2.3 Inequalities involving modulus signs Now we consider inequalities involving the modulus of a real number. Recall that if a
, then its modulus, or abso
1.1 Mathematics and you Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood. Read 6 Curves from parameters In Section 5 we show how functions may be used to sketch curves in the plane, even when these curves are not necessarily the graphs of functions. Click 'View document' below to open Section 5 (8 pages, 151KB). 3.1 Expressing numbers in scientific notation Earlier you looked at place values for numbers, and why they were called powers of ten. 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 1 First-order differential equations 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, 1.6 MB). 1.2.2 Content School mathematics curricula often focus on lists of content objectives in areas like number, arithmetic, statistics, measurement, geometry, trigonometry, and algebra. A typical list of content objectives might contain over one hundred objectives to be introduced or revisited and learned each year. These can be seen as hierarchical in nature but many textbooks do not attempt to organise the objectives in ways that enable the bigger underpinning ideas to become apparent to the pupils. In addit 4.2.3 Business needs sustainability The second argument is more profound: long-term profitability, and the existence of business itself, is threatened if companies can't transform themselves. This assumes that although the costs of environmental and social impacts can be ignored for a period, in the context of globalisation of environmental, social and political processes, they will come back to haunt businesses, and ultimately threaten their survival. There are several communications and management tools that have been develop 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 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 Learning outcomes By the end of this unit you should be able to: appreciate how chemical processes in the rest of the world affect the Arctic environment and the species inhabiting it; recognise the physical processes that determine atmosphere and oceanic flows in the Arctic; appreciate the scientific research process and the use of scientific evidence; use quantitative scientific evidence to examine the link between atmospheric carbon dioxide levels a 2.6 An evolving consensus on attribution The fact that the Earth really is warming up now commands near-universal support. However, it is one thing to detect a global warming trend that appears to be unprecedented in the past millennium (Subsection 2.2.2), and quite another to establish with a given level of confidence that it has been caused by (i.e. can be attributed to) human activity – specifically, the increase in greenhouse gas concentrations and associated radiative forcing since pre-industrial times (reviewed in Sec 2.2.2 Temperature changes over the past millennium One of the most striking images in the IPCC TAR is reproduced (in adapted form) in Figure 24. Together, these two temperature records tell a compelling story, crystallised in our earlier quotes from the SPM. So let's just pause to take a closer look at each of them. 1.4 An overview of the global energy budget 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 References 1.3.4 Bringing remote sweatshops within reach continued Another claim made by the movement is that we are all in some way connected to a market system which effectively allows sweatshops to exist in the first place. This is about more than targeting the big brand names and linking them directly to exploitation abroad; rather, it is about piecing together the global market machinery that ties the corporate buyer, the boardroom executive, the factory owner and the consumer into a system which establishes particular lines of responsibility (Ha Learning outcomes On completion of this unit you should be able to: explain the main characteristics of ‘sweatshops’, and their presence in today's system of globalised production; set out the arguments for and against overseas sweatshop exploitation; consider how far the consumption of cheap branded goods makes consumers responsible for the conditions under which they are made; show how consumers are distanced from overseas sweatshop exploitation, 2.4.2 Ecological restoration The changing science of ecology, coupled with a greater awareness and development of alternative styles of managing natural resources, continues to influence our notion of what is good and what is right for nature. One of the first and most influential formal expressions of an environmental ethic that arose from early organic and ecosystems models of ecology was that of Aldo Leopold. Leopold’s argument is regarded as an environmental ethic because it explicitly gives moral consideration to, 1 Natural climate change? The chart below shows a record of the global mean surface temperature of the Earth compiled for the past 140 years. Clearly there is an upward trend, but what does a chart like this really show? Learning outcomes The learning outcomes for this unit are to: Develop an understanding of the current evidence for global warming. Model and apply the techniques of ‘measuring’ the Earth's temperature. Understand the current warming in relation to climate changes throughout the Earth's history. Explain factors forcing climate change, and the extent of anthropogenic influence. Assess the ‘best predictions’ of current climate model
Activity 1 Carl Jung's school days
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