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For more than 30 years, this comprehensive manual has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. This sixth edition uses a slightly changed title, Text and Math into LaTeX, to emphasize the importance of text in mathematical/scientific composition. Sections that contained commands no longer much needed (such as \includeonly) and the introductory sections to PDF (now ubiquitous) have been omitted. Many sections are now enhanced with discussion of new and useful packages. An occasional encouragement for the reader to consult ChatGPT for confirmation on various points illustrates the positive relationship between ChatGPT and LaTeX. The new Chapter 17 describes recent developments that enhance, or replace, BibTeX and the new Appendix C, introduces the reader to ChatGPT. Key features: An example-based, visual approach and agentle introduction with the Short Course A detailed exposition of multiline math formulas with a Visual Guide A unified approach to TeX, LaTeX, and the AMS enhancements A quick introduction to creating presentations with formulas A detailed approach to creating illustrations Extras are provided on SpringerLink for the following chapters: 1, 2, 3, 4, 6, 7, 10, 11, 13, 14, 15, 16, 17, 18 and Appendices A, B. Readers must visit the HTML version of each chapter and access the Electronic Supplementary Material. Extras for Appendices A & B can be found in Extras for Chapter 18.

Written by an experienced operations research practitioner with a strong applied mathematics background, this book offers practical insights into how to approach optimization problems, how to develop intelligent and efficient mathematical models and algorithms, and how to implement and deliver software products to customers. With a focus on revealing the similarities and differences between academia and industry in mathematical modeling, the book provides useful tips and advice based on the author's extensive experience as a principal developer working to solve real-world optimization problems for several major high-tech companies.The book offers valuable food for thought for researchers and practical guidance for graduate students preparing for their future projects in the industry. It is also an essential resource for practitioners working in the industrial, business, and service sectors.

This book covers the basics of numerical methods. Avoiding the definition-theorem-proof style, it instead focuses on numerical examples and simple pseudo-codes. The text begins with a chapter on floating point arithmetic before moving on to discuss norms, conditions numbers, solutions of systems of equations, the least squares problem, eigenvalue problems, interpolation, numerical integration, ordinary differential equations, optimization (including a detailed case study), and practical error estimations. Exercises (partly in MATLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.

Learn how to leverage the scientific computing and data analysis capabilities of Python, its standard library, and popular open-source numerical Python packages like NumPy, SymPy, SciPy, matplotlib, and more. This book demonstrates how to work with mathematical modeling and solve problems with numerical, symbolic, and visualization techniques. It explores applications in science, engineering, data analytics, and more. Numerical Python, Third Edition, presents many case study examples of applications in fundamental scientific computing disciplines, as well as in data science and statistics. This fully revised edition, updated for each library's latest version, demonstrates Python's power for rapid development and exploratory computing due to its simple and high-level syntax and many powerful libraries and tools for computation and data analysis. After reading this book, readers will be familiar with many computing techniques, including array-based and symbolic computing, visualization and numerical file I/O, equation solving, optimization, interpolation and integration, and domain-specific computational problems, such as differential equation solving, data analysis, statistical modeling, and machine learning. What You'll Learn Work with vectors and matrices using NumPy Review Symbolic computing with SymPy Plot and visualize data with Matplotlib Perform data analysis tasks with Pandas and SciPy Understand statistical modeling and machine learning with statsmodels and scikit-learn Optimize Python code using Numba and Cython Who This Book Is For Developers who want to understand how to use Python and its ecosystem of libraries for scientific computing and data analysis.

This book is a self-guided tour of MATLAB for engineers and life scientists. It introduces the most commonly used programming techniques through biologically inspired examples. Although the text is written for undergraduates, graduate students and academics, as well as those in industry, will find value in learning MATLAB. The book takes the emphasis off of learning syntax so that the reader can focus more on algorithmic thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra class, there are short introductions to many of these concepts. Following a short history of computing, the MATLAB environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector operations. The core programming elements of MATLAB are introduced in three successive chapters on scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output of data, create professional quality graphics and find and use MATLAB toolboxes. Throughout, biomedical and life science examples are used to illustrate MATLAB's capabilities.

