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Author: Akihito Kikuchi
Publisher: Springer
ISBN: 3319942263
Category : Technology & Engineering
Languages : en
Pages : 159
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Book Description
This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way. The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups). The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible.
Author: Akihito Kikuchi
Publisher: Springer
ISBN: 3319942263
Category : Technology & Engineering
Languages : en
Pages : 159
Get Book Here
Book Description
This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way. The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups). The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible.
Author: Frank Y. Wang
Publisher: John Wiley & Sons
ISBN: 3527618945
Category : Science
Languages : en
Pages : 625
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Book Description
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/
Author: Carsten Schneider
Publisher: Springer Science & Business Media
ISBN: 3709116163
Category : Science
Languages : en
Pages : 422
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Book Description
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.
Author: Johannes Grabmeier
Publisher: Springer Science & Business Media
ISBN: 3642558267
Category : Computers
Languages : en
Pages : 656
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Book Description
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
Author: Richard Enns
Publisher: Springer Science & Business Media
ISBN: 1461301718
Category : Mathematics
Languages : en
Pages : 785
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Book Description
Computer algebra systems allow students to work on mathematical models more efficiently than in the case of pencil and paper. The use of such systems also leads to fewer errors and enables students to work on complex and computationally intensive models. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, and chemistry. The text includes a large number of Maple(R) recipes.
Author: Richard H. Enns
Publisher:
ISBN: 9780817670337
Category :
Languages : en
Pages : 412
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Book Description
Author: Edmund A. Lamagna
Publisher: CRC Press
ISBN: 1351605836
Category : Mathematics
Languages : en
Pages : 350
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Book Description
The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience — a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems
Author: W.-H. Steeb
Publisher: World Scientific
ISBN: 9814307173
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explantory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages --- Mathematica and Maple --- while some problems are implemented in C++. --
Author: Dietrich Stauffer
Publisher: Springer Science & Business Media
ISBN: 3642970915
Category : Computers
Languages : en
Pages : 161
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Book Description
Computers play an increasingly important role in many of today's activities, and correspondingly physicists find employment after graduation in computer related jobs, often quite remote from their physics education. The present lectures, on the other hand, emphasize how we can use computers for the purposes of fundamental research in physics. Thus we do not deal with programs designed for newspapers, banks, or travel agencies, i.e., word processing and storage of large amounts of data. Instead, our lectures concentrate on physics problems, where the computer often has to work quite hard to get a result. Our programs are necessarily 5 quite short, excluding for example quantum chemistry programs with 10 program lines. The reader will learn how to handle computers for well-defined purposes. Therefore, in the end, this course will also enable him to orient himself in computer-related jobs. The first chapter deals mainly with solutions of the Newtonian equation of motion, that force equals mass times acceleration, which is a precursor to the molecular dynamics method in statistical physics. The second chap ter considers, by means of several examples, another method for statistical physics, Monte Carlo simulation. These two chapters deal with numbers, the traditional territory of computers. In contrast, analytic formula manipulation, 3 5 4 3 such as (a+27b -4c)5 = a + 135a b - ... , is taught in the last chapter and is important, for instance, in analytic integration or for evaluating expressions in Einstein's general theory of relativity.
Author: N MacDonald
Publisher: CRC Press
ISBN: 1000157245
Category : Science
Languages : en
Pages : 182
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Book Description
The use of computer algebra systems in science and engineering has grown rapidly as more people realize their potential to solve tedious and extensive mathematical problems. REDUCE for Physicists provides a comprehensive introduction to one of the most widely available and simple to use computer algebra systems, focusing primarily on the needs of physicists. As a means of performing symbolic computation, REDUCE reduces tedious manual algebraic calculations and the dangers of casual errors. Each chapter introduces some aspects of REDUCE and illustrates them with applications from various branches of physics including mechanics, dynamics, dimensional analysis, quantum mechanics, and plasma physics. Emphasizing hands-on work with REDUCE to tackle real physical problems, the book includes exercises to test understanding throughout. Students and researchers in the physical sciences and engineering using REDUCE for the first time will find this book an invaluable aid to learning.
