A First Course on Numerical Methods

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Author: Uri M. Ascher,Chen Greif

Publisher: SIAM

ISBN: 0898719976

Category: Mathematics

Page: 552

View: 7551

Offers students a practical knowledge of modern techniques in scientific computing.

Finite Difference Computing with PDEs

A Modern Software Approach

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Author: Hans Petter Langtangen,Svein Linge

Publisher: Springer

ISBN: 3319554565

Category: Computers

Page: 507

View: 4695

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Programming for Computations - MATLAB/Octave

A Gentle Introduction to Numerical Simulations with MATLAB/Octave

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Author: Svein Linge,Hans Petter Langtangen

Publisher: Springer

ISBN: 3319324527

Category: Computers

Page: 216

View: 7739

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Numerik für Ingenieure und Naturwissenschaftler

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Author: Wolfgang Dahmen,Arnold Reusken

Publisher: Springer-Verlag

ISBN: 3540764933

Category: Mathematics

Page: 633

View: 9452

Neben einer Einführung in alle grundlegenden numerischen Methodenbausteine illustriert das Lehrbuch anhand komplexer Anwendungen, wie diese Bausteine zu kombinieren sind. Die Themen sind so aufbereitet, dass auf Basisdarstellungen vertiefende Abschnitte folgen. Dem vorangestellt ist jeweils eine mit Beispielen untermauerte Diskussion der Begriffe Kondition und Stabilität. Das Buch ist sowohl für die Numerikausbildung im Mathematikstudium geeignet als auch für eine einsemestrige oder weiterführende Numerik-Vorlesung im Ingenieurstudium.

A First Course in Computational Physics

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Author: Paul L. DeVries,Javier E. Hasbun

Publisher: Jones & Bartlett Publishers

ISBN: 1449636195

Category: Technology & Engineering

Page: 433

View: 5472

Computers and computation are extremely important components of physics and should be integral parts of a physicist s education. Furthermore, computational physics is reshaping the way calculations are made in all areas of physics. Intended for the physics and engineering students who have completed the introductory physics course, A First Course in Computational Physics, Second Edition covers the different types of computational problems using MATLAB with exercises developed around problems of physical interest. Topics such as root finding, Newton-Cotes integration, and ordinary differential equations are included and presented in the context of physics problems. A few topics rarely seen at this level such as computerized tomography, are also included. Within each chapter, the student is led from relatively elementary problems and simple numerical approaches through derivations of more complex and sophisticated methods, often culminating in the solution to problems of significant difficulty. The goal is to demonstrate how numerical methods are used to solve the problems that physicists face. Read the review published in Computing in Science & Engineering magazine, March/April 2011 (Vol. 13, No. 2) (c) 2011 IEEE, Published by the IEEE Computer Society"

A Short Course in Computational Science and Engineering

C++, Java and Octave Numerical Programming with Free Software Tools

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Author: David Yevick

Publisher: Cambridge University Press

ISBN: 0521116813

Category: Computers

Page: 265

View: 2402

"Building on his highly successful textbook on C++, David Yevick provides a concise yet comprehensive one-stop course in three key programming languages, C++, Java and Octave (a freeware alternative to MATLAB). Employing only public-domain software to ensure straightforward implementation for all readers, this book presents a unique overview of numerical and programming techniques relevant to scientific programming, including object-oriented programming, elementary and advanced topics in numerical analysis, physical system modeling, scientific graphics, software engineering and performance issues. Relevant features of each programming language are illustrated with short, incisive examples, and the installation and application of the software is describedin detail. Compact, transparent code in all three programming languages is applied to the fundamental equations of quantum mechanics, electromagnetics, mechanics and statistical mechanics. Uncommented versions of the code that can be immediately modifiedand adapted are provided online for the more involved programs. This compact, practical text is an invaluable introduction for students in all undergraduate- and graduate-level courses in the physical sciences or engineering that require numerical modeling, and also a key reference for instructors and scientific programmers"--

A First Course in Finite Element Analysis

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Author: Xin-She Yang

Publisher: Luniver Press

ISBN: 1905986084

Category: Mathematics

Page: 212

View: 7369

The book endeavors to strike a balance between mathematical and numerical coverage of a wide range of topics in fi nite element analysis. It strives to provide an introduction, especially for undergraduates and graduates, to fi nite element analysis and its applications. Topics include advanced calculus, differential equations, vector analysis, calculus of variations, fi nite difference methods, fi nite element methods and time-stepping schemes. The book also emphasizes the application of important numerical methods with dozens of worked examples. The applied topics include elasticity, heat transfer, and pattern formation. A few self-explanatory Matlab programs provide a good start for readers to try some of the methods and to apply the methods and techniques to their own modelling problems with some modifi cations. The book will perfectly serve as a textbook in fi nite element analysis, computational mathematics, mathematical modelling, and engineering computations.

Computational Technologies

A First Course

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Author: Petr N. Vabishchevich

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110391031

Category: Computers

Page: 248

View: 2811

In this book we describe the basic elements of present computational technologies that use the algorithmic languages C/C++. The emphasis is on GNU compilers and libraries, FOSS for the solution of computational mathematics problems and visualization of the obtained data. Many examples illustrate the basic features of computational technologies.

A First Course in Scientific Computing

Symbolic, Graphic, and Numeric Modeling Using Maple, Java, Mathematica, and Fortran90

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Author: Rubin H. Landau

Publisher: Princeton University Press

ISBN: 1400841178

Category: Computers

Page: 512

View: 5416

This book offers a new approach to introductory scientific computing. It aims to make students comfortable using computers to do science, to provide them with the computational tools and knowledge they need throughout their college careers and into their professional careers, and to show how all the pieces can work together. Rubin Landau introduces the requisite mathematics and computer science in the course of realistic problems, from energy use to the building of skyscrapers to projectile motion with drag. He is attentive to how each discipline uses its own language to describe the same concepts and how computations are concrete instances of the abstract. Landau covers the basics of computation, numerical analysis, and programming from a computational science perspective. The first part of the printed book uses the problem-solving environment Maple as its context, with the same material covered on the accompanying CD as both Maple and Mathematica programs; the second part uses the compiled language Java, with equivalent materials in Fortran90 on the CD; and the final part presents an introduction to LaTeX replete with sample files. Providing the essentials of computing, with practical examples, A First Course in Scientific Computing adheres to the principle that science and engineering students learn computation best while sitting in front of a computer, book in hand, in trial-and-error mode. Not only is it an invaluable learning text and an essential reference for students of mathematics, engineering, physics, and other sciences, but it is also a consummate model for future textbooks in computational science and engineering courses. A broad spectrum of computing tools and examples that can be used throughout an academic career Practical computing aimed at solving realistic problems Both symbolic and numerical computations A multidisciplinary approach: science + math + computer science Maple and Java in the book itself; Mathematica, