MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work in linear algebra with ease. In addition to exploring MATLAB's matrix algebra capabilities, it describes the MATLAB commands that are used to create two- and three-dimensional graphics, including explicit, implicit and parametric curve and surface plotting, and various methods of data representation. Methods for solving systems of equations are detailed.

later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me (pkattan@tedata. net. jo and pkattan@lsu. edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .

This textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using Mathematica code, the book is fully supported by downloadable sessions in Mathematica, Maple, and Maxima. Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration. Computer Algebra is an indispensable resource for mathematics and computer science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java.MATLAB Control Systems Engineering introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to design and analyze control systems using MATLAB's specialized Control Systems Toolbox. The Control Systems Toolbox offers an extensive range of tools for classical and modern control design. Using these tools you can create models of linear time-invariant systems in transfer function, zero-pole-gain or state space format. You can manipulate both discrete-time and continuous-time systems and convert between various representations. You can calculate and graph time response, frequency response and loci of roots. Other functions allow you to perform pole placement, optimal control and estimates. The Control System Toolbox is open and extendible, allowing you to create customized M-files to suit your specific applications.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science. "Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... " MIT Technology Review "These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used." A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing. "I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science." D. Trigiante, Computational Management Science. "Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural". R. Gangle, G. Caterina, F. Tohme, Soft Computing. "The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort." P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing

The matrix laboratory interactive computing environment MATLAB has brought creativity to research in diverse disciplines, particularly in designing and programming experiments. More commonly used in mathematics and the sciences, it also lends itself to a variety of applications across the field of psychology. For the novice looking to use it in experimental psychology research, though, becoming familiar with MATLAB can be a daunting task.

"MATLAB for Psychologists"expertly guides readers through the component steps, skills, and operations of the software, with plentiful graphics and examples to match the reader s comfort level. Using an extended illustration, this concise volume explains the program s usefulness at any point in an experiment, without the limits imposed by other types of software. And the authors demonstrate the responsiveness of MATLAB to the individual s research needs, whether the task is programming experiments, creating sensory stimuli, running simulations, or calculating statistics for data analysis.

Key features of the coverage:

Thinking in a matrix way.Handling and plotting data.Guidelines for improved programming, sound, and imaging.Statistical analysis and signal detection theory indexes.The Graphical User Interface.The Psychophysics Toolbox.

"MATLAB for Psychologists"serves a wide audience of advanced undergraduate and graduate level psychology students, professors, and researchers as well as lab technicians involved in programming psychology experiments."

The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald's test, their relationship with the likelihood ratio test and Karl Pearson's chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson's chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.

An overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data, such as longitudinal data, repeated measures, and multilevel data. The authors present a unified model-building strategy for both models and apply this to the analysis of over 20 real datasets from a wide variety of areas, including pharmacokinetics, agriculture, and manufacturing. Much emphasis is placed on the use of graphical displays at the various phases of the model-building process, starting with exploratory plots of the data and concluding with diagnostic plots to assess the adequacy of a fitted model. The NLME library for analyzing mixed-effects models in S and S-PLUS, developed by the authors, provides the underlying software for implementing the methods presented. This balanced mix of real data examples, modeling software, and theory makes the book a useful reference for practitioners who use, or intend to use, mixed-effects models in their data analyses. It can also be used as a text for a one-semester graduate-level applied course.

Hurricanes are nature's most destructive storms and they are becoming more powerful as the globe warms. Hurricane Climatology explains how to analyze and model hurricane data to better understand and predict present and future hurricane activity. It uses the open-source and now widely used R software for statistical computing to create a tutorial-style manual for independent study, review, and reference. The text is written around the code that when copied will reproduce the graphs, tables, and maps. The approach is different from other books that use R. It focuses on a single topic and explains how to make use of R to better understand the topic. The book is organized into two parts, the first of which provides material on software, statistics, and data. The second part presents methods and models used in hurricane climate research.

