A Concrete Approach to Mathematical Modelling

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.

An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.

Insightful modelling of dynamic systems for better business strategy The business environment is constantly changing and organisations need the ability to rehearse alternative futures. By mimicking the interlocking operations of firms and industries, modelling serves as a ‘dry run’ for testing ideas, anticipating consequences, avoiding strategic pitfalls and improving future performance. Strategic Modelling and Business Dynamics is an essential guide to credible models; helping you to understand modelling as a creative process for distilling and communicating those factors that drive business success and sustainability. Written by an internationally regarded authority, the book covers all stages of model building, from conceptual to analytical. The book demonstrates a range of in-depth practical examples that vividly illustrate important or puzzling dynamics in firm operations, strategy, public policy, and everyday life. This updated new edition also offers a rich Learners' website with models, articles and videos, as well as a separate Instructors' website resource, with lecture slides and other course materials (see Related Websites/Extra section below). Together the book and websites deliver a powerful package of blended learning materials that: Introduce the system dynamics approach of modelling strategic problems in business and society Include industry examples and public sector applications with interactive simulators and contemporary visual modelling software Provide the latest state-of-the-art thinking, concepts and techniques for systems modelling The comprehensive Learners' website features models, microworlds, journal articles and videos. Easy-to-use simulators enable readers to experience dynamic complexity in business and society. Like would-be CEOs, readers can re-design operations and then re-simulate in the quest for well-coordinated strategy and better performance. The simulators include a baffling hotel shower, a start-up low-cost airline, an international radio broadcaster, a diversifying tyre maker, commercial fisheries and the global oil industry. «Much more than an introduction, John Morecroft’s Strategic Modelling and Business Dynamics uses interactive ‘mini-simulators and microworlds’ to create an engaging and effective learning environment in which readers, whatever their background, can develop their intuition about complex dynamic systems.» John Sterman, Jay W. Forrester Professor of Management, MIT Sloan School of Management «Illustrated by examples from everyday life, business and policy, John Morecroft expertly demonstrates how systems thinking aided by system dynamics can improve our understanding of the world around us.» Stewart Robinson, Associate Dean Research, President of the Operational Research Society, Professor of Management Science, School of Business and Economics, Loughborough University

Praise for the First Edition of Quantitative Business Valuation A Mathematical Approach for Today's Professionals «Jay Abrams' book is close to the equivalent of several graduate dissertations rolled into one book. For each topic (covered), he presents a scholarly summary of past research, new empirical research of his own, and his conclusions. It is a well-documented contribution to in-depth understanding of important business valuation issues, and should not be overlooked by the serious practitioner.» —Shannon Pratt, DBAManaging Director, Willamette Management AssociatesCoauthor, Valuing a Business «A must-read for the serious business appraiser.» —Jay E. Fishman, ASA, CBAPresident, Financial Research, Inc. «The problem of simplified valuation procedures and coherent theory still remains complex and is ever evolving. Jay Abrams deals very effectively with this complexity through the use of mathematical formulas. Input to his models is explained with clarity and effectiveness, which adds to the overall value of this advanced text on business valuation.» —Terry A. Isom, Chairman, National Association of Certified Valuation Analysts «Jay Abrams' book strives to provide mathematical modeling for what practitioners often do by reasoning alone. This book is a must-read for practitioners who are searching for additional techniques for dealing with some of business valuation's imponderables.» —David M. Bishop, FIBA, BVAL, ASA, MCBAPresident, American Business Appraisers, Inc. «Jay Abrams' book will not only challenge the top theoreticians in the field; his step-by-step explanations will make advanced quantitative techniques available to the many appraisers who are not capable of independently creating the underlying mathematical analysis.» —Kent Osborne, ASAChairman, Editorial Review Board of the American Society of Appraisers «While a proliferation of business valuation treatises and guides exists in the market, most are very general in nature and do nothing more than rehash fundamental concepts. I am unaware of any author who has stepped into the unknown as Jay Abrams has and compiled and developed a treatise of extremely useful analytical tools for the serious valuator.» —Robert J. Grossman, CPA/ABV, ASA, CVAPartner, Grossman Yanak & Ford «Jay Abrams develops unusual approaches which merit consideration when 'cookie cutter' methodologies are inadequate. This manuscript contributes to the dialogue among practitioners and strengthens the theoretical foundations of business valuation.» —Herbert T. SpiroPresident, American Valuation Group, Inc. «There is no question about it, the use of rigorous quantitative methods is the cure for subjective valuation analysis. This book not only satisfies this need—which has grown considerably in recent years—but is chock-full of new tools that have been carefully developed.» —Edward MurrayValuation Partner, Arthur Andersen, LLP

