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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 Section 2, in which you will also work with bearings.

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This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers.

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This unit is the third in the MSXR209 series of five units on mathematical modellng. It provides an overview of the processes involved in developing models, starting by explaining how to specify the purpose of the model. It then moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models. This unit assumes that you have previously studied Modelling pollution in the Great Lakes (MSXR209_1) and Analysing skid marks (MSXR209_2).

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This unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will also look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You wil also look at the important statistical and mathematical ideas that contribute to the construction of a price index.

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Scientific calculators are a wonderful invention, but they're only as good as the people who use them. If you often get an unexpected – or ridiculous – result when you press the ‘enter’ button, this unit is for you. Learn how to do a calculation correctly and get the right answer every time.

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Diagrams, charts and graphs are used by all sorts of people to express information in a visual way, whether it's in a report by a colleague or a plan from your interior designer. This unit will teach you how to interpret these tools and how to use them yourself to convey information more effectively.

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Observation, measurement and the recording of data are central activities in science. Speculation and the development of new theories are crucial as well, but ultimately the predictions resulting from those theories have to be tested against what actually happens and this can only be done by making further measurements. Whether measurements are made using simple instruments such as rulers and thermometers, or involve sophisticated devices such as electron microscopes or lasers, there are decisions to be made about how the results are to be represented, what units of measurements will be used and the precision to which the measurements will be made. In this unit we will consider these points in turn.

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Some of the most unusual and versatile of all the mammals are the groups that live, feed and reproduce underwater. In this unit we will see how these formerly land-based mammals adapted to a return to the water, discussing such challenges as breathing, movement and communication. This is the seventh unit in the ‘Studying mammals’ series.

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Jupiter has long been an object of wonder, with its dramatic Great Red Spot, its numerous and varied satellites and the stunning collision of the comet Shoemaker Levy 9 with the Jovian atmosphere in 1994. This unit will introduce you to our solar system's largest planet and its major satellites and the history of their exploration.

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The extreme challenges of life in the polar regions require the animals who make their habitat there to make many adaptations. This unit explores the polar climate and how animals like reindeer, polar bears, penguins, sea life and even humans manage to survive there. It looks at the adaptations to physiological proceses, the environmental effects on diet, activity and fecundity, and contrasts the strategies of aquatic and land-based animals in surviving in this extreme habitat. This unit builds on and develops ideas from two other 'Animals at the extreme' units: The desert environment (S324_1) and Hibernation and torpor (S324_2).

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The search for new medicinal products is one of the major driving forces behind the development and application of new synthetic methods. This unit focuses on a specific case study, which follows the development of a drug for the treatment of high blood pressure. It is a particularly good example of the application of organic chemistry in the pharmaceutical industry, and illustrates the scientific processes that are involved in the development of any new drug.

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Active galaxies provide a prime example of high energy processes operating in the Universe. This unit gives an overview of active galaxies, including the supermassive black holes that power the engines at their centres, and the emission processes by which we detect and study them. It also gives practice in mathematical techniques for analysing data and theoretical models.

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There are a wide range of interactions between ‘science’ and ‘the public’. Examples range from visiting a museum, or indulging in a science-related hobby, to reading a newspaper article about a breakthrough in the techniques of therapeutic cloning. Many of these interactions could be said to be ‘passive’. This unit explores the practicalities of the public becoming more ‘active’ in the direction of science practice by ‘two-way’ interactions, with dialogue taking place between science and some part of ‘the public’,

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X-rays, CT scans and MRI scans are all medical imaging techniques of great practical importance that have been encountered by a great many people in their medical histories. This unit illustrates how these techniques work – and their limitations and advantages.

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How do we become individuals? This unit looks at how genes and the environment interact making each of us unique. Looking at the period between conception and birth you will examine the issues of nature or nurture to see which has the greatest impact.

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This unit looks at two topics that are of immense worldwide social, economic, ethical, and political importance – ‘addiction’ and ‘neural ageing’. You will develop a Master's level approach to the study of specific issues within these two important subject areas.

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What impact does alcohol have on the body? From a ‘hangover’ to cirrhosis this unit looks at the harmful effects of alcohol both in the short and long term.

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Your heart beats around 100,000 times every day and, in that time, pumps about 23,000 litres of blood around your body. But what happens when it doesn’t work as well as it should? This unit explains what happens in cardiovascular disease, when the heart’s performance is affected, how the normal function of blood vessels is impaired, and what treatments are available. Whether you are a patient, relative, friend or healthcare professional, you will find the unit interesting.

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Both vitamins and minerals are essential in the diet in small quantities.The term ‘vitamin’ was not coined until early in the 20th century, to describe those chemicals in food without which a pattern of deficiency symptoms (often called a deficiency syndrome) occurs. Minerals, also called mineral elements, are those elements other than carbon, hydrogen, oxygen and nitrogen that are found in the body. This unit looks at the two main groups of vitamins: the fat-soluble vitamins A, D, E and K, and the water-soluble vitamins, those of the B group and vitamin C. It also examines the major mineral elements, and the importance of fluid balance in the body.

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Genomes are composed of DNA, and a knowledge of the structure of DNA is essential to understand how it can function as hereditary material. DNA is remarkable, breathtakingly simple in its structure yet capable of directing all the living processes in a cell, the production of new cells and the development of a fertilized egg to an individual adult. DNA has three key properties: it is relatively stable; its structure suggests an obvious way in which the molecule can be duplicated, or replicated; and it carries a store of vital information that is used in the cell to produce proteins. The first two properties of DNA are analysed in this unit.

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This unit explores how information contained in DNA is used, explaining the flow of information from DNA to RNA to protein. Also introduced are the concepts of transcription (as occurs between DNA and RNA) and translation.

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Have you ever wondered how scientists analyse the environment? This unit introduces you to the techniques used by science students at residential schools. You will learn how to determine where rocks have come from and how they were made. You will also examine the processes involved in determining the ecology of a particular area.

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Some of Britain’s most dramatic scenery is to be found in the Scottish Highlands. The sight of mighty Ben Nevis, the desolate plateau of the Cairngorms, or the imposing landscapes of Glen Coe can unleash the call of the wild in all of us. Although these landforms were largely carved by glacial activity that ended some 10,000 years ago, the rocks themselves tell of a much older history. The Highlands are merely eroded stumps of a much higher range of ancient mountains. This unit is an account of the origin and demise of that ancient mountain range, based on the geological evidence laid before us in rock exposures.

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How are designs turned into products? What resources, materials and methods used and what set of activities that goes under the heading of ‘manufacturing’ ? This unit will introduce manufacturing as a system and will describe some of the many different ways of making products. We will illustrate how the required properties of the materials in a product influence the choice of manufacturing process used.

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Online shopping – think of it as a shopping centre in cyberspace, with online auctions as the car-boot sale in the car park. This unit will help you understand how to use online shopping sites, how to ensure that you are using the best sites and the best ways to protect your security.