After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables.Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels.Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.

The book is intended to serve as an introductory course in group theory geared towards second-year university students. It aims to provide them with the background needed to pursue more advanced courses in algebra and to provide a rich source of examples and exercises. Studying group theory began in the late eighteenth century and is still gaining importance due to its applications in physics, chemistry, geometry, and many fields in mathematics. The text is broadly divided into three parts. The first part establishes the prerequisite knowledge required to study group theory. This includes topics in set theory, geometry, and number theory. Each of the chapters ends with solved and unsolved exercises relating to the topic. By doing this, the authors hope to fill the gaps between all the branches in mathematics that are linked to group theory. The second part is the core of the book which discusses topics on semigroups, groups, symmetric groups, subgroups, homomorphisms, isomorphism, and Abelian groups. The last part of the book introduces SAGE, a mathematical software that is used to solve group theory problems. Here, most of the important commands in SAGE are explained, and many examples and exercises are provided.

This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author's lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

This book provides a unique tour of university mathematics with the help of Python. Written in the spirit of mathematical exploration and investigation, the book enables students to utilise Python to enrich their understanding of mathematics through: Calculation: performing complex calculations and numerical simulations instantly Visualisation: demonstrating key theorems with graphs, interactive plots and animations Extension: using numerical findings as inspiration for making deeper, more general conjectures. This book is for all learners of mathematics, with the primary audience being mathematics undergraduates who are curious to see how Python can enhance their understanding of core university material. The topics chosen represent a mathematical overview of what students typically study in the first and second years at university, namely analysis, calculus, vector calculus and geometry, differential equationsand dynamical systems, linear algebra, abstract algebra and number theory, probability and statistics. As such, it can also serve as a preview of university mathematics for high-school students. The prerequisites for reading the book are a familiarity with standard A-Level mathematics (or equivalent senior high-school curricula) and a willingness to learn programming. For mathematics lecturers and teachers, this book is a useful resource on how Python can be seamlessly incorporated into the mathematics syllabus, assuming only basic knowledge of programming.

This textbook provides a compact but comprehensive treatment that guides students through applied numerical analysis, using MATLAB®/Simulink®. Ideal as a hands-on source for courses in Numerical Analysis, this text focuses on solving problems using market-standard software, corresponding to all key concepts covered in the classroom. The author uses his extensive classroom experience to guide students toward deeper understanding of key concepts, while they gain facility with software they will need to master for later studies and practical use in their engineering careers.

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.

This book discusses the development of the Rosenbrock—Wanner methods from the origins of the idea to current research with the stable and efficient numerical solution and differential-algebraic systems of equations, still in focus. The reader gets a comprehensive insight into the classical methods as well as into the development and properties of novel W-methods, two-step and exponential Rosenbrock methods. In addition, descriptive applications from the fields of water and hydrogen network simulation and visual computing are presented.

This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere. The contents comprise the proceedings of the 2018 INdAM “International Meeting on Numerical Semigroups”, held in Cortona, Italy. Talks at the meeting centered not only on traditional types of numerical semigroups, such as Arf or symmetric, and their usual properties, but also on related types of semigroups, such as affine, Puiseux, Weierstrass, and primary, and their applications in other branches of algebra, including semigroup rings, coding theory, star operations, and Hilbert functions. The papers in the book reflect the variety of the talks and derive from research areas including Semigroup Theory, Factorization Theory, Algebraic Geometry, Combinatorics, Commutative Algebra, Coding Theory, and Number Theory. The book is intended for researchers and students who want to learn about recent developments in the theory of numerical semigroups and its connections with other research fields.

This book discusses enterprise hierarchies, which view a target system with varying degrees of abstraction. These requirement refinement hierarchies can be represented by goal models. It is important to verify that such hierarchies capture the same set of rationales and intentions and are in mutual agreement with the requirements of the system being designed. The book also explores how hierarchies manifest themselves in the real world by undertaking a data mining exercise and observing the interactions within an enterprise. The inherent sequence-agnostic property of goal models prevents requirement analysts from performing compliance checks in this phase as compliance rules are generally embedded with temporal information. The studies discussed here seek to extract finite state models corresponding to goal models with the help of model transformation. The i•ToNuSMV tool implements one such algorithm to perform model checking on i• models. In turn, the AFSR framework provides a new goal model nomenclature that associates semantics with individual goals. It also provides a reconciliation machinery that detects entailment or consistency conflicts within goal models and suggests corrective measures to resolve such conflicts. The authors also discuss how the goal maintenance problem can be mapped to the state-space search problem, and how A• search can be used to identify an optimal goal model configuration that is free from all conflicts. In conclusion, the authors discuss how the proposed research frameworks can be extended and applied in new research directions. The GRL2APK framework presents an initiative to develop mobile applications from goal models using reusable code component repositories.

The Distributed and Unified Numerics Environment (Dune) is a set of open-source C++ libraries for the implementation of finite element and finite volume methods. Over the last 15 years it has become one of the most commonly used libraries for the implementation of new, efficient simulation methods in science and engineering. Describing the main Dune libraries in detail, this book covers access to core features like grids, shape functions, and linear algebra, but also higher-level topics like function space bases and assemblers. It includes extensive information on programmer interfaces, together with a wealth of completed examples that illustrate how these interfaces are used in practice. After having read the book, readers will be prepared to write their own advanced finite element simulators, tapping the power of Dune to do so.

This volume, Statistical Methods in Psychiatry Research and SPSS, now going into its second edition, has been helping psychiatrists expand their knowledge of statistical methods and fills the gaps in their applications as well as introduces data analysis software. It addresses the statistical needs of physicians and presents a simplified approach. The book emphasizes the classification of fundamental statistical methods in psychiatry research that are precise and simple. Professionals in the field of mental health and allied subjects without any mathematical background will easily understand all the relevant statistical methods and carry out the analysis and interpret the results in their respective field without consulting any statistician. This new volume has over 100 pages of new material, including several new appendixes.The sequence of the chapters, the sections within the chapters, the subsections within the sections, and the points within the subsections have all been arranged to help professionals in classification refine their knowledge in statistical methods and fills the gaps.

This book introduces recently developed mixed finite element methods for large-scale geophysical flows that preserve essential numerical properties for accurate simulations. The methods are presented using standard models of atmospheric flows and are implemented using the Firedrake finite element library. Examples guide the reader through problem formulation, discretisation, and automated implementation. The so-called “compatible” finite element methods possess key numerical properties which are crucial for real-world operational weather and climate prediction. The authors summarise the theory and practical implications of these methods for model problems, introducing the reader to the Firedrake package and providing open-source implementations for all the examples covered. Students and researchers with engineering, physics, mathematics, or computer science backgrounds will benefit from this book. Those readers who are less familiar with the topic are providedwith an overview of geophysical fluid dynamics.

Heuristics are strategies using readily accessible, loosely applicable information to control problem solving. Algorithms, for example, are a type of heuristic. By contrast, Metaheuristics are methods used to design Heuristics and may coordinate the usage of several Heuristics toward the formulation of a single method. GRASP (Greedy Randomized Adaptive Search Procedures) is an example of a Metaheuristic. To the layman, heuristics may be thought of as ‘rules of thumb'but despite its imprecision, heuristics is a very rich field that refers to experience-based techniques for problem-solving, learning, and discovery. Any given solution/heuristic is not guaranteed to be optimal but heuristic methodologies are used to speed up the process of finding satisfactory solutions where optimal solutions are impractical. The introduction to this Handbook provides an overview of the history of Heuristics along with main issues regarding the methodologies covered. This is followed by Chapters containing various examples of local searches, search strategies and Metaheuristics, leading to an analyses of Heuristics and search algorithms. The reference concludes with numerous illustrations of the highly applicable nature and implementation of Heuristics in our daily life. Each chapter of this work includes an abstract/introduction with a short description of the methodology. Key words are also necessary as part of top-matter to each chapter to enable maximum search engine optimization. Next, chapters will include discussion of the adaptation of this methodology to solve a difficult optimization problem, and experiments on a set of representative problems.

This second edition is an intensively revised and updated version of the book MATLAB® and Design Recipes for Earth Sciences. It aims to introduce students to the typical course followed by a data analysis project in earth sciences. A project usually involves searching relevant literature, reviewing and ranking published books and journal articles, extracting relevant information from the literature in the form of text, data, or graphs, searching and processing the relevant original data using MATLAB, and compiling and presenting the results as posters, abstracts, and oral presentations using graphics design software. The text of this book includes numerous examples on the use of internet resources, on the visualization of data with MATLAB, and on preparing scientific presentations. As with the book MATLAB Recipes for Earth Sciences–4rd Edition (2015), which demonstrates the use of statistical and numerical methods on earth science data, this book uses state-of-the art software packages, including MATLAB and the Adobe Creative Suite, to process and present geoscientific information collected during the course of an earth science project. The book's supplementary electronic material (available online through the publisher's website) includes color versions of all figures, recipes with all the MATLAB commands featured in the book, the example data, exported MATLAB graphics, and screenshots of the most important steps involved in processing the graphics.

The contributions gathered here provide an overview of current research projects and selected software products of the Fraunhofer Institute for Algorithms and Scientific Computing SCAI. They show the wide range of challenges that scientific computing currently faces, the solutions it offers, and its important role in developing applications for industry. Given the exciting field of applied collaborative research and development it discusses, the book will appeal to scientists, practitioners, and students alike. The Fraunhofer Institute for Algorithms and Scientific Computing SCAI combines excellent research and application-oriented development to provide added value for our partners. SCAI develops numerical techniques, parallel algorithms and specialized software tools to support and optimize industrial simulations. Moreover, it implements custom software solutions for production and logistics, and offers calculations on high-performance computers. Its services and products are based on state-of-the-art methods from applied mathematics and information technology.

This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.

This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite. Taking a hands-on approach, the reader is guided from basic concepts to modern research topics. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. The book begins with an efficient tutorial introduction to Mathematica, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at:http://library.wolfram.com/infocenter/Books/9563/The author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum, though references are included for the inquisitive reader. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many of the chapters are especially useful as reference material for senior undergraduate independent project work. New to the second edition:Since the first printing of this book in 2007, Mathematica has evolved from version 6.0 to version 11.2 in 2017. Accordingly, the second edition has been thoroughly updated and new material has been added. There are many more applications, examples and exercises, all with solutions, and new sections on series solutions of ordinary differential equations and Newton fractals, have been added. There are also new chapters on delay differential equations, image processing, binary oscillator computing, and simulation with Wolfram SystemModeler. Praise for the first edition:“[This book's] content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the firstplace.” —Dynamical Systems Magazine“This book presents an original, cheap and powerful solution to the problem of analysis of large data sets.” —Studia Universitatis Babes'-Bolyai Mathematica“The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.” —Datafile, The Journal of the HPCC

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.

This textbook introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked-out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented; - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and - the third presents more challenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool.This new edition has been extensively revised and updated, and includes new chapters with problems and worked examples.

This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems. All derivation processes are presented in detail to aid in comprehension. The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice.