Perfect your transferable dental clinical skills with this new and highly practical reference A Practical Approach to Operative Dentistry delivers a thorough exploration of the theoretical and practical aspects of operative dentistry, followed by an illustrated step-by-step guide of common clinical procedures. Designed to remind students of the key steps of a variety of operative procedures, it is heavily illustrated with over 400 images of clinical procedures and covers core topics such as: Instruments and matrices, isolation, dental charting, and the use of minimally invasive dentistry Treatment of intracoronal restorations, including pit and fissure caries, posterior approximal restorations, anterior restorations and restorations in the cervical third Exploration of extracoronal restorations, including gold restorations, porcelain fused to metal and ceramic crowns A Practical Approach to Operative Dentistry is the perfect textbook for undergraduate dental students. It is also useful to dentistry graduates undertaking clinical rotations during their Dental Foundation Training, and overseas graduates preparing to take the Overseas Registration Examination (ORE) held by the General Dental Council, or the License in Dental Surgery (LDS) exam of the Royal College of Surgeons.

An insightful examination of the numerical methods used to develop finite element methods A Variational Approach to Structural Analysis provides readers with the underpinnings of the finite element method (FEM) while highlighting the power and pitfalls of virtual methods. In an easy-to-follow, logical format, this book gives complete coverage of the principle of virtual work, complementary virtual work and energy methods, and static and dynamic stability concepts. The first two chapters prepare the reader with preliminary material, introducing in detail the variational approach used in the book as well as reviewing the equilibrium and compatibility equations of mechanics. The next chapter, on virtual work, teaches how to use kinematical formulations for the determination of the required strain relationships for straight, curved, and thin walled beams. The chapters on complementary virtual work and energy methods are problem-solving chapters that incorporate Castigliano's first theorem, the Engesser-Crotti theorem, and the Galerkin method. In the final chapter, the reader is introduced to various geometric measures of strain and revisits straight, curved, and thin walled beams by examining them in a deformed geometry. Based on nearly two decades of work on the development of the world's most used FEM code, A Variational Approach to Structural Analysis has been designed as a self-contained, single-source reference for mechanical, aerospace, and civil engineering professionals. The book's straightforward style also provides accessible instruction for graduate students in aeronautical, civil, mechanical, and engineering mechanics courses.

Written, reviewed, and edited in a collaborative effort by cardiology fellows and faculty of one of the most prestigious academic centers in the country, this concise volume gives cardiology fellows the book they have long needed. Keeping coverage of the underlying pathophysiology and mechanism of disease to a minimum, the authors focus on the diagnosis and treatment of cardiac disorders. Practical and easily accessible at the time of decision making, the book relays important concepts through concise and to-the-point pearls and by utilizing algorithm charts and illustrations.

Explores practical advantages of Grid Computing and what is needed by an organization to migrate to this new computing paradigm This self-contained reference makes both the concepts and applications of grid computing clear and understandable to even non-technical managers Explains the underlying networking mechanism and answers such questions critical to the business enterprise as «What is grid computing?» «How widespread is its present/potential penetration?» «Is it ready for prime time?» «Are there firm standards?» «Is it secure?» «How do we bill this new product?» and «How can we deploy it (at a macro level)?»

With resources at a premium, and ecological concerns paramount, the need for clean, efficient and low-cost processes is one of the most critical challenges facing chemical engineers. The ability to control these processes, optimizing one, two or several variables has the potential to make more substantial savings in time, money and resources than any other single factor. Building on the success of the previous editions, this new third edition of A Real-Time Approach to Process Control employs both real industry practice and process control education without the use of complex or highly mathematical techniques, providing a more practical and applied approach. Updated throughout, this edition: • Includes a brand new chapter on Model predictive Control (MPC) • Now includes wireless and web-based technologies • Covers bio-related systems • Details the new multivariable control measure developed by the authors • Includes PowerPoint slides and solutions to Workshop problems on the accompanying website: http://www.wiley.com/go/svrcek-real-time-3e From the reviews of previous editions: “Would appeal to practising engineers due to its “hands on” feel for the subject matter. But more importantly, the authors present these concepts as fundamentals of chemical engineering, in a way that is consistent with how professor teach at the universities.” –Chemical Engineering Process (CEP) “The book has been beautifully crafted” –Engineering Subject Centre “Provides a refreshing approach to the presentation of process analysis and control” –The Chemical Engineer

This is the second edition of the successful textbook written by the prize-winning scientist Andreas Ziegler, former President of the German Chapter of the International Biometric Society, and Inke Konig, who has been teaching the subject over many years. The book gives a comprehensive introduction into the relevant statistical methods in genetic epidemiology. The second edition is thoroughly revised, partly rewritten and includes now chapters on segregation analysis, twin studies and estimation of heritability. The book is ideally suited for advanced students in epidemiology, genetics, statistics, bioinformatics and biomathematics. Like in the first edition the book contains many problems and solutions and it comes now optionally with an e-learning course created by Friedrich Pahlke. This e-learning course has been developed to complement the book. Both provide a unique support tool for teaching the subject.