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Spatial Statistical Methods for Geography
by Peter A. RogersonThis accessible new textbook offers a straightforward introduction to doing spatial statistics. Grounded in real world examples, it shows you how to extend traditional statistical methods for use with spatial data. The book assumes basic mathematical and statistics knowledge but also provides a handy refresher guide, so that you can develop your understanding and progress confidently. It also: · Equips you with the tools to both interpret and apply spatial statistical methods · Engages with the unique considerations that apply when working with geographic data · Helps you build your knowledge of key spatial statistical techniques, such as methods of geographic cluster detection.
Spatial Statistics and Spatio-Temporal Data
by Michael ShermanIn the spatial or spatio-temporal context, specifying the correct covariance function is fundamental to obtain efficient predictions, and to understand the underlying physical process of interest. This book focuses on covariance and variogram functions, their role in prediction, and appropriate choice of these functions in applications. Both recent and more established methods are illustrated to assess many common assumptions on these functions, such as, isotropy, separability, symmetry, and intrinsic correlation.After an extensive introduction to spatial methodology, the book details the effects of common covariance assumptions and addresses methods to assess the appropriateness of such assumptions for various data structures.Key features:An extensive introduction to spatial methodology including a survey of spatial covariance functions and their use in spatial prediction (kriging) is given.Explores methodology for assessing the appropriateness of assumptions on covariance functions in the spatial, spatio-temporal, multivariate spatial, and point pattern settings.Provides illustrations of all methods based on data and simulation experiments to demonstrate all methodology and guide to proper usage of all methods.Presents a brief survey of spatial and spatio-temporal models, highlighting the Gaussian case and the binary data setting, along with the different methodologies for estimation and model fitting for these two data structures.Discusses models that allow for anisotropic and nonseparable behaviour in covariance functions in the spatial, spatio-temporal and multivariate settings.Gives an introduction to point pattern models, including testing for randomness, and fitting regular and clustered point patterns. The importance and assessment of isotropy of point patterns is detailed.Statisticians, researchers, and data analysts working with spatial and space-time data will benefit from this book as well as will graduate students with a background in basic statistics following courses in engineering, quantitative ecology or atmospheric science.
Spatial Statistics for Data Science: Theory and Practice with R (Chapman & Hall/CRC Data Science Series)
by Paula MoragaSpatial data is crucial to improve decision-making in a wide range of fields including environment, health, ecology, urban planning, economy, and society. Spatial Statistics for Data Science: Theory and Practice with R describes statistical methods, modeling approaches, and visualization techniques to analyze spatial data using R. The book provides a comprehensive overview of the varying types of spatial data, and detailed explanations of the theoretical concepts of spatial statistics, alongside fully reproducible examples which demonstrate how to simulate, describe, and analyze spatial data in various applications. Combining theory and practice, the book includes real-world data science examples such as disease risk mapping, air pollution prediction, species distribution modeling, crime mapping, and real state analyses. The book utilizes publicly available data and offers clear explanations of the R code for importing, manipulating, analyzing, and visualizing data, as well as the interpretation of the results. This ensures contents are easily accessible and fully reproducible for students, researchers, and practitioners. Key Features: Describes R packages for retrieval, manipulation, and visualization of spatial data Offers a comprehensive overview of spatial statistical methods including spatial autocorrelation, clustering, spatial interpolation, model-based geostatistics, and spatial point processes Provides detailed explanations on how to fit and interpret Bayesian spatial models using the integrated nested Laplace approximation (INLA) and stochastic partial differential equation (SPDE) approaches
Spatial Synthesis: Computational Social Science and Humanities (Human Dynamics in Smart Cities)
by Xinyue Ye Hui LinThis book describes how powerful computing technology, emerging big and open data sources, and theoretical perspectives on spatial synthesis have revolutionized the way in which we investigate social sciences and humanities. It summarizes the principles and applications of human-centered computing and spatial social science and humanities research, thereby providing fundamental information that will help shape future research. The book illustrates how big spatiotemporal socioeconomic data facilitate the modelling of individuals’ economic behavior in space and time and how the outcomes of such models can reveal information about economic trends across spatial scales. It describes how spatial social science and humanities research has shifted from a data-scarce to a data-rich environment. The chapters also describe how a powerful analytical framework for identifying space-time research gaps and frontiers is fundamental to comparative study of spatiotemporal phenomena, and how research topics have evolved from structure and function to dynamic and predictive. As such this book provides an interesting read for researchers, students and all those interested in computational and spatial social sciences and humanities.
