Search

This book provides a practical and comprehensive introduction to computational problem solving from the viewpoints of practitioners in both academic and industrial worlds. The authors present scientific problem-solving using computation and aim to increase computational thinking, which is the mindset and skillset required to solve scientific problems with computational methodologies via model building, simulation, data analysis, and visualization using the Python programming language. Topics and examples span fundamental areas of physical science as well as contemporary topics including quantum computing, neural networks, machine learning, global warming, and energy balance. The book features unique and innovative techniques and practices including: intentional scaffolding to help beginners learn computational problem solving; multimodal computing environments including cloud-based platforms and just-in-time computing; emphasis and connection between both numerical and symbolic computations; and extensive exercise sets carefully designed for further exploration as project assignments or self-paced study. The book is suitable for introductory level readers in physical sciences, engineering, and related STEM disciplines. Specifically, the book is appropriate for use in either a standalone course on computation and modeling and as a resource for readers interested in learning about proven techniques in interactive computing.

Ce livre a pour but de présenter, à travers de très nombreux exemples, le langage de programmation informatique Python, à un public de non expert en programmation qui désire acquérir rapidement une autonomie dans la manipulation d'outils numériques puissants, pour calculer, tracer des courbes, présenter des résultats ou conduire une analyse physique. Il s'appuie sur des exemples tirés de la physique, couvrant des domaines enseignés au collège-lycée et en licence à l'université (et peut à ce titre intéresser les enseignants de ces deux niveaux qui auront à utiliser ce langage). Les programmes servant d'exemple sont courts, lisibles et fonctionnent à partir d'un fichier disponible en ligne. Le résultat de chaque programme est présenté, qu'il s'agisse de texte, de nombres ou de figures.

Maple is a comprehensive symbolic mathematics application which is well suited for demonstrating physical science topics and solving associated problems. Because Maple is such a rich application, it has a somewhat steep learning curve. Most existing texts concentrate on mathematics; the Maple help facility is too detailed and lacks physical science examples, many Maple-related websites are out of date giving readers information on older Maple versions. This book records the author's journey of discovery; he was familiar with SMath but not with Maple and set out to learn the more advanced application. It leads readers through the basic Maple features with physical science worked examples, giving them a firm base on which to build if more complex features interest them.

The book contains a detailed account of numerical solutions of differential equations of elementary problems of Physics using Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.

Computational properties of use to biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.

The contents of this book include chapters on floating point computer arithmetic, natural and generalized interpolating polynomials, uniform approximation, numerical integration, polynomial splines and many more. This book is intended for undergraduate and graduate students in institutes, colleges, universities and academies who want to specialize in this field. The readers will develop a solid understanding of the concepts of numerical methods and their application. The inclusion of Lagrane and Hermite approximation by polynomials, Trapezian rule, Simpsons rule, Gauss methods and Romberg`s methods with illustrative examples is a valuable resource for the readers. Each chapter ends with examples and test questions.

Philosophy of the Text This text has been designed to be an introductory survey of the basic concepts and applied mathematical methods of nonlinear science. Students in engineer­ ing, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this text. In an effort to provide the students with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of Maple V Release 4 applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The diskette which accompanies the text gives a wide variety of illustrative nonlinear examples solved with Maple. An accompanying laboratory manual of experimental activities keyed to the text allows the student the option of'hands on'experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated. The Level of the Text The essential prerequisites for the first eight chapters of this text would nor­ mally be one semester of ordinary differential equations and an intermediate course in classical mechanics.

The goal of this book is to teach undergraduate students how to use Scientific Notebook (SNB) to solve physics problems. SNB software combines word processing and mathematics in standard notation with the power of symbolic computation. As its name implies, SNB can be used as a notebook in which students set up a math or science problem, write and solve equations, and analyze and discuss their results. Written by a physics teacher with over 20 years experience, this text includes topics that have educational value, fit within the typical physics curriculum, and show the benefits of using SNB. This easy-to-read text: Provides step-by-step instructions for using Scientific Notebook (SNB) to solve physics problems Features examples in almost every section to enhance the reader's understanding of the relevant physics and to provide detailed instructions on using SNB Follows the traditional physics curriculum, so it can be used to supplement teaching at all levels of undergraduate physics Includes many problems taken from the author's class notes and research Aimed at undergraduate physics and engineering students, this text teaches readers how to use SNB to solve some everyday physics problems.

