Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem.

This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool.

Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study.

Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior."

This volume provides essential guidance for transforming mathematics learning in schools through the use of innovative technology, pedagogy, and curriculum. It presents clear, rigorous evidence of the impact technology can have in improving students learning of important yet complex mathematical concepts -- and goes beyond a focus on technology alone to clearly explain how teacher professional development, pedagogy, curriculum, and student participation and identity each play an essential role in transforming mathematics classrooms with technology. Further, evidence of effectiveness is complemented by insightful case studies of how key factors lead to enhancing learning, including the contributions of design research, classroom discourse, and meaningful assessment. The volume organizes over 15 years of sustained research by multiple investigators in different states and countries who together developed an approach called "SimCalc" that radically transforms how Algebra and Calculus are taught. The SimCalc program engages students around simulated motions, such as races on a soccer field, and builds understanding using visual representations such as graphs, and familiar representations such as stories to help students to develop meaning for more abstract mathematical symbols. Further, the SimCalc program leverages classroom wireless networks to increase participation by all students in doing, talking about, and reflecting on mathematics. Unlike many technology programs, SimCalc research shows the benefits of balanced attention to curriculum, pedagogy, teacher professional development, assessment and technology -- and has proven effectiveness results at the scale of hundreds of schools and classrooms. Combining the findings of multiple investigators in one accessible volume reveals the depth and breadth of the research program, and engages readers interested in: * Engaging students in deeply learning the important concepts in mathematics * Designing innovative curriculum, software, and professional development * Effective uses of technology to improve mathematics education * Creating integrated systems of teaching that transform mathematics classrooms * Scaling up new pedagogies to hundreds of schools and classrooms * Conducting research that really matters for the future of mathematics learning * Engaging students in deeply learning the important concepts in mathematics * Designing innovative curriculum, software, and professional development * Effective uses of technology to improve mathematics education * Creating integrated systems of teaching that transform mathematics classrooms * Scaling up new pedagogies to hundreds of schools and classrooms * Conducting research that really matters for the future of mathematics learning

Explaining how graph theory and social network analysis can be applied to team sports analysis, This book presents useful approaches, models and methods that can be used to characterise the overall properties of team networks and identify the prominence of each team player. Exploring the different possible network metrics that can be utilised in sports analysis, their possible applications and variances from situation to situation, the respective chapters present an array of illustrative case studies. Identifying the general concepts of social network analysis and network centrality metrics, readers are shown how to generate a methodological protocol for data collection. As such, the book provides a valuable resource for students of the sport sciences, sports engineering, applied computation and the social sciences.

This book is intended for someone learning functions of a complex variable and who enjoys using MATLAB. It will enhance the exprience of learning complex variable theory and will strengthen the knowledge of someone already trained in ths branch of advanced calculus. ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB (R). Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses. A MATLAB (R) Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables, the book allows professors to quickly find and assign MATLAB programming problems that will strengthen students' knowledge of the language and concepts of complex variable theory. The book shows students how MATLAB can be a powerful learning aid in such staples of complex variable theory as conformal mapping, infinite series, contour integration, and Laplace and Fourier transforms. In addition to MATLAB programming problems, the text includes many examples in each chapter along with MATLAB code. Fractals, the most recent interesting topic involving complex variables, demands to be treated with a language such as MATLAB. This book concludes with a Coda, which is devoted entirely to this visually intriguing subject. MATLAB is not without constraints, limitations, irritations, and quirks, and there are subtleties involved in performing the calculus of complex variable theory with this language. Without knowledge of these subtleties, engineers or scientists attempting to use MATLAB for solutions of practical problems in complex variable theory suffer the risk of making major mistakes. This book serves as an early warning system about these pitfalls.

Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied. Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical. Numerical Methods with MATLAB presents each topic in a concise and readable format to help you learn fast and effectively. It is not intended to be a reference work to the conceptual theory that underpins the numerical methods themselves. A wide range of reference works are readily available to supply this information. If, however, you want assistance in applying numerical methods then this is the book for you.

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 Symbolic Algebra and Calculus Tools introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic variables and functions, you will learn how to solve equations in MATLAB, both symbolically and numerically, and how to simplify the results. Extensive coverage of polynomial solutions, inequalities and systems of equations are covered in detail. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful symbolic manipulator which enables you to factorize, expand and simplify complex algebraic expressions over all common fields (including over finite fields and algebraic field extensions of the rational numbers). With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to find eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can use MATLAB to explore mathematical analysis, finding limits of sequences and functions, sums of series, integrals, derivatives and solving differential equation.