The richly illustrated Interactive Web-Based Data Visualization with R, plotly, and shiny focuses on the process of programming interactive web graphics for multidimensional data analysis. It is written for the data analyst who wants to leverage the capabilities of interactive web graphics without having to learn web programming. Through many R code examples, you will learn how to tap the extensive functionality of these tools to enhance the presentation and exploration of data. By mastering these concepts and tools, you will impress your colleagues with your ability to quickly generate more informative, engaging, and reproducible interactive graphics using free and open source software that you can share over email, export to pdf, and more. Key Features: Convert static ggplot2 graphics to an interactive web-based form Link, animate, and arrange multiple plots in standalone HTML from R Embed, modify, and respond to plotly graphics in a shiny app Learn best practices for visualizing continuous, discrete, and multivariate data Learn numerous ways to visualize geo-spatial data This book makes heavy use of plotly for graphical rendering, but you will also learn about other R packages that support different phases of a data science workflow, such as tidyr, dplyr, and tidyverse. Along the way, you will gain insight into best practices for visualization of high-dimensional data, statistical graphics, and graphical perception. The printed book is complemented by an interactive website where readers can view movies demonstrating the examples and interact with graphics.

The 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.

A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

This book evolved from lectures, courses and workshops on missing data and small-area estimation that I presented during my tenure as the ?rst C- pion Fellow (2000-2002). For the Fellowship I proposed these two topics as areas in which the academic statistics could contribute to the development of government statistics, in exchange for access to the operational details and background that would inform the direction and sharpen the focus of a- demic research. After a few years of involvement, I have come to realise that the separation of 'academic' and 'industrial' statistics is not well suited to either party, and their integration is the key to progress in both branches. Most of the work on this monograph was done while I was a visiting l- turer at Massey University, Palmerston North, New Zealand. The hospitality and stimulating academic environment of their Institute of Information S- ence and Technology is gratefully acknowledged. I could not name all those who commented on my lecture notes and on the presentations themselves; apart from them, I want to thank the organisers and silent attendees of all the events, and, with a modicum of reluctance, the 'grey ?gures' who kept inquiring whether I was any nearer the completion of whatever stage I had been foolish enough to attach a date.

This is the first book to show the capabilities of Microsoft Excel to teach biological and life sciences statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical science problems. If understanding statistics isn t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.

Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, "Excel 2010 for Biological and Life Sciences Statistics: A Guide to Solving Practical Problems" is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work.

Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand science problems. Practice problems are provided at the end of each chapter with their solutions in an appendix. Separately, there is a full Practice Test (with answers in an Appendix) that allows readers to test what they have learned. "

Six Sigma has arisen in the last two decades as a breakthrough Quality Management Methodology. With Six Sigma, we are solving problems and improving processes using as a basis one of the most powerful tools of human development: the scientific method. For the analysis of data, Six Sigma requires the use of statistical software, being R an Open Source option that fulfills this requirement. R is a software system that includes a programming language widely used in academic and research departments. Nowadays, it is becoming a real alternative within corporate environments. The aim of this book is to show how R can be used as the software tool in the development of Six Sigma projects. The book includes a gentle introduction to Six Sigma and a variety of examples showing how to use R within real situations. It has been conceived as a self contained piece. Therefore, it is addressed not only to Six Sigma practitioners, but also to professionals trying to initiate themselves in this management methodology. The book may be used as a text book as well.

This book presents a study of the COVID-19 pandemic using computational social scientific analysis that draws from, and employs, statistics and simulations. Combining approaches in crisis management, risk assessment and mathematical modelling, the work also draws from the philosophy of sacrifice and futurology. It makes an original contribution to the important issue of the stability of society by highlighting two significant factors: the COVID-19 crisis as a catalyst for change and the rise of AI and Big Data in managing society. It also emphasizes the nature and importance of sacrifices and the role of politics in the distribution of sacrifices. The book considers the treatment of AI and Big Data and their use to both "good" and "bad" ends, exposing the inevitability of these tools being used. Relevant to both policymakers and social scientists interested in the influence of AI and Big Data on the structure of society, the book re-evaluates the ways we think of lifestyles, economic systems and the balance of power in tandem with digital transformation.

The first part of this title contained all statistical tests that are relevant for starters on SPSS, and included standard parametric and non-parametric tests for continuous and binary variables, regression methods, trend tests, and reliability and validity assessments of diagnostic tests. The current part 2 of this title reviews multistep methods, multivariate models, assessments of missing data, performance of diagnostic tests, meta-regression, Poisson regression, confounding and interaction, and survival analyses using log tests and segmented time-dependent Cox regression. Methods for assessing non linear models, data seasonality, distribution free methods, including Monte Carlo methods and artificial intelligence, and robust tests are also covered.

