspect of human
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3.3.3 Obligations to trees?

Citizenship is generally held to be based on a contractual view, where rights and obligations are balanced. In other words, you get various rights in return for your commitment to live by your society's rules and expectations. Political philosopher Andrew Dobson suggests that ecological citizenship is based in a non-reciprocal sense of justice or compassion. The discussion of our relationships with past and future generations in Section 5.2 establishes that our obligations to future generatio
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3.1 Who will make the decisions?

Where will the decisions be made that will result in meaningful action on climate change, and who will make them stick? Following climate change politics in the media can give the impression that most of the action on climate change is going on between national decision makers in international forums. It is important to keep in mind that these forums have resulted from persistent pressure from a combination of grassroots environmental activists and a global network of science and policy exper
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Summary

In this part I have presented evidence showing that even apparently remote regions of our planet are intimately connected through physical processes. For example, once an organic POP is transported to the poles, then biological processes can take over and through bioaccumulation perhaps cause harm. But this physical connection has allowed the ice to preserve unique proxy records of the past climate of our planet. Directly measuring the gases trapped in the ice has enabled histories of past at
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Introduction

The scientific theory of plate tectonics suggests that at least some of these Arctic lands were once tropical. Since then the continents have moved and ice has changed the landscape. This unit will concentrate on evidence from the last 800,000 years using information collected from ice cores from Greenland and Antarctica, and will use this evidence to discuss current and possible future climate. The cores show that there have been nine periods in the recent past when large areas of the Earth
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References

Baggott, S. L., Cardenas, L., Garnett, E., Jackson, J., Mobbs, D. C., Murrells, T., Passant, N., Thomson, A. and Watterson, J. D. (2007) UK Greenhouse Gas Inventory, 1990 to 2005, Harwell, Oxfordshire, AEA Technology.
Brower, M. and Leon, W. (1999) The Consumer's Guide to Effective Environmental Choices, New York, Three Rivers Press.
Cabinet Office (2007) Po
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4.2 Carbon reduction targets

Let's now look at carbon footprint reduction targets in a bit more detail.

The first international agreement to set carbon reduction targets was the 1997 United Nations Kyoto Protocol, which requires developed countries to reduce their human-generated greenhouse gas emissions by an average of just over 5% on 1990 levels by 2008 to 2012. By the time the treaty came into force in 2005, only the USA and Australia had refused to sign. (A new Australian government finally signe
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2.3.2 Total carbon footprints

Of course, the picture changes when you consider total CO2 emissions for different countries rather than emissions per person. Figure 8(b) is another chart that shows that America was by far the greatest total emitter of CO2 in 2002, but, owing to their huge population
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2.2 The carbon footprint of UK individuals and households

The simplest way of calculating the average (mean) carbon footprint of an individual living in the UK can be obtained by dividing total UK annual CO2 emissions by the number of people in the country. Using the official government information in Figure 3(a), this produces a mean footprint
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Introduction

This unit focuses on the problem of greenhouse gas emissions, especially carbon dioxide, and explore what you can do to lighten those emissions to help reduce the rate of climate change. You will assess your ‘carbon footprint’ and see what actions you and, if relevant, other household members could take to lighten that footprint. You will also better understand which actions are more and less effective, and the scope and limits of what individuals can do at the personal and household leve
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