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A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including constrained non-linear, linear-programming, least-squares, multi-objective, and global optimization problems.
The new edition of The Cambridge Illustrated History of Warfare, written and updated by a team of nine distinguished military historians, examines how war was waged by Western powers across a sweeping timeframe, beginning with classical Greece and Rome, moving through the Middle Ages and the early modern period, down to the wars of the twenty-first century in Afghanistan, Iraq, and Syria. The book stresses five essential aspects of the Western way of war: a combination of technology, discipline, and an aggressive military tradition with an extraordinary capacity to respond rapidly to challenges and to use capital rather than manpower to win. Although the focus remains on the West, and on the role of violence in its rise, each chapter also examines the military effectiveness of its adversaries and the regions in which the West's military edge has been - and continues to be - challenged.
A basic tenet of our pluriliteracies model is that deeper learning is fundamental for an individual’s learning progression and development. This is not new. However, closer investigation reveals the complex and dynamic nature of the processes involved. Whilst a great deal has been written about deeper learning and its importance for engaging learners ‘through discovering and mastering existing knowledge and then creating new knowledge’, (Fullan & Langworthy, 2014, p. 2), there is little to guide in-depth understanding of the nature of those processes – that is, what it means to master existing knowledge and create new knowledge which can then be ‘translated’ into pedagogic practices to support and ‘grow’ classroom learning. In seeking to understand better the nature of deeper learning and its implications for learning and teaching, two strands have emerged: the mechanics or cognitive-linguistic processes through which deeper learning evolves, and the drivers of and for deeper learning. We define drivers as those factors that promote or inhibit the processes or mechanics of deeper learning, such as student and teacher engagement.
This book is about Britain, and the people who dwelt there, between about 500 and 1000. At this stage Britain was not thought of as the basis of a shared nationality or government: it was an island that contained numerous distinct groups with different languages and ways of life, as well as strong views of their own history and ethnicity. Its population was a small fraction of what it is now, with precious few towns, and most people devoted their time to producing food from land and livestock. Resources and education were distributed very unevenly according to status and gender – and justice, too, was harsh and often slow and imbalanced. By modern standards, early medieval Britain was in many ways a very harsh place. Nonetheless, its people had much to take pride and interest in. They would have seen important changes going on around them as a sequence of new kingdoms took shape, and as Christianity came to be a force at all levels of society. They would have learnt their place in that society, and in the world at large, by swapping stories and poems. At times they would also have seen new immigrants enter their community, or been migrants themselves, or adopted – either bit by bit or by a sudden leap – a whole new identity, taking on new customs and languages in the process. They would have been conscious of several intersecting layers and kinds of belonging, from families and localities upwards to kingdoms and a religious community that spanned the whole continent. All of this is interesting partly because of what it sets up – most obviously, the modern nations of England, Scotland and Wales as cultural and/or political entities – but the early Middle Ages are also interesting in themselves, as an era of possibility and change in Britain without regard for outcomes that lay centuries in the future. This book seeks to show how the latter approach can challenge and enrich the former.
How did people get the things they needed but could not grow or make from their own resources? This chapter examines networks of exchange; that is to say, of people exchanging things among themselves. It surveys first the major kinds of exchange – gift, tribute and purchase – before looking at the means and mechanics of exchange, including money and precious metal. Finally, we will look at the locations of exchange, among which were various forms of towns; the functions of these will be considered, including military and administrative roles as well as trade.
This chapter is framed around a very simple question with many complex answers: how do we know about the early Middle Ages? There are a number of secondary questions that lie behind this one: what don’t we know about the early Middle Ages? How reliable and representative is the material that does survive? What factors have affected the preservation of that information? All of these should be kept in mind when reading the rest of this book, as the sources for this period are often unusual and challenging. Much can depend on short or ambiguous texts. Readers may also notice unaccustomed forms of evidence playing a prominent role: place names, archaeological finds, inscriptions and literary texts all feature.