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4.1 The rate of evolution

I now want to move away from looking at the challenges facing all aquatic mammals, to examine very briefly what we know about the evolutionary history of the cetaceans. This group has travelled furthest from its terrestrial roots and made the fullest adaptation to life in the sea.

Since mammals evolved on land, it has long seemed reasonable to suggest that the origin of whales must have involved an evolutionary transition from the land to the water. But how can we explain the fact that
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3.2 Natural dives

The physiology of the diving response can be studied in the laboratory, but investigating the behaviour of a diving mammal in its natural environment can be more of a problem. However, modern physiological techniques have made it possible to record continuously physiological variables (such as heart rate) and information on depth and position during the spontaneous dives in the wild that are part of the animal's normal behaviour. Most such findings show that the majority of an animal's dives
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2.7 … and becoming more intelligent

Intelligence is a useful commodity: it can help an animal to make sense of its environment and cope with the demands of social behaviour (including courtship and competition). Hunters tend to be relatively intelligent, and otters, pinnipeds and cetaceans, for example, share a playful curiosity that is characteristic of animals that catch other animals for a living. Some especially extravagant claims have been made for the intelligence of the toothed whales, largely because these animals use c
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Introduction

The versatility of mammals is a central theme of the ‘Studying mammals’ series of units, but surely no environment has tested that versatility as much as the rivers and oceans of the world. Mammals are essentially a terrestrial group of animals, but three major groups have independently adopted an aquatic way of life. In moving to the water, aquatic mammals have had to survive, feed and reproduce using a set of biological characteristics that evolved in association with life on land. This
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Mathematical language
In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this unit we examine ways in which language is adapted to express mathematical ideas. First published on Tue, 28 Jun 2011 as Author(s): Creator not set

Modelling heat transfer

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, 0.4 MB).

Pressing onwards

Activity 15

  1. Work through Sections 1.6 and 1.7 of the Calculator Book, using the method suggested above of glancing ahead-pressing on-glancing back, if you find it useful.

  2. A num
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1 Overview

A fundamental concept in mathematics is that of a function.

Consider, for example, the function f defined by

This is an example of a real function, because it associates with a given real number x the real number 2x2 − 1: it maps real numbers to real n
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Introduction

This unit lays the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit – Modelling static problems – considers why objects stay put.

Please note that this unit assumes you have a good working knowledge of vectors.

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

First-order differential equations

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.

This unit is an adapted extract from the course Mathematical methods and
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Acknowledgements

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


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1.3: Summing vectors given in geometric form

The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

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1.2: Converting to geometric form

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector a = a 1 i + a 2 j, what are its magnitude |a| and direction θ?

The first part of this question is dealt with using Pythagoras’ Theorem: the magnitude of a v
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Acknowledgements

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


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4.3.3 Pipe dreams?

The idea underlying complementary currencies – that there is a great well of social capital waiting to be drawn upon to make society more sustainable – is an idea that is becoming quietly influential. ‘Social capital’ is a term frequently used by those mainstream politicians and civil servants tasked with addressing the widening gap between rich and poor people within societies throughout the world. Indeed, investing in and enhancing social capital is now the starting point in
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Acknowledgements

The material acknowledged below is Proprietary and used under licence, see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following:

Figures

Figur
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1 A climate change icon

The polar bear has become an international climate change icon. But how much is known about this bear, its habitat and life? This unit will talk about the role of language, but by way of introduction how about the name of this bear? To me it is the polar bear; to a German it is an Eisbär (ice bear) and to a French person it is an ours blanc (white bear). In these three examples the bear is referred to as polar, white, or an ice bear – eminently sensible. The Latin name for th
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Introduction

The scientific theory of plate tectonics suggests that at least some of these Arctic lands were once tropical. Since then the continents have moved and ice has changed the landscape. This unit will concentrate on evidence from the last 800,000 years using information collected from ice cores from Greenland and Antarctica, and will use this evidence to discuss current and possible future climate. The cores show that there have been nine periods in the recent past when large areas of the Earth
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6.1 ‘I’, ‘we’ or ‘they’?

We must abandon the conceit that individual, isolated, private actions are the answer. They can and do help. But they will not take us far enough without collective action.

(Al Gore, 2007)

There are some things that we can do as individuals: making this an energy-efficient house and making smart transport choices. Then there a
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5.3 Moving towards a sustainable carbon footprint

So far, you've been considering reductions in average individual or household carbon footprints by 20% to 30% or more.

But it is becoming increasingly clear that this will not be enough. As I mentioned in Section 4, developed countries, like Britain, Germany and America, will have to reduce their CO2e emissions by 60% to 80% or more by 2050 to prevent climate change running out of control, while at the same time allowing the growing populations of Africa, India and China to r
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