Appropriately for a book having the title'Computer Simulation Methods in Theoretical Physics', this book begins with a disclai­ mer. It does not and cannot give a complete introduction to simu­ lational physics. This exciting field is too new and is expanding too rapidly for even an attempt to be made. The intention here is to present a selection of fundamental techniques that are now being widely applied in many areas of physics, mathematics, chem­ istry and biology. It is worth noting that the methods are not only applicable in physics. They have been successfully used in other sciences, showing their great flexibility and power. This book has two main chapters (Chaps. 3 and 4) dealing with deterministic and stochastic computer simulation methods. Under the heading'deterministic'are collected methods involving classical dynamics, i.e. classical equations of motion, which have become known as the molecular dynamics simulation method. The se­ cond main chapter deals with methods that are partly or entirely of a stochastic nature. These include Brownian dynamics and the Monte Carlo method. To aid understanding of the material and to develop intuition, problems are included at the end of each chapter. Upon a first reading, the reader is advised to skip Chapter 2, which is a general introduction to computer simUlation methods.

Computational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural processes that do not have analytic solutions. The next step beyond Landau's First Course in Scientific Computing and a follow-up to Landau and Páez's Computational Physics, this text presents a broad survey of key topics in computational physics for advanced undergraduates and beginning graduate students, including new discussions of visualization tools, wavelet analysis, molecular dynamics, and computational fluid dynamics. By treating science, applied mathematics, and computer science together, the book reveals how this knowledge base can be applied to a wider range of real-world problems than computational physics texts normally address. Designed for a one- or two-semester course, A Survey of Computational Physics will also interest anyone who wants a reference on or practical experience in the basics of computational physics. Accessible to advanced undergraduates Real-world problem-solving approach Java codes and applets integrated with text Companion Web site includes videos of lectures

More stimulating mathematics puzzles from bestselling author Paul NahinHow do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

Written by an experienced physicist who is active in applying computer algebra to relativistic astrophysics and education, this is the resource for mathematical methods in physics using MapleTM and MathematicaTM. Through in-depth problems from core courses in the physics curriculum, the author guides students to apply analytical and numerical techniques in mathematical physics, and present the results in interactive graphics. Around 180 simulating exercises are included to facilitate learning by examples. This book is a must-have for students of physics, electrical and mechanical engineering, materials scientists, lecturers in physics, and university libraries. • Free online MapleTM material at http://www.wiley-vch.de/templates/pdf/maplephysics.zip • Free online MathematicaTM material at http://www.wiley-vch.de/templates/pdf/physicswithmathematica.zip • Solutions manual for lecturers available at www.wiley-vch.de/supplements/

Computers are one of the most important tools available to physicists, whether for calculating and displaying results, simulating experiments, or solving complex systems of equations. Introducing students to computational physics, this textbook, first published in 2006, shows how to use computers to solve mathematical problems in physics and teaches students about choosing different numerical approaches. It also introduces students to many of the programs and packages available. The book relies solely on free software: the operating system chosen is Linux, which comes with an excellent C++ compiler, and the graphical interface is the ROOT package available for free from CERN. This broad scope textbook is suitable for undergraduates starting on computational physics courses. It includes exercises and many examples of programs. Online resources at www.cambridge.org/0521828627 feature additional reference information, solutions, and updates on new techniques, software and hardware used in physics.

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

Arithmetic Applied Mathematics deals with concepts of arithmetic applied mathematics and uses a computer, rather than a continuum, approach to the deterministic theories of particle mechanics. Models of classical physical phenomena are formulated from both Newtonian and special relativistic mechanics using only arithmetic. Definitions of energy and momentum are presented that are identical to those of continuum mechanics. Comprised of nine chapters, this book begins by exploring discrete modeling as it relates to Newtonian mechanics and special relativistic mechanics, paying particular attention to gravity. The reader is then introduced to long-range forces such as gravitation and short-range forces such as molecular attraction and repulsion; the N-body problem; and conservative and non-conservative models of complex physical phenomena. Subsequent chapters focus on the foundational concepts of special relativity; arithmetic special relativistic mechanics in one space dimension and three space dimensions; and Lorentz invariant computations. This monograph will be of interest to students and practitioners in the fields of mathematics and physics.

This book series in the rapidly growing field of computational physics offers up-to-date (submitted to the publisher by electronic mail) reviews for the researcher.The first volume, written by authors from four continents, emphasizes statistical physics. For example, Ising problems are reviewed where theoretical approaches led to contradictory approaches and only quality computing answered who is right. In addition, fields as diverse as neural networks, granular materials, and computer algebra are reviewed.The next volume on percolation and other fields is already in preparation.