Berthold Heinrich stellt die mathematischen und zeichnerischen Grundlagen für die Darstellung von Objekten im Raum auf kariertem Papier vor. Dabei präsentiert er auch die Nutzung von Software. In der Schule wird oft kariertes Papier als Raster zur Darstellung von Flächen und Körpern genutzt. Allerdings werden, selbst in einigen Druckwerken, z.B. die entstehenden Ellipsen und Winkelbögen ungenau gezeichnet oder eine Kugelkontur falsch als Kreis dargestellt. Im vorliegenden Essential werden die korrekten Verfahren sowohl theoretisch als auch an konkreten Beispielen vorgestellt und können meist direkt umgesetzt werden. Einige aufwändigere Abläufe stellt der Autor anschaulich an Beispielen dar.

Learn from state-of-the-art examples in robotics, motors, detection filters, chemical processes, aircraft, and spacecraft. This is a practical reference for industry engineers using MATLAB to solve everyday problems. With MATLAB Recipes: A Problem-Solution Approach you will review contemporary MATLAB coding including the latest language features and use MATLAB as a software development environment including code organization, GUI development, and algorithm design and testing. This book provides practical guidance for using MATLAB to build a body of code you can turn to time and again for solving technical problems in your line of work. Develop algorithms, test them, visualize the results, and pass the code along to others to create a functional code base for your firm.

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application. Answers may be verified using Sage. The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®. Sage is open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity withany programming language is a plus. Moreover, the code can be written using any web browser and is therefore useful with Laptops, Tablets, iPhones, Smartphones, etc. All Sage code that is presented in the text is openly available on SpringerLink.com.

This comprehensive and stimulating introduction to Matlab, a computer language now widely used for technical computing, is based on an introductory course held at Qian Weichang College, Shanghai University, in the fall of 2014. Teaching and learning a substantial programming language aren't always straightforward tasks. Accordingly, this textbook is not meant to cover the whole range of this high-performance technical programming environment, but to motivate first- and second-year undergraduate students in mathematics and computer science to learn Matlab by studying representative problems, developing algorithms and programming them in Matlab. While several topics are taken from the field of scientific computing, the main emphasis is on programming. A wealth of examples are completely discussed and solved, allowing students to learn Matlab by doing: by solving problems, comparing approaches and assessing the proposed solutions.

Software reliability is one of the most important characteristics of software product quality. Its measurement and management technologies during the software product life cycle are essential to produce and maintain quality/reliable software systems. Part 1 of this book introduces several aspects of software reliability modeling and its applications. Hazard rate and nonhomogeneous Poisson process (NHPP) models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are discussed with reference to incorporating practical factors of dynamic software behavior. Three software management problems are presented as application technologies of software reliability models: the optimal software release problem, the statistical testing-progress control, and the optimal testing-effort allocation problem.Part 2 of the book describes several recent developments in software reliability modeling andtheir applications as quantitative techniques for software quality/reliability measurement and assessment. The discussion includes a quality engineering analysis of human factors affecting software reliability during the design review phase, which is the upper stream of software development, as well as software reliability growth models based on stochastic differential equations and discrete calculus during the testing phase, which is the lower stream. The final part of the book provides an illustration of quality-oriented software management analysis by applying the multivariate analysis method and the existing software reliability growth models to actual process monitoring data.

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™.The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek 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.

Legged robots are a promising locomotion system, capable of performing tasks that conventional vehicles cannot. Even more exciting is the fact that this is a rapidly developing field of study for researchers from a variety of disciplines. However, only a few books have been published on the subject of multi-legged robots. The main objective of this book is to describe some of the major control issues concerning walking robots that the authors have faced over the past 10 years. A second objective is to focus especially on very large hydraulically driven hexapod robot locomotion weighing more than 2,000 kg, making this the first specialized book on this topic. The 10 chapters of the book touch on diverse relevant topics such as design aspects, implementation issues, modeling for control, navigation and control, force and impedance control-based walking, fully autonomous walking, walking and working tasks of hexapod robots, and the future of walking robots. The construction machines of the future will very likely resemble hydraulically driven hexapod robots like the ones described in this book – no longer science fiction but now a reality.