Spatial Temporal Information Systems: An Ontological Approach using STK
by Linda M. McNeil T.S. KelsoDesigned to be a high-level, approachable resource for engineers who need further insight into spatial temporal information systems from an ontological perspective, Spatial Temporal Information Systems: An Ontological Approach using STK explains the dynamics of objects interaction from signal analysis to trajectory design, spatial modeling, and oth
Spatio-Temporal Data Analytics for Wind Energy Integration
by Lei Yang Miao He Junshan Zhang Vijay VittalThis SpringerBrief presents spatio-temporal data analytics for wind energy integration using stochastic modeling and optimization methods. It explores techniques for efficiently integrating renewable energy generation into bulk power grids. The operational challenges of wind, and its variability are carefully examined. A spatio-temporal analysis approach enables the authors to develop Markov-chain-based short-term forecasts of wind farm power generation. To deal with the wind ramp dynamics, a support vector machine enhanced Markov model is introduced. The stochastic optimization of economic dispatch (ED) and interruptible load management are investigated as well. Spatio-Temporal Data Analytics for Wind Energy Integration is valuable for researchers and professionals working towards renewable energy integration. Advanced-level students studying electrical, computer and energy engineering should also find the content useful.
Spatio-temporal Design
by Werner G. Müller Jorge MateuA state-of-the-art presentation of optimum spatio-temporal sampling design - bridging classic ideas with modern statistical modeling concepts and the latest computational methods.Spatio-temporal Design presents a comprehensive state-of-the-art presentation combining both classical and modern treatments of network design and planning for spatial and spatio-temporal data acquisition. A common problem set is interwoven throughout the chapters, providing various perspectives to illustrate a complete insight to the problem at hand.Motivated by the high demand for statistical analysis of data that takes spatial and spatio-temporal information into account, this book incorporates ideas from the areas of time series, spatial statistics and stochastic processes, and combines them to discuss optimum spatio-temporal sampling design.Spatio-temporal Design: Advances in Efficient Data Acquisition:Provides an up-to-date account of how to collect space-time data for monitoring, with a focus on statistical aspects and the latest computational methodsDiscusses basic methods and distinguishes between design and model-based approaches to collecting space-time data.Features model-based frequentist design for univariate and multivariate geostatistics, and second-phase spatial sampling.Integrates common data examples and case studies throughout the book in order to demonstrate the different approaches and their integration. Includes real data sets, data generating mechanisms and simulation scenarios.Accompanied by a supporting website featuring R code. Spatio-temporal Design presents an excellent book for graduate level students as well as a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.
Spatio-Temporal Models for Ecologists (Chapman & Hall/CRC Applied Environmental Statistics)
by James Thorson Kasper KristensenEcological dynamics are tremendously complicated and are studied at a variety of spatial and temporal scales. Ecologists often simplify analysis by describing changes in density of individuals across a landscape, and statistical methods are advancing rapidly for studying spatio-temporal dynamics. However, spatio-temporal statistics is often presented using a set of principles that may seem very distant from ecological theory or practice. This book seeks to introduce a minimal set of principles and numerical techniques for spatio-temporal statistics that can be used to implement a wide range of real-world ecological analyses regarding animal movement, population dynamics, community composition, causal attribution, and spatial dynamics. We provide a step-by-step illustration of techniques that combine core spatial-analysis packages in R with low-level computation using Template Model Builder. Techniques are showcased using real-world data from varied ecological systems, providing a toolset for hierarchical modelling of spatio-temporal processes. Spatio-Temporal Models for Ecologists is meant for graduate level students, alongside applied and academic ecologists.Key Features: Foundational ecological principles and analyses Thoughtful and thorough ecological examples Analyses conducted using a minimal toolbox and fast computation Code using R and TMB included in the book and available online
Spatio-Temporal Statistics with R (Chapman & Hall/CRC The R Series)
by Christopher K. Wikle Andrew Zammit-Mangion Noel CressieThe world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps.Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.
