Experiments or surveys usually generate a lot of information from which it is possible to draw conclusions. Such information is called data. Data are often presented in newspapers or books.

One convenient way to present data is in a table. For instance, the nutrition panel on the back of a food packet:

### Nutrition Information

Author(s): The Open University

This unit is an adapted extract from the course Mathematical methods and models (MST209)

This unit lays the foundations of Newtonian mechanics and in particular the procedure for solving dynamics problems. The prerequisite skills needed for this unit are the ability to solve first- and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

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

Author(s): The Open University

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

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

The content acknowledged below is Proprietary (see terms and conditions) and is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

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

Author(s): The Open University

## Exercise 1

A vector a has magnitude |a|Â =Â 7 and direction Î¸Â =Â âˆ’70Â°. Calculate the component form of a, giving the components correct to two decimal places.

<
Author(s): The Open University

In the following subsections, we apply the vector ideas introduced so far to displacements and velocities. The examples will feature directions referred to points of the compass, known as bearings.

The direction of Leeds relative to Bristol can be described as â€˜15Â° to the East of due Northâ€™, or NÂ 15Â°Â E. This is an instance of a bearing. Directions on the ground are typically given like this, in terms of the directions NorthÂ (N), SouthÂ (S), EastÂ (E)
Author(s): The Open University

On completion of this unit you should be able to:

• convert a vector from geometric form (in terms of magnitude and direction) to component form;

• convert a vector from component form to geometric form;

• understand the use of bearings to describe direction;

• understand the difference between velocity and speed;

• find resultant displacements and velocities in geometric form, via the use of components.

Author(s): The Open University

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in SectionÂ 2, in which you will also work with bearings.

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

You will come to this unit with many memories of mathematics, both as a teacher and a learner. It may help if you start by recalling memories of learning mathematics and making a record of them in your notebook.

When you work on a task, get into the habit of having your notebook to hand to record your thinking. Use the notebook in any way that helps you to think about the work you have done. Some people find it helpful to divide a page into two columns using the left-hand side to record
Author(s): The Open University

Sustainable development emerged as a prominent environmental policy discourse at a time of deep introspection in policy communities. In the 1970s and early 1980s it was widely felt that something was badly wrong with the political process. Commentators from both left and right argued that nation states were losing the authority to govern and the capacity to act effectively. Expressions such as â€˜ungovernabilityâ€™, â€˜legitimation crisisâ€™ and â€˜crisis of the welfare stateâ€™ were coined t
Author(s): The Open University

Figure 36 (again adapted from the TAR) takes your thoughts on Question 11 on a stage. It gives estimates of the cumulative effect since pre-industrial times of the various climate change agents, with the contributions expressed in terms of radiative forcing. Note that the figure also includes yet another device for communicating the IPCC's confidence in a particular finding â€“ an indication of the â€˜level of scientific understandingâ€™ that accompanies each estimate. This reflects the autho
Author(s): The Open University

## Question 5

Since its first major report in 1990, the IPCC has used the concept of â€˜radiative forcingâ€™ as a simple measure of the importance of a potential climate change mechanism. The basic idea is straightforward. Any factor that disturbs the radiation balance at the top of the atmosphere has the potential to â€˜forceâ€™ the global climate to change: it will either warm up or cool down until a balance is restored. The perturbation to the energy balance of the whole Earth-atmosphere system i
Author(s): The Open University

Figure 12 incorporates the additional factors considered in Section 1.3, including the non-radiative energy transfers across the surface-air boundary (green arrow). Essentially a more detailed version of Figure 7, this figure gives quantified estimates of the globally averaged energy budget for the whole Earth-atmosphere system, and its component parts. Question 3 should help you to find your way around Figure 12, and to draw together many of the key points developed so far in this chapter. M
Author(s): The Open University

We come now to our final refinement to the simple picture in Figure 7. Recall that the troposphere is heated from below, with temperature then falling with increasing altitude. This situation sets the scene for the onset of convection â€“ the bulk flow or circulation of a fluid driven by differences in temperature. Convection in the atmosphere plays a vital role in two further mechanisms â€“ quite apart from the emission of longwave radiation â€“ whereby energy is transferred from the
Author(s): The Open University

The atmosphere is not a simple, uniform slab of absorbing material. On the contrary, it gets progressively â€˜thinnerâ€™ or less dense with increasing altitude (height above mean sea level); i.e. the total number of molecules in a given volume of air is lower, and so is the pressure. About 80% of the total mass of the atmosphere is within some 10 km of the surface; 99.9% lies below 50 km.

The important corollary is that the key greenhouse gas molecules (H2O and CO
Author(s): The Open University

As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial rays, produces a local heightening of the temperature at the Earth's surface.

(Tyndall, 1862, quoted in Weart, 2004)

Thus, writing in 1862, John Tyndall (Figure 6) described the key to our modern understanding of why the Earth's surface is so much warmer than t
Author(s): The Open University

As I mentioned in Section 2, what was happening in the factories of overseas contractors was said to have appeared remote to most, if not all, the chief executive officers of the clothing multinationals in the 1980s. Overseas contractors were selected on the basis of market price, quality and reliability, not on whether forced or child labour happened to be employed to stitch the product together. However, all that changed in the early 1990s when the geographical ties between the big retailer
Author(s): The Open University

• The shift of the world's manufacturing base from developed to developing economies in the 1970s heralded the beginning of a new global division of labour and the rise of global factories to produce for Western markets. The search for ever-cheaper labour sources undertaken by multinational firms established a new geography of low-cost manufacturing operations which, to this day, remains controversial.

• The rise of subcontracting as the most flex
Author(s): The Open University