This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.
This volume provides a synthetic review of the background and archaeology that has emerged through archaeological interventions associated with the quarrying of sand, gravel, and rock for aggregates. The book covers all periods from the Lower Palaeolithic to Medieval, and is organized on a regional basis. The review, which also contains as yet unpublished data, shows how the variety and preservation of archaeology can greatly expand our understanding of the relationships of humans to their changing environments.
This book recognises the organisational, professional and emotional challenges of social care training, and provides a theoretical framework for training and professional development.
The family history and genealogy of the Foley family from the late 1500s. The book also deals with those families associated with the Foleys, e.g. Minshull, Barlow, Downe, and Freer. It gives fascinating insights into the notable historical events of the times, many of which involved these families directly.
The latest in the 'River' series, chronicling England's biggest river, the Trent, as it flows through the industrial heartland of England. Stunning photography paired with historic anecdotes of the river's past uses and features make for a fascinating read on the 'wandering invader'.
A contemporary reflection on current practice, this book gets to the heart of what 'youth work' is about. It provides an in-depth overview and analysis of practice,addressing the many experiences of working with young people through insightful chapters written by practitioners themselves.
Social Working provides a framework for thinking about the daily (and not so daily) experiences of being a social worker. Each chapter of the book focuses on a key process including organising the daily round; keeping records; policing clients, counselling; educating; advising and advocating; living alongside; supervision of staff and teamworking.
From the peat bogs and woodlands that help to secure our water supply, to the bees and soils that produce most of the food we eat, Britain is rich in 'natural capital'. Yet we take supplies of clean water and secure food for granted, rarely considering the free work nature does for Britain. In fact for years we have damaged the systems that sustain us under the illusion that we are keeping prices down, through intensive farming, drainage of bogs, clearing forests and turning rivers into canals. As Tony Juniper's new analysis shows, however, the ways in which we meet our needs often doesn't make economic sense. Through vivid first hand accounts and inspirational examples of how the damage is being repaired, Juniper takes readers on a journey to a different Britain from the one many assume we inhabit, not a country where nature is worthless or an impediment to progress, but the real Britain, the one where we are supported by nature, wildlife and natural systems at almost every turn.
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
A set of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area. Detailed proofs of key results are provided. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians.
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