Spatiotemporal Data Analysis
by Gidon EshelA severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics--origin, rates, and frequencies--of these phenomena. This comprehensive text introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine. Gidon Eshel begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. He then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams.
Spatiotemporal Data Analytics and Modeling: Techniques and Applications (Big Data Management)
by John A Satheesh Abimannan El-Sayed M. El-Alfy Yue-Shan ChangWith the growing advances in technology and transformation to digital services, the world is becoming more connected and more complex. Huge heterogeneous data are generated at rapid speed from various types of sensors. Augmented with artificial intelligence and machine learning and internet of things, latent relations, and new insights can be captured helping in optimizing plans and resource utilization, improving infrastructure, and enhancing quality of services. A “spatial data management system” is a way to take care of data that has something to do with space. This could include data such as maps, satellite images, and GPS data. A temporal data management system is a system designed to manage data that has a temporal component. This could include data such as weather data, financial data, and social media data. Some advanced techniques used in spatial and temporal data management systems include geospatial indexing for efficient querying and retrieval of location-based data, time-series analysis for understanding and predicting temporal patterns in datasets like weather or financial trends, machine learning algorithms for uncovering hidden patterns and correlations in large and complex datasets, and integration with Internet of Things (IoT) technologies for real-time data collection and analysis. These techniques, augmented with artificial intelligence, enable the extraction of latent relations and insights, thereby optimizing plans, improving infrastructure, and enhancing the quality of services. This book provides essential technical knowledge, best practices, and case studies on the state-of-the-art techniques of artificial intelligence and machine learning for spatiotemporal data analysis and modeling. The book is composed of several chapters written by experts in their fields and focusing on several applications including recommendation systems, big data analytics, supply chains and e-commerce, energy consumption and demand forecasting,and traffic and environmental monitoring. It can be used as academic reference at graduate level or by professionals in science and engineering related fields such as data science and engineering, big data analytics and mining, artificial intelligence, machine learning and deep learning, cloud computing, and internet of things.
Spatiotemporal Modeling of Cancer Immunotherapy: Partial Differential Equation Analysis in R
by William E. SchiesserThe focus of this book is a detailed discussion of a dual cancer vaccine (CV)-immune checkpoint inhibitor (ICI) mathematical model formulated as a system of partial differential equations (PDEs) defining the spatiotemporal distribution of cells and biochemicals during tumor growth.A computer implementation of the model is discussed in detail for the quantitative evaluation of CV-ICI therapy. The coding (programming) consists of a series of routines in R, a quality, open-source scientific computing system that is readily available from the internet. The routines are based on the method of lines (MOL), a general PDE algorithm that can be executed on modest computers within the basic R system. The reader can download and use the routines to confirm the model solutions reported in the book, then experiment with the model by varying the parameters and modifying/extending the equations, and even studying alternative models with the PDE methodology demonstrated by the CV-ICI model.Spatiotemporal Modeling of Cancer Immunotherapy: Partial Differential Equation Analysis in R facilitates the use of the model, and more generally, computer- based analysis of cancer immunotherapy mathematical models, as a step toward the development and quantitative evaluation of the immunotherapy approach to the treatment of cancer.
Spear Operators Between Banach Spaces (Lecture Notes in Mathematics #2205)
by Vladimir Kadets Miguel Martín Javier Merí Antonio PérezThis monograph is devoted to the study of spear operators, that is, bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar $\omega$ such that$\|G + \omega\,T\|=1+ \|T\|$.This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on $L_1$. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.
Special Functions
by Richard Beals Roderick WongSpecial functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics. This book presents the state-of-the-art of the subject and its applications.
Special Functions and Analysis of Differential Equations
by Praveen Agarwal, Ravi P. Agarwal and Michael RuzhanskyDifferential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.
Special Functions and Generalized Sturm-Liouville Problems (Frontiers in Mathematics)
by Mohammad Masjed-JameiThis book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions.Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.