Through analysis of the European Union Emissions Trading Scheme (EU ETS) and the Clean Development Mechanism (CDM), this book demonstrates how to use a variety of econometric techniques to analyze the evolving and expanding carbon markets sphere, techniques that can be extrapolated to the worldwide marketplace. It features stylized facts about carbon markets from an economics perspective, as well as covering key aspects of pricing strategies, risk and portfolio management.

This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.

Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica provides a general framework useful for the applications on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use of ODEs and Mathematica in the dynamics of rigid bodies.

Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ODEs such as phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica.

Topics and Features:

* Explanation of how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving

* End-of-chapter exercise sets incorporating the use of Mathematica programs

* Detailed description of the mathematical procedures underlying the twenty-eight programs written in Mathematica

* Appendix describing the use of ten notebooks to guide the reader through all the exercises.

This book is an essential text/reference for students, graduates and practitioners in engineering and applied mathematics interested in problems of ODEs in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-study resource for professionals and others seeking an understanding of how to use ODEs in modeling physical, biological, and economic phenomena.

Scientific Computing with MATLAB (R), Second Edition improves students' ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter. The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

Intended for anyone needing to apply statistical analysis to a large variety of science and engineering problems, this book shows how to use SPSS, MATLAB, STATISTICA and R for data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics. The 2nd edition includes the R language, a new section on bootstrap estimation methods and an improved treatment of tree classifiers, plus additional examples and exercises.

A state-of-the-art research monograph providing consistent treatment of supervisory control, by one of the world's leading groups in the area of Bayesian identification, control, and decision making.

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

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.

This book provides insight and enhanced appreciation of analysis, modeling and control of dynamic systems. The reader is assumed to be familiar with calculus, physics and some programming skills. It might develop the reader's ability to interpret physical significance of mathematical results in system analysis. The book also prepares the reader for more advanced treatment of subsequent knowledge in the automatic control field. Learning objectives are performance-oriented, using for this purpose interactive MATLAB and SIMULINK software tools. It presents realistic problems in order to analyze, design and develop automatic control systems. Learning with computing tools can aid theory and help students to think, analyze and reason in meaningful ways. The book is also complemented with classroom slides and MATLAB and SIMULINK exercise files to aid students to focus on fundamental concepts treated.

This book is intended for use as the textbook in a second course in applied statistics that covers topics in multiple regression and analysis of variance at an intermediate level. Generally, students enrolled in such courses are p- marily graduate majors or advanced undergraduate students from a variety of disciplines. These students typically have taken an introductory-level s- tistical methods course that requires the use a software system such as SAS for performing statistical analysis. Thus students are expected to have an - derstanding of basic concepts of statistical inference such as estimation and hypothesis testing. Understandably, adequate time is not available in a ?rst course in stat- tical methods to cover the use of a software system adequately in the amount of time available for instruction. The aim of this book is to teach how to use the SAS system for data analysis. The SAS language is introduced at a level of sophistication not found in most introductory SAS books. Important features such as SAS data step programming, pointers, and line-hold spe- ?ers are described in detail. The powerful graphics support available in SAS is emphasized throughout, and many worked SAS program examples contain graphic components.

This book provides anintroduction to multistate event history analysis. It is an extension of survival analysis, in which a single terminal event (endpoint) is considered and the time-to-event is studied. Multistate models focus on life histories or trajectories, conceptualized as sequences of states and sequences of transitions between states. Life histories are modeled as realizations of continuous-time Markov processes. The model parameters, transition rates, are estimated from data on event counts and populations at risk, using the statistical theory of counting processes.

The Comprehensive R Network Archive (CRAN) includes several packages for multistate modeling. This book is about "Biograph." The package is designed to (a) enhance exploratory analysis of life histories and (b) make multistate modeling accessible. The package incorporates utilities that connect to several packages for multistate modeling, including "survival," "eha," "Epi," "mvna," " etm," "mstate," "msm," and "TraMineR" for sequence analysis. The book is a hands-on presentation of "Biograph" and the packages listed. It is written from the perspective of the user. To help the user master the techniques and the software, a single data set is used to illustrate the methods and software. It is the subsample of the German Life History Survey, which was also used by Blossfeld and Rohwer in their popular textbook on event history modeling. Another data set, the Netherlands Family and Fertility Survey, is used to illustrate how "Biograph" can assist in answering questions on life paths of cohorts and individuals.

The book is suitable as a textbook for graduate courses on event history analysis and introductory courses on competing risks and multistate models. It may also be used as a self-study book. The R code used in the book is available online.

