Mathematical Modelling. A Graduate Textbook

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. « . . . [a] treasure house of material for students and teachers alike . . . can be dipped into regularly for inspiration and ideas. It deserves to become a classic.» —London Times Higher Education Supplement «The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking.» —SIAM Review «Each chapter discusses a wealth of examples ranging from old standards . . . to novelty . . . each model is developed critically, analyzed critically, and assessed critically.» —Mathematical Reviews A Concrete Approach to Mathematical Modelling provides in-depth and systematic coverage of the art and science of mathematical modelling. Dr. Mesterton-Gibbons shows how the modelling process works and includes fascinating examples from virtually every realm of human, machine, natural, and cosmic activity. Various models are found throughout the book, including how to determine how fast cars drive through a tunnel, how many workers industry should employ, the length of a supermarket checkout line, and more. With detailed explanations, exercises, and examples demonstrating real-life applications in diverse fields, this book is the ultimate guide for students and professionals in the social sciences, life sciences, engineering, statistics, economics, politics, business and management sciences, and every other discipline in which mathematical modelling plays a role.

This up-to-date textbook on mathematical methods of physics is designed for a one-semester graduate or two-semester advanced undergraduate course. The formal methods are supplemented by applications that use MATHEMATICA to perform both symbolic and numerical calculations. The book is written by a physicist lecturer who knows the difficulties involved in applying mathematics to real problems. As many as 40 exercises are included at the end of each chapter. A student CD includes a basic introduction to MATHEMATICA, notebook files for each chapter, and solutions to selected exercises. * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Geo-mathematical modelling: models from complexity science Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London Mathematical and computer models for a complexity science tool kit Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models. In this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to ‘emerge’, and hence the current notion of ‘emergent behaviour’. The range of models demonstrated include account-based models and biproportional fitting, structural dynamics, space-time statistical analysis, real-time response models, Lotka-Volterra models representing ‘war’, agent-based models, epidemiology and reaction-diffusion approaches, game theory, network models and finally, integrated models. Geo-mathematical modelling: Presents mathematical models with spatial dimensions. Provides representations of path dependence and phase changes. Illustrates complexity science using models of trade, migration, security and development aid. Demonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations This book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students.

As a consequence of recent increased awareness of the social and political dimensions of climate, many non-specialists discover a need for information about the variety of available climate models. A Climate Modelling Primer, Third Edition explains the basis and mechanisms of all types of current physically-based climate models. A thoroughly revised and updated edition, this book assists the reader in understanding the complexities and applicabilities of today’s wide range of climate models. Topics covered include the latest techniques for modelling the coupled biosphere-ocean-atmosphere system, information on current practical aspects of climate modelling and ways to evaluate and exploit the results, discussion of Earth System Models of Intermediate Complexity (EMICs), and interactive exercises based on Energy Balance Model (EBM) and the Daisyworld model. Source codes and results from a range of model types allows readers to make their own climate simulations and to view the results of the latest high resolution models. The accompanying CD contains: A suite of resources for those wishing to learn more about climate modelling. A range of model visualisations. Data from climate models for use in the classroom. Windows and Macintosh programs for an Energy Balance Model. Selected figures from the book for inclusion in presentations and lectures. Suitable for 3rd/4th year undergraduates taking courses in climate modelling, economic forecasting, computer science, environmental science, geography and oceanography. Also of relevance to researchers and professionals working in related disciplines with climate models or who need accessible technical background to climate modelling predictions.

Newly revised and updated, A Textbook of Neuroanatomy, Second Edition is a concise text designed to help students easily master the anatomy and basic physiology of the nervous system. Accessible and clear, the book highlights interrelationships between systems, structures, and the rest of the body as the chapters move through the various regions of the brain. Building on the solid foundation of the first edition, A Textbook of Neuroanatomy now includes two new chapters on the brainstem and reflexes, as well as dozens of new micrographs illustrating key structures. Throughout the book the clinical relevance of the material is emphasized through clinical cases, questions, and follow-up discussions in each chapter, motivating students to learn the information. A companion website is also available, featuring study aids and artwork from the book as PowerPoint slides. A Textbook of Neuroanatomy, Second Edition is an invaluable resource for students of general, clinical and behavioral neuroscience and neuroanatomy.