This is a book for people who love finite elements and MATLAB I. We will use the popular computer package MATLAB as a matrix calculator for doing finite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulationsespecially when applying the boundary conditions. In particular the steps ofthe finite element method are emphasized in this book. The reader will not find ready-made MATLAB programsfor use as blackboxes. Insteadstep-by-stepsolutionsoffiniteelementprob­ lems are examined in detail using MATLAB. Problems from linearelastic structural mechanics are used throughout the book. The emphasis is not on mass computation or programming, but rather on leaming the finite element method computations and understanding of the underlying concepts. In addition to MATLAB, the MATLAB Symbolic Math'Ioolbox? is used in Chapters 12, 13, and 14. Many types of finite elements are studied in this book including the spring ele­ ment, the bar element, two-dimensional and three-dimensional truss elements, plane and space beam and frame elements, two-dimensional elasticity elements for plane stress and plane strain problems,and one three-dimensional solid element. Each chap­ ter deals with only one type ofelement. Also each chapter starts with a summary of the basic equations for the elementfollowed by a numberofexamples demonstrating the use of the element using the provided MATLAB functions. Special MATLAB functions for finite elements are provided as M-files on the accompanying CD-ROM to be used in the examples.

Das Buch wendet sich an alle, die empirisch erhobenes Datenmaterial mit ihrem PC statistisch auswerten wollen. Als anwendungsorientierte Einführung ist es so konzipiert, daß es sowohl als Begleitlektüre für Lehrveranstaltungen als auch zum Selbststudium geeignet ist. Thema ist der Einsatz des Programmsystems'SPSS für Windows'zur statistischen Datenanalyse, wobei die aktuelle Version 8 zu Grunde gelegt wird. Vorzug des Buches ist, dass am Beispiel einer empirischen Untersuchung die möglichen Anforderungen dargestellt werden, die Form der ausgegebenen Analyseergebnisse erläutert und die Interpretation angegeben wird. Es werden vom Leser keine besonderen Erfahrungen im Umgang mit dem PC oder der Software vorausgesetzt. Ein zuverlässiger Leitfaden zur aktuellen Version 8 von'SPSS für Windows', sei es unter Windows NT oder in der'kleinen'Windowswelt.

Vor ziemlich genau zehn Jahren stand ich (im Zusammenhang mit Stabilitätsuntersu­ chungen an Hamiltonschen Systemen) vor der Aufgab~, komplizierte Koordinaten­ transformationen bis zu höheren Ordnungen zu berechnen. Nach mehrmonatigen, fruchtlosen Versuchen von Hand - und Blöcken voll Formeln - war ich dabei, die Flinte ins Kom zu werfen. Durch einen Zufall wurde ich aber von Stan Lomecki (im Militärdienst!) auf das Computer-Algebra-Programm Reduce aufmerksam gemacht. Unter Ausnutzung vieler Tricks gelang mir damit tatsächlich, die Transformationen und die Stabilitätsdiskussion symbolisch zu Ende zu führen. Schon damals fragte ich mich, weshalb derartige Programme bei Ingenieuren und Wissenschaftlern bzw. Wissenschaftlerinnen so wenig bekannt sind. Viele Problem­ stellungen dieser Disziplinen führen auf Rechnungen, die sich von Hand höchstens mühevoll und mit großem Zeitaufwand bewältigen lassen. Mit Hilfe eines Computer­ Algebra-Programms können sie oft rasch symbolisch gelöst werden. Falls dies nicht möglich ist, so resultiert mindestens eine Vereinfachung, bevor eventuell mit dem grö­ beren Werkzeug der Numerik weitergearbeitet wird.

In diesem Buch finden Sie alles, was Sie als Maple-Anwender wissen müssen: Als Neueinsteiger finden Sie eine ausführliche Einführung in die Fähigkeiten des Systems. Als versierter Benutzer können Sie die genaue Bedeutung der verschiedenen Parameter und Optionen für einen bestimmten Befehl nachschauen. Und als'Quereinsteiger'mit Mathematica-Kenntnissen können Sie nachschauen, wie die ihm bekannten Befehle in Maple heißen. Sämtliche Befehle aller Maple-Versionen bis Maple V 3 sind hier sowohl systematisch als auch alphabetisch aufgelistet und erklärt, Bezugs- und Informationsquellen sowie ein Glossar runden das Werk ab, das neben jedem Maple-Rechner liegen sollte.

