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2.2 Breathing air

A swimming elephant can breathe by holding the end of its trunk out of the water, but if it tried to find its food under the surface, like the desman, it would have to hold its breath. Neither the mammalian lung nor the skin can extract enough oxygen from water to sustain life, so aquatic mammals must come to the surface at intervals to breathe; and all of them – pinnipeds, sirenians and cetaceans – drown if they are prevented from doing so for prolonged periods.

Lungs form 7% of th
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6.3 Valence-shell electron-pair repulsion theory

The theory of molecular shape that we have been working towards is called valence-shell electron-pair repulsion theory (VSEPR theory). When applied to molecules and ions of the typical elements, its success rate is high. Here is a stepwise procedure that you can follow when applying this theory. It is illustrated with the molecule XeF4 and the ion C1O3. Xenon tetrafluoride is one of the select band of noble gas compounds that were unknown before 1962
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6.1 Introduction

Structural formulae of, for example, hexan-1-ol (Structure 6.1) and PF5 (Structure 5.13) merely tell us the immediate neighbours of any particular atom. They are two-dimensional drawings, which ignore the three-dimensional shapes of the molecules. But in studying the structures obtained by X-ray crystallography in Sectio
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3.4 Outer electronic configurations and the Periodic Table

The essential message of Figure 22 is that the Groups of elements that appear in columns of the Periodic Table usually have atoms with similar outer electronic configurations. Figure 23 incorporates these configurations into our mini-Periodic Table of typical elements; they appear at the top of each Group. They imply that the typi
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3.3 Electronic configurations and the Periodic Table

Figure 21 has been designed for use in a particular thought experiment. The purpose of the thought experiment is to see how the electronic configuration of the atoms changes as one moves through the Periodic Table from beginning to end. We start with the hydrogen atom, which has one proton and one electron. Then we
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3.2 The electronic configurations of atoms

The quantum theory of the atom tells us that we cannot say exactly where an electron in an atom will be at any particular moment; we can speak only of the probability of finding an electron at a particular point. So the precise orbits shown in the Rutherford model of Figure 1 misrepresent the arrangement of electrons about
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4.4 Further exercises

Exercise 29

In this exercise, take

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4.4 Self-assessment questions and problems

SAQ 25

Find the distance between the numbers 2 − i and 1 + 3i.

Answer

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1.2.1 Try some yourself

1 Without using your calculator, find the following:

  • (a) 102

  • (b) 1002

  • (c) 0.12

  • (d) 0.012

  • (e)
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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
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1.5 Exercises

Exercise 1

A vector a has magnitude |a| = 7 and direction θ = −70°. Calculate the component form of a, giving the components correct to two decimal places.

<
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Learning outcomes

After studying this unit you should:

  • be able to perform basic algebraic manipulation with complex numbers;

  • understand the geometric interpretation of complex numbers;

  • know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.


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Introduction

This unit is an adapted extract from the Open University course Complex analysis (M337)

This unit is devoted solely to complex numbers.

In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.

Section 2 is devoted to the geometric representation of complex numbers. You will find that
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1.3.5 Journals

Journals and articles written by academics or experts are an excellent source of information. Journals are usually published monthly or quarterly, and contain a selection of articles providing details of recent research. Often they will also contain reviews of relevant books. They are usually published more quickly than books, and so are often more up to date.

To access content of journals, most publishers require a subscription. There are, however, some journals which you can freely ac
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1.1.3 Searching for information on maths and statistics

How well does the following statement match what you do when you begin a new search for information?

Before I begin a new search for information (maybe for an assignment, or to help you choose your next holiday destination), I spend some time thinking about what I already know, what the gaps in my knowledge are, and the best types of information to meet my needs.

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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
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6.3 The role of active citizens and communities

Few people agree that individuals should take the main responsibility for tackling environmental issues. For example, in a 2007 poll of over 2000 UK citizens, 70% agreed that the government should take a lead in combating climate change, even if it means using the law to change people's behaviour. However, over 60% disagreed that there was nothing they could do to avert climate change and over half agreed that they would do more if others did more too, although 40% thought that recycling was
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1.1.1 Carbon dioxide and other greenhouse gases

Carbon dioxide (CO2) is used as the basis for the carbon footprint because it is by far the main contributor to the enhanced greenhouse effect from human activity (mainly burning fossil fuels, clearing forests and making cement). So, often only CO2 is counted in the carbon footprint. However, for a more complete measure of the carbon footprint the other human-generated greenhouse gases are converted into a CO2 equivalent (in kilograms or tonnes CO2e
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1.1 What is the carbon footprint and why is it important?

The carbon footprint is the annual amount of greenhouse gas emissions, mainly carbon dioxide, that result from the activities of an individual or a group of people, especially their use of energy and transport and consumption of goods and services. It's measured as the mass, in kilograms or tonnes per year, either of carbon dioxide (CO2) emissions alone, or of the carbon dioxide equivalent (CO2e) effect of other greenhouse gas emissions.


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2.6.2 The role of modelling studies

State-of-the-art models are designed to simulate the workings of the climate system (in so far as this is currently understood), and include the ‘internal’ interactions that generate short-term natural variability in the real world. They provide modellers with a means of carrying out ‘virtual’ experiments on the climate system. In the present context, an important aim of these experiments is to identify the ‘signal’ of a human influence on climate, so studies typically involve ‘
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