2.1 Layout As mentioned in the animation in Section 1.2 writing mathematics has a lot in common with writing English. When you write mathematics, you should write in the equivalent of sentences, with full stops at the end. As in English, each new statement should follow on logically from the previous one or it should contain an indication that a new idea is being introduced. However, laying out mathematics differs from laying out English: because mathematics is more condensed than written English
4 Two identities Section 4 introduces some important mathematical theorems. Click the link below to open Section 4 (7 pages, 237KB).
6.3 (b) Switching to renewable energy sources The use of renewable energy usually involves environmental impacts of some kind, but these are normally lower than those of fossil or nuclear sources. Approaches (a) and (b) are essentially 'supply-side' measures – applied at the supply end of the long chain that leads from primary energy production to useful energy consumption.
6.1 Introduction So far, we have briefly introduced three key approaches to improving the sustainability of human energy use in the future. These are: (a) 'cleaning-up' fossil and nuclear technologies; (b) switching to renewable energy sources; (c) using energy more efficiently.
5.1.1 Linking supply and demand But apart from these relatively few enlightened examples, the efficiency with which humanity currently uses its energy sources is generally extremely low. At present, only about one-third of the energy content of the fuel the world uses emerges as 'useful' energy, at the end of the long supply chains we have established to connect our coal and uranium mines, our oil and gas wells, with our energy-related needs for warmth, light, motion, communication, etc. 5.1 Energy services Except in the form of food, no one needs or wants energy as such. That is to say, no one wants to eat coal or uranium, drink oil, breathe natural gas or be directly connected to an electricity supply. What people want is energy services – those services which energy uniquely can provide. Principally, these are: heat, for warming rooms, for washing and for processing materials; lighting, both interior and exterior; motive power, for a myriad of uses from pumping fluids to lifti 4.5 Sustainability of renewable energy sources Renewable energy sources are generally sustainable in the sense that they cannot 'run out' – although, as noted above, both biomass and geothermal energy need wise management if they are to be used sustainably. For all of the other renewables, almost any realistic rate of exploitation by humans would be unlikely to approach their rate of replenishment by nature, though of course the use of all renewables is subject to various practical constraints. Renewable energies are also relative 5.1 Food preservation and the development of refrigeration Most societies have had traditional methods of preserving food: drying, baking, pickling, salting, smoking, the use of sugar, and in cold climates, freezing or chilling, with the use of ice houses in the summer. These techniques were usually carried out at a local level, which meant that most perishable food was consumed near to where it was produced, and any food processing was usually small-scale and localised. Cattle and livestock, for example, were moved 'on the hoof' from their pastures Acknowledgements Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence This free course is adapted from a former Open University course called 'Living in a globalis 2.7 Representing feedback through system dynamics diagrams System dynamics diagrams, also sometimes called ‘stock flow’ diagrams, can be derived from causal diagrams, although in some cases it might be easier to start directly with the system dynamics diagramming technique, especially if you need to explore around one particular object’s attribute, such as population number. System dynamics diagrams are drawn using four symbols: boxes representing attributes or ‘stocks’ of objects (e.g. level of water in a tank); valves representing Conclusion This free course provided an introduction to studying Environment & Development. It took you through a series of exercises designed to develop your approach to study and Author(s): Learning outcomes After studying this course, you should be able to: practise a very basic implementation of cybernetic optimisation through the use of the Author(s): 3.3 Thermal stresses When the temperature of an object increases (say, by ΔT) it expands. According to the linear model of thermal expansion the length increase is described by What if there is a temperature change, but some constraint prevents the proper thermal size Acknowledgements The following material is Proprietary and is used under licence: Course image: The Cookiemonster in Flickr made available under Creative Commons Attribution-NonCommercial 2.0 Licence. Stage 1: The problem situation unstructured The approach begins with a situation in which one or more people perceive that there is a problem. It will not be possible to define the problem or its setting with any precision and, in any event, the different people involved will have different ideas. Acknowledgements Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence Grateful acknowledgement is made to the following sources for permission to reproduce 6.5 Appreciating some implications for practice I think for most people, the National Health Service would be experienced as a complex situation. If so this would be a good example of perceived complexity. Remember though, if you engaged with it as if it were a difficulty you would not describe the situation as one of perceived complexity. I could not call it a complex system unless I had tried to make sense of it using systems thinking and found, or formulated, a system of interest within it. This means I would have to have a stake in the 6.2 Natural frequency of free oscillations Most of us have a fairly accurate understanding of what is meant by resonance – it's what causes a bell to continue to make a sound long after it has been struck. Yet this is just one example of resonance, a phenomenon that occurs in nature in a surprisingly large number of places. It is all to do with the reversible transfer of energy from one form to another in a system. The common feature associated with mechanical systems that are able to store energy by oscillating is that they h 4.5.1 Mathematical models Computers in the last few decades have, in many cases, made mathematical modelling a lot easier. Models that used to require hours of manual cranking through long equations can now be created on a screen using specialist software. Processes can be recreated – modelled – in the time it takes to press a few buttons. For example, when designing a pipe network to carry a gas or fluid, such as in the village water supply problem, you might wish to know how the flow would be distributed w Conclusion This free course provided an introduction to studying Engineering. It took you through a series of exercises designed to develop your approach to study and learning at a distance, and helped to improve your confidence as an independent learner.