This book is intended for undergraduates and young researchers who wish to understand the role that different branches of physics and mathematics play in the execution of actual experiments. The unique feature of the book is that all the subjects addressed are strictly interconnected within the context of the execution of a single experiment with very high accuracy, namely the redetermination of the Avogadro constant NA, one of the fundamental physical constants. The authors illustrate how the basic laws of physics are applied to describe the behavior of the quantities involved in the measurement of NA and explain the mathematical reasoning and computational tools that have been exploited. It is emphasized that all these quantities, although pertaining to a specific experiment, are of wide and general interest. The book is organized into chapters covering the interaction of electromagnetic radiation with single crystals, linear elasticity and anisotropy, propagation of thermal energy, anti-vibration mounting systems, and data analysis and B-spline interpolation. An essential feature is the focus on the role of Mathematica, an invaluable, fully integrated software environment for handling diverse scientific and technical computations.

Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re­ cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith­ mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv­ ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi­ mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all.

S is a powerful environment for the statistical and graphical analysis of data. It provides the tools to implement many statistical ideas that have been made possible by the widespread availability of workstations having good graphics and computational capabilities. This book is a guide to using S environments to perform statistical analyses and provides both an introduction to the use of S and a course in modern statistical methods. Implementations of S are available commercially in S-PLUS(R) workstations and as the Open Source R for a wide range of computer systems. The aim of this book is to show how to use S as a powerful and graphical data analysis system. Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics. Throughout, the emphasis is on presenting practical problems and full analyses of real data sets. Many of the methods discussed are state of the art approaches to topics such as linear, nonlinear and smooth regression models, tree-based methods, multivariate analysis, pattern recognition, survival analysis, time series and spatial statistics. Throughout modern techniques such as robust methods, non-parametric smoothing and bootstrapping are used where appropriate. This fourth edition is intended for users of S-PLUS 6.0 or R 1.5.0 or later. A substantial change from the third edition is updating for the current versions of S-PLUS and adding coverage of R. The introductory material has been rewritten to emphasis the import, export and manipulation of data. Increased computational power allows even more computer-intensive methods to be used, and methods such as GLMMs,

Dieses Buch zeigt dem Ingenieurstudenten - und dem in der Praxis tätigen Ingenieur - die für ihn wichtigen Einsatzmöglichkeiten der Computeralgebra und weist auf geeignete mathematische Formulierungen hin. Das geschieht anhand von Fragestellungen aus den Grundlagenfächern (Höhere Mathematik, Technische Mechanik, Physikalisches Praktikum, Elemente des Programmierens), für die der Leser auf diese Weise zugleich ein vertieftes Verständnis gewinnt.

MuPAD ist ein Computeralgebra-System, mit dem nicht nur Problemstellungen der Mathematik sondern auch mathematische Aufgaben in den Natur- und Ingenieurwissenschaften behandelt werden können. Das Tutorium für Einsteiger führt grundlegend in MuPAD ein (ab Version 3.0.). In nachvollziehbaren Schritten werden die wichtigsten Bausteine vorgestellt. Systemfunktionen, Graphik sowie Programmierung können Nutzer anhand zahlreicher Beispiele einüben. Zukünftige Änderungen und Erweiterungen werden unter http://www.mupad.de/doc.html dokumentiert.