Special Functions and Orthogonal Polynomials
by Richard Beals Roderick WongThe subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-first century'.
Special Functions and their Application
by Bipin Singh Koranga Sanjay Kumar Padaliya Vivek Kumar NautiyalSpecial functions are mathematical functions that have established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials. Each chapter finishes with a description of how the function is most commonly applied and a set of examples for the student to work through.
Special Functions in Fractional Calculus and Engineering (Mathematics and its Applications)
by Harendra Singh H. M. Srivastava R. K. PandeySpecial functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations.This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.
Special Functions in Physics with MATLAB
by Wolfgang SchweizerThis handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.
Special Functions of Mathematical (Applied and Numerical Harmonic Analysis)
by Willi Freeden Martin GuttingSpecial functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.
Special Functions, Partial Differential Equations, and Harmonic Analysis
by Constantine Georgakis Alexander M. Stokolos Wilfredo UrbinaThis volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.
Special Functions & Their Applications (Dover Books on Mathematics)
by N. N. Lebedev Richard R. SilvermanRichard Silverman's new translation makes available to English readers the work of the famous contemporary Russian mathematician N. N. Lebedev. Though extensive treatises on special functions are available, these do not serve the student or the applied mathematician as well as Lebedev's introductory and practically oriented approach. His systematic treatment of the basic theory of the more important special functions and the applications of this theory to specific problems of physics and engineering results in a practical course in the use of special functions for the student and for those concerned with actual mathematical applications or uses. In consideration of the practical nature of the coverage, most space has been devoted to the application of cylinder functions and particularly of spherical harmonics. Lebedev, however, also treats in some detail: the gamma function, the probability integral and related functions, the exponential integral and related functions, orthogonal polynomials with consideration of Legendre, Hermite and Laguerre polynomials (with exceptional treatment of the technique of expanding functions in series of Hermite and Laguerre polynomials), the Airy functions, the hypergeometric functions (making this often slighted area accessible to the theoretical physicist), and parabolic cylinder functions. The arrangement of the material in the separate chapters, to a certain degree, makes the different parts of the book independent of each other. Although a familiarity with complex variable theory is needed, a serious attempt has been made to keep to a minimum the required background in this area. Various useful properties of the special functions which do not appear in the text proper will be found in the problems at the end of the appropriate chapters. This edition closely adheres to the revised Russian edition (Moscow, 1965). Richard Silverman, however, has made the book even more useful to the English reader. The bibliography and references have been slanted toward books available in English or the West European languages, and a number of additional problems have been added to this edition.
Special Matrices and Their Applications in Numerical Mathematics: Second Edition
by Miroslav FiedlerThis revised and corrected second edition of a classic book on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference.Author Miroslav Fiedler, a Professor at the Institute of Computer Science of the Academy of Sciences of the Czech Republic, Prague, begins with definitions of basic concepts of the theory of matrices and fundamental theorems. In subsequent chapters, he explores symmetric and Hermitian matrices, the mutual connections between graphs and matrices, and the theory of entrywise nonnegative matrices. After introducing M-matrices, or matrices of class K, Professor Fiedler discusses important properties of tensor products of matrices and compound matrices and describes the matricial representation of polynomials. He further defines band matrices and norms of vectors and matrices. The final five chapters treat selected numerical methods for solving problems from the field of linear algebra, using the concepts and results explained in the preceding chapters.
Special Needs and Drug Education (nasen spotlight)
by Richard IvesTaking drugs is complex and there are concerns about the best ways of addressing drugs issues in schools - particularly for pupils with special educational needs. Many teachers are worried about discussing drugs with their pupils. They fear that they know too little and that some of their pupils may know too much. They also worry that talking about drugs to naive children may raise their interest. Yet the government expects all pupils to receive drug education and requires all schools to have a drug policy. It has ambitious targets in reducing the use of drugs by young people. This book aims to help teachers of pupils with special educational needs to assess what their contribution should be and identify what the particular issues associated with their pupils are. It will help schools to: create or revise a drugs policy plan a program of study deliver drug education appropriate to their pupils deal with drug related incident.