Each method of testing is explained using a data example from clinical practice, including every step in SPSS, and a text with interpretations of the results and hints convenient for data reporting. In order to facilitate the use of this cookbook the data files of the examples is made available by the editor through extras.springer.com.

Both part 1 and 2 of this title contain a minima amount of text and maximal technical details, but we believe that this property will not refrain students from mastering the SPSS software systematics, and that, instead, it will be a help to that aim. Yet, we recommend that it will used together with the textbook "Statistics Applied to Clinical Trials" (5th edition, Springer, Dordrecht 2012) and the e-books "Statistics on a Pocket Calculator Part 1 and 2 (Springer, Dordrecht, 2011 and 2012) from the same authors.

Stata is the most flexible and extensible data analysis package available from a commercial vendor. R is a similarly flexible free and open source package for data analysis, with over 3,000 add-on packages available. This book shows you how to extend the power of Stata through the use of R. It introduces R using Stata terminology with which you are already familiar. It steps through more than 30 programs written in both languages, comparing and contrasting the two packages' different approaches. When finished, you will be able to use R in conjunction with Stata, or separately, to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses.

A glossary defines over 50 R terms using Stata jargon and again using more formal R terminology. The table of contents and index allow you to find equivalent R functions by looking up Stata commands and vice versa. The example programs and practice datasets for both R and Stata are available for download.

Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.

Metrics are a hot topic. Executive leadership, boards of directors, management, and customers are all asking for data-based decisions. As a result, many managers, professionals, and change agents are asked to develop metrics, but have no clear idea of how to produce meaningful ones. Wouldn't it be great to have a simple explanation of how to collect, analyze, report, and use measurements to improve your organization? Metrics: How to Improve Key Business Results provides that explanation and the tools you'll need to make your organization more effective. Not only does the book explain the why of metrics, but it walks you through a step-by-step process for creating a report card that provides a clear picture of organizational health and how well you satisfy customer needs. Metrics will help you to measure the right things, the right way - the first time. No wasted effort, no chasing data. The report card provides a simple tool for viewing the health of your organization, from the outside in.You will learn how to measure the key components of the report card and thereby improve real measures of business success, like repeat customers, customer loyalty, and word-of-mouth advertising.This book: * Provides a step-by-step guide for building an organizational effectiveness report card * Takes you from identifying key services and products and using metrics, to determining business strategy * Provides examples of how to identify, collect, analyze, and report metrics that will be immediately useful for improving all aspects of the enterprise, including IT What you'll learn * Understand the difference between data, measures, information, and metrics * Identify root performance questions to ensure you build the right metrics * Develop meaningful and accurate metrics using concrete, easy-to-follow instructions * Avoid the high risks that come with collecting, analyzing, reporting, and using complex data * Formulate practical answers to data-based questions * Select and use the proper tools for creating, implementing, and using metrics * Learn one of the most powerful methods yet invented for improving organizational results Who this book is for Metrics: How to Improve Key Business Results was written for senior managers who need to improve key results.Equally, the book is for the department heads, middle managers, analysts, IT professionals, and change agents responsible for collecting, analyzing, and reporting metrics. Finally, it's for those who have to chase data and find meaningful answers to the interesting questions executives ponder. Table of Contents * Introduction: Who, What, Where, When, Why, and How You Use Metrics * Establishing a Common Language * Where to Begin: Planning a Good Metric * Using Metrics as Indicators * Using the Answer Key * Start with Effectiveness * Triangulation: Essential to Creating Effective Metrics * Expectations: How to View Data in a Meaningful Way * Creating and Interpreting the Metrics Report Card * Final Product: the Metrics Report Card * Employing Advanced Metrics * Creating the Service Catalog * Establishing Standards and Benchmarks * Respecting the Power of Metrics * Avoiding the Research Trap * Embracing Your Organization's Uniqueness * Appendix: Metrics Tools to Use and Useful Resources

• Plenty of examples and case studies utilize Mathematica 7's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting.
• Emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas.
• Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, and new and surprising formulas for p.
• Visualization is emphasized throughout, with finely crafted graphics in each chapter.
• All Mathematica code is included on a CD, saving the reader hours of typing.