This book explains the basic use of the software package called MuPAD and gives an insight into the power of the system. MuPAD is a so-called com­ puter algebra system, which is developed mainly by Sciface Software and the MuPAD Research Group of the University of Paderborn in Germany. This introduction addresses mathematicians, engineers, computer scientists, natural scientists and, more generally, all those in need of mathematical com­ putations for their education or their profession. Generally speaking, this book addresses anybody who wants to use the power of a modern computer algebra package. There are two ways to use a computer algebra system. On the one hand, you may use the mathematical knowledge it incorporates by calling system functions interactively. For example, you can compute symbolic integrals or generate and invert matrices by calling appropriate functions. They comprise the system's mathematical intelligence and may implement sophisticated al­ gorithms. Chapters 2 through 15 discuss this way of using MuPAD. On the other hand, with the help of MuPAD's programming language, you can easily add functionality to the system by implementing your own algorithms as MuPAD procedures. This is useful for special purpose applications if no ap­ propriate system functions exist. Chapters 16 through 18 are an introduction to programming in MuPAD.

The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as'symbolic and algebraic computation'or'formula manipulation'. Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms.

In many fields of modern mathematics specialised scientific software becomes increasingly important. Hence, tremendous effort is taken by numerous groups all over the world to develop appropriate solutions.This book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volume's other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general framework for modular systems.

Das Buch befaßt sich mit der nichtkooperativen Spieltheorie unter Zuhilfenahme eines Computer-Algebra-Systems (Mathematica). Der Schwerpunkt des Buches liegt bei der Bestimmung von Techniken und Algorithmen für die Lösung von Zweipersonenspielen und deren Implementierung am Rechner. Die Ideen werden anhand von Standardbeispielen wie das Gefangenendilemma, Krieg der Geschlechter oder Falke-Taube-Spiel illustriert und erklärt. Aber auch praktische Probleme, vor allem Inspektionssituationen, werden mittels Spieltheorie modelliert und mit Mathematica gelöst. Durch den algorithmischen Ansatz, und durch die enge Verknüpfung des Textes mit Mathematica-Notebooks wird dem Leser ein unterhaltsamer und nachvollziehbarer Zugang zu den grundlegenden Prinzipien der nichtkooperativen Spieltheorie geboten. Auf einer begleitenden Diskette befinden sich Mathematica-Notebooks sowie ein Mathematica-Package mit Implementierungen zu allen im Text entwickelten Algorithmen.

Mathematik lernen mit DERIVE entwickelt die mathematischen Grundlagen, die in den Natur- und Ingenieurwissenschaften benötigt werden, und ist gleichzeitig eine praktische Einführung in das Computer Algebra Programm DERIVE. Die Autoren legen auf zwei Aspekte von DERIVE besonderen Wert: Zum einen können Lernende DERIVE zu eigenen Untersuchungen nutzen, um grundlegende mathematische Ideen zu verstehen. Andererseits dient DERIVE als Werkzeug, um naturwissenschaftliche und technische Probleme zu lösen. Besonders nützlich für Lehrende und Lernende ist hierbei die Fülle von Aufgaben, die mitsamt ihren Lösungen in diesem Buch zu finden sind.Dieses Buch ist in erster Linie für diejenigen gedacht, die sich den Stoff der Sekundarstufe II erst aneignen müssen, um zur Hochschulreife zu gelangen. Es bietet aber auch jenen, die mit den angebotenen Inhalten aus der Analysis und der linearen Algebra schon vertraut sind, eine vorzügliche Gelegenheit, diese Themen, verbunden mit einem Einstieg in die Anwendung von DERIVE, zu wiederholen und zu vertiefen.Mathematik lernen mit DERIVE zeigt eine neue erfrischende Art, Mathematik zu lernen und zu lehren. Die Autoren haben als Mathematiklehrer an der Universität von Plymouth die Überzeugung gewonnen, dass der Einsatz von DERIVE einen wesentlichen Beitrag zur Verbesserung des Verständnisses und damit des Studienerfolges geleistet hat und immer noch leistet.Die vorliegende Übersetzung bezieht sich auf die deutschsprachige Version von DERIVE und berücksichtigt die aktuelle DERIVE Version 3.