Frans Willekens is affiliated with the Max Planck Institute for Demographic Research (MPIDR) in Rostock, Germany. He is Emeritus Professor of Demography at the University of Groningen, a Honorary Fellow of the Netherlands Interdisciplinary Demographic Institute (NIDI) in the Hague, and a Research Associate of the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria. He is a member of Royal Netherlands Academy of Arts and Sciences (KNAW). He has contributed to the modeling and simulation of life histories, mainly in the context of population forecasting."

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. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become familiar with the MATLAB environment, and then you will begin to harness the power of MATLAB. You will learn the MATLAB language, starting with an introduction to variables, and how to manipulate numbers, vectors, matrices, arrays and character strings. You will learn about MATLAB's high-precision capabilities, and how you can use MATLAB to solve problems, making use of arithmetic, relational and logical operators in combination with the common functions and operations of real and complex analysis and linear algebra. You will learn to implement various numerical methods for optimization, interpolation and solving non-linear equations. You will discover how MATLAB can solve problems in differential and integral calculus, both numerically and symbolically, including techniques for solving ordinary and partial differential equations, and how to graph the solutions in brilliant high resolution. You will then expand your knowledge of the MATLAB language by learning how to use commands which enable you to investigate the convergence of sequences and series, and explore continuity and other analytical features of functions in one and several variables.

This small book addresses different kinds of datafiles, as commonly encountered in clinical research, and their data-analysis on SPSS Software. Some 15 years ago serious statistical analyses were conducted by specialist statisticians using ma- frame computers. Nowadays, there is ready access to statistical computing using personal computers or laptops, and this practice has changed boundaries between basic statistical methods that can be conveniently carried out on a pocket calculator and more advanced statistical methods that can only be executed on a computer. Clinical researchers currently perform basic statistics without professional help from a statistician, including t-tests and chi-square tests. With help of user-friendly software the step from such basic tests to more complex tests has become smaller, and more easy to take. It is our experience as masters' and doctorate class teachers of the European College of Pharmaceutical Medicine (EC Socrates Project Lyon France) that s- dents are eager to master adequate command of statistical software for that purpose. However, doing so, albeit easy, still takes 20-50 steps from logging in to the final result, and all of these steps have to be learned in order for the procedures to be successful.

MATLAB Mathematical Analysis is a reference book that presents the techniques of mathematical analysis through examples and exercises resolved with MATLAB software. The purpose is to give you examples of the mathematical analysis functions offered by MATLAB so that you can use them in your daily work regardless of the application. The book supposes proper training in the mathematics and so presents the basic knowledge required to be able to use MATLAB for calculational or symbolic solutions to your problems for a vast amount of MATLAB functions. The book begins by introducing the reader to the use of numbers, operators, variables and functions in the MATLAB environment. Then it delves into working with complex variables. A large section is devoted to working with and developing graphical representations of curves, surfaces and volumes. MATLAB functions allow working with two-dimensional and three-dimensional graphics, statistical graphs, curves and surfaces in explicit, implicit, parametric and polar coordinates. Additional work implements twisted curves, surfaces, meshes, contours, volumes and graphical interpolation. The following part covers limits, functions, continuity and numerical and power series. Then differentiation is addressed in one and several variables including differential theorems for vector fields. Thereafter the topic of integration is handled including improper integrals, definite and indefinite integration, integration in multiple variables and multiple integrals and their applications. Differential equations are exemplified in detail, Laplace transforms, Tayor series, and the Runga-Kutta method and partial differential equations.

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 Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving a short introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work with ease in differential and integral calculus in one and several variables. Among other core topics of calculus, you will use MATLAB to investigate convergence, find limits of sequences and series and, for the purpose of exploring continuity, limits of functions. Various kinds of local approximations of functions are introduced, including Taylor and Laurent series. Symbolic and numerical techniques of differentiation and integration are covered with numerous examples, including applications to finding maxima and minima, areas, arc lengths, surface areas and volumes. You will also see how MATLAB can be used to solve problems in vector calculus and how to solve differential and difference equations.

Python Algorithms, Second Edition explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science in a highly readable manner. It covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data structures that are built into the Python language are explained, and the user is shown how to implement and evaluate others.

This volume presents theoretical developments, applications and computational methods for the analysis and modeling in behavioral and social sciences where data are usually complex to explore and investigate. The challenging proposals provide a connection between statistical methodology and the social domain with particular attention to computational issues in order to effectively address complicated data analysis problems.
The papers in this volume stem from contributions initially presented at the joint international meeting JCS-CLADAG held in Anacapri (Italy) where the Japanese Classification Society and the Classification and Data Analysis Group of the Italian Statistical Society had a stimulating scientific discussion and exchange.

Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models.

The goal of input modeling is to find a stochastic model to describe a sequence ofmeasurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published.

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Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.