This complete, yet concise text is designed to help students easily master the anatomy and basic physiology of the nervous system. Accessible and clear, the text highlights interrelationships between systems, structures and the rest of the body as it moves through various regions of the brain. The first nine chapters introduce the main principles and terms in neuroanatomy, and the remaining chapters then use this information to describe the anatomy and function of the various pathways and discrete systems. Navigates students through the general principles and integrative components of the Nervous System Highlights interrelationships between systems, structures, and the rest of the body Emphasizes clinical relevance through clinical cases, questions, and follow-up discussions in each chapter Indicates medical conditions relevant to each chapter in the Clinical Considerations Features an accompanying website, www.blackwellpublishing.com/patestas, which includes all the illustrations, along with animations of key processes; also available on CD-ROM. Please contact our Higher Education team at HigherEducation@wiley.com for more information.

The essential resource to an integrated approach to reservoir modelling by highlighting both the input of data and the modelling results Reservoir Modelling offers a comprehensive guide to the procedures and workflow for building a 3-D model. Designed to be practical, the principles outlined can be applied to any modelling project regardless of the software used. The author – a noted practitioner in the field – captures the heterogeneity due to structure, stratigraphy and sedimentology that has an impact on flow in the reservoir. This essential guide follows a general workflow from data QC and project management, structural modelling, facies and property modelling to upscaling and the requirements for dynamic modelling. The author discusses structural elements of a model and reviews both seismic interpretation and depth conversion, which are known to contribute most to volumetric uncertainty and shows how large-scale stratigraphic relationships are integrated into the reservoir framework. The text puts the focus on geostatistical modelling of facies and heterogeneities that constrain the distribution of reservoir properties including porosity, permeability and water saturation. In addition, the author discusses the role of uncertainty analysis in the static model and its impact on volumetric estimation. The text also addresses some typical approaches to modelling specific reservoirs through a mix of case studies and illustrative examples and: Offers a practical guide to the use of data to build a successful reservoir model Draws on the latest advances in 3-D modelling software Reviews facies modelling, the different methods and the need for understanding the geological interpretation of cores and logs Presents information on upscaling both the structure and the properties of a fine-scale geological model for dynamic simulation Stresses the importance of an interdisciplinary team-based approach Written for geophysicists, reservoir geologists and petroleum engineers, Reservoir Modelling offers the essential information needed to understand a reservoir for modelling and contains the multidisciplinary nature of a reservoir modelling project.

Already the market leader in the field, Modelling Transport has become still more indispensible following a thorough and detailed update. Enhancements include two entirely new chapters on modelling for private sector projects and on activity-based modelling; a new section on dynamic assignment and micro-simulation; and sizeable updates to sections on disaggregate modelling and stated preference design and analysis. It also tackles topical issues such as valuation of externalities and the role of GPS in travel time surveys. Providing unrivalled depth and breadth of coverage, each topic is approached as a modelling exercise with discussion of the roles of theory, data, model specification, estimation, validation and application. The authors present the state of the art and its practical application in a pedagogic manner, easily understandable to both students and practitioners. Follows on from the highly successful third edition universally acknowledged as the leading text on transport modelling techniques and applications Includes two new chapters on modelling for private sector projects and activity based modeling, and numerous updates to existing chapters Incorporates treatment of recent issues and concerns like risk analysis and the dynamic interaction between land use and transport Provides comprehensive and rigorous information and guidance, enabling readers to make practical use of every available technique Relates the topics to new external factors and technologies such as global warming, valuation of externalities and global positioning systems (GPS).

Simulation models are an established method used to investigate processes and solve practical problems in a wide variety of disciplines. Central to the concept of this second edition is the idea that environmental systems are complex, open systems. The authors present the diversity of approaches to dealing with environmental complexity and then encourage readers to make comparisons between these approaches and between different disciplines. Environmental Modelling: Finding Simplicity in Complexity 2nd edition is divided into four main sections: An overview of methods and approaches to modelling. State of the art for modelling environmental processes Tools used and models for management Current and future developments. The second edition evolves from the first by providing additional emphasis and material for those students wishing to specialize in environmental modelling. This edition: Focuses on simplifying complex environmental systems. Reviews current software, tools and techniques for modelling. Gives practical examples from a wide variety of disciplines, e.g. climatology, ecology, hydrology, geomorphology and engineering. Has an associated website containing colour images, links to WWW resources and chapter support pages, including data sets relating to case studies, exercises and model animations. This book is suitable for final year undergraduates and postgraduates in environmental modelling, environmental science, civil engineering and biology who will already be familiar with the subject and are moving on to specialize in the field. It is also designed to appeal to professionals interested in the environmental sciences, including environmental consultants, government employees, civil engineers, geographers, ecologists, meteorologists, and geochemists.