الصفحة 1
الصفحة 1
Multibody Mechanics and Visualization
Multibody Mechanics and Visualization is designed to appeal to computer-savvy students who will acquire significant skills in mathematical and physical modelling of mechanical systems in the process of producing attractive computer simulations and animations.
Modeling and Simulation in Scilab
Scilab is a free open-source software package for scientific computation. It includes hundreds of general purpose and specialized functions for numerical computation, organized in libraries called toolboxes, which cover such areas as simulation, optimization, systems and control, and signal processing. One important Scilab toolbox is Scicos. Scicos provides a block diagram graphical editor for the construction and simulation of dynamical systems. The objective of this book is to provide a tutorial for the use of Scilab/Scicos with a special emphasis on modeling and simulation tools. The book is divided into two parts. The first part concerns Scilab and includes a tutorial covering the language features, the data structures and specialized functions for doing graphics, importing, exporting data and interfacing external routines. It also covers in detail Scilab numerical solvers for ordinary differential equations and differential-algebraic equations. Even though the emphasis is placed on modeling and simulation applications, this part provides a global view of Scilab. The second part is dedicated to modeling and simulation of dynamical systems in Scicos. This type of modeling tool is widely used in industry because it provides a means for constructing modular and reusable models. This part contains a detailed description of the editor and its usage, which is illustrated through numerous examples.
Introduction to the Tools of Scientific Computing
The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike widely used standard approaches, it does not focus on any particular language but aims to explain the key underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and MATLAB to Maple. This includes different approaches to distributed computing.
Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
Algebraic Geometry is the study of systems of polynomial equations in one or more variables.The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
Generalized collocations methods : Solutions to nonlinear problems
This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and pollution. Based on a unified approach combining modeling, mathematical methods, and scientific computation, each chapter begins with several examples and problems solved by computational methods; full details of the solution techniques used are given. The last section of each chapter provides problems and exercises giving readers the opportunity to practice using the mathematical tools already presented.
Fuzzy Probability and Statistics
This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions.
Experimenting with Dynamic Macromodels : Growth and Cycles
This book presents a macroeconomic dynamic model à la Solow-Swan, including the market for labour, in a discrete time structure. Labour supply is modelled as a reversed S curve (derived in the appendix). The models are expanded to include expenditure on R&D (thus endogenous technical progress), and public expenditure on infrastructures. For each of the three models, numerical simulations are implemented in MAPLE, and the results are shown in time series figures, which make it easy to detect that even small changes in the parameters produce responses in the time behaviour of the main variables: from steady growth, to regular cycles, to chaotic-like time paths. The simulations show that cycles do not promote material welfare, as measured by total undiscounted consumption along the time horizon, and that the comparative action of R&D versus public expenditure is strictly linked to the values assigned to the parameters.
Dynamical Systems with Applications Using Mathematica®
Dynamical Systems with Applications using Mathematica® provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material.
Cours doptique : Simulations et exercices résolus avec Maple, Matlab, Mathematica, Mathcad = Optics course: Simulations and exercises solved with Maple, Matlab, Mathematica, Mathcad
Intended for students at the L and M levels of the university as well as for engineers wishing to study certain subjects in greater depth. It covers all the themes of a traditional optics course, from geometric optics to holography, interference, diffraction, coherence and the use of the Fourier transform for spectroscopy. The presentation is developed from mathematical models deriving from typical situations and fundamental examples which are presented in the form of computer programs ready to be implemented. These programs are also available on the CD accompanying the book, for each of the following scientific programming environments: Matlab, Maple, Mathematica and Mathcad. Thus, the reader will be able to modify the parameters of the examples proposed to adapt them to new situations.
Computer Algebra Recipes for Mathematical Physics
Over two hundred novel and innovative computer algebra worksheets or ""recipes"" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn.
Computer Algebra Recipes : An Introductory Guide to the Mathematical Models of Science
Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry.
Computer Algebra Recipes : An Advanced Guide to Scientific Modeling
The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking.
Computer algebra in scientific computing ; Vol. 3718 ; 8th International workshop, CASC 2005, Kalamata, Greece, September 12-16, 2005, Proceedings
This volume contains the proceedings of the CASC 2005 continued a tradition — started in 1998 — of international con-ferences on the latest advances in the application of computer algebra systems(CASs) and methods to the solution of various problems in scientific computing.The methods of scientific computing play an important role in research andengineering applications in the natural and the engineering sciences. The signif-icance and impact of computer algebra methods and computer algebra systemsfor scientific computing has increased considerably in recent times. Nowadays,such general-purpose computer algebra systems as Maple, Magma, Mathematica,MuPAD, Singular, CoCoA and others enable their users to solve the followingthree important tasks within a uniform framework:(a) symbolic manipulation;(b) numerical computation;(c) visualization. The result of this job is reflected in this volume, which contains revised versionsof the accepted papers. The collection of papers included in the proceedingscovers various topics of computer algebra methods, algorithms, and softwareapplied to scientific computing:
Computational Probability : Algorithms and Applications in the Mathematical Sciences
Computational probability encompasses data structures and algorithms that have emerged over the past decade that allow researchers and students to focus on a new class of stochastic problems. COMPUTATIONAL PROBABILITY is the first book that examines and presents these computational methods in a systematic manner. The techniques described here address problems that require exact probability calculations, many of which have been considered intractable in the past. The first chapter introduces computational probability analysis, followed by a chapter on the Maple computer algebra system. The third chapter begins the description of APPL, the probability modeling language created by the authors. The book ends with three applications-based chapters that emphasize applications in survival analysis and stochastic simulation.
Computational Ergodic Theory
Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory.
Maple and Mathematica : A Problem Solving Approach for Mathematics
the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. the history of computing the number began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - prove the result sthatahumancanobtain without anytechnology
Calculus of one variable
Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas.
