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.

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 Optimization Techniques introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. It begins by introducing the MATLAB environment and the structure of MATLAB programming before moving on to the mathematics of optimization. The central part of the book is dedicated to MATLAB's Optimization Toolbox, which implements state-of-the-art algorithms for solving multiobjective problems, non-linear minimization with boundary conditions and restrictions, minimax optimization, semi-infinitely constrained minimization and linear and quadratic programming. A wide range of exercises and examples are included, illustrating the most widely used optimization methods.

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.

"

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.

Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run several times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. Over 100 numerical examples are presented as part of the appendix to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. Very little has been published in the area of computer Monte Carlo simulation methods, and this book will appeal to students and researchers in the fields of Mathematics and Statistics.

This book provides a complete and comprehensive reference/guide to Pyomo (Python Optimization Modeling Objects) for both beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. The text illustrates the breadth of the modeling and analysis capabilities that are supported by the software and support of complex real-world applications. Pyomo is an open source software package for formulating and solving large-scale optimization and operations research problems. The text begins with a tutorial on simple linear and integer programming models. A detailed reference of Pyomo's modeling components is illustrated with extensive examples, including a discussion of how to load data from data sources like spreadsheets and databases. Chapters describing advanced modeling capabilities for nonlinear and stochastic optimization are also included. The Pyomo software provides familiar modeling features within Python, a powerful dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions. The software supports a different modeling approach than commercial AML (Algebraic Modeling Languages) tools, and is designed for flexibility, extensibility, portability, and maintainability but also maintains the central ideas in modern AMLs.

The theme of the meeting was Statistical Methods for the Analysis of Large Data-Sets . In recent years there has been increasing interest in this subject; in fact a huge quantity of information is often available but standard statistical techniques are usually not well suited to managing this kind of data. The conference serves as an important meeting point for European researchers working on this topic and a number of European statistical societies participated in the organization of the event.
The book includes 45 papers from a selection of the 156 papers accepted for presentation and discussed at the conference on Advanced Statistical Methods for the Analysis of Large Data-sets. "

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."

Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new sections, in addition to fully-updated examples, tables, figures, and a revised appendix. Intended primarily for practitioners, this book does not require sophisticated mathematical skills or deep understanding of the underlying theory and methods nor does it discuss alternative technologies for reasoning under uncertainty. The theory and methods presented are illustrated through more than 140 examples, and exercises are included for the reader to check his or her level of understanding. The techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.

The interaction of the solar and heat radiation with the atmosphere and surface is the subject of the book. It is useful also for wide circle scientists involved in environmental studies. The book contains the description of 17 computer studying programs supporting different topics of courses. It includes only the base ground for comprehension of key topics and provides the accomplishment of practical works with using specially elaborated computer programs. Themes of practical works reflect main sections of mentioned courses of lectures. The packet of computer programs is added for solution of direct and inverse problems. It promotes deep and reliable comprehension of corresponding topics by students. All described approaches and computer programs are valuable resources for solving radiative transfer problems and they could be used by students for courses and diploma studies concerned atmospheric optics.

Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple (TM). The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovsek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.

This book presents methods for computing correlation equations. All the topics treated hefe are eluci dated in terms of concrete examples, which have been chosen, for the most part, from the Held of analysis of the mechanical properties of steel, wood, and other materials. A necessary prerequisite for any study of correlation equations is so me knowledge of the moments of random variables. In the Appendix, there is provided a brief treatment of moments, as well as a discussion of the simplest methods of computing them. We have paid particular attention in this book to the techniques of computing correlation equations, and to the use of tables for alleviating the computationalload. The mathematical bases of the methods used in setting up correlation equations are expounded in the books cited at the end of this volume. A. M. December 1965 PIe ase note that the abbreviation 19 is used in this book to designate the logarithm to base ten, Note further that the comma has been retained as the decimal point in tabular material."

Separation of signal from noise is the most fundamental problem in data analysis, arising in such fields as: signal processing, econometrics, actuarial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, with extensions to local likelihood and density estimation. Practical information is also included on how to implement these methods in the programs S-PLUS and LOCFIT.

PAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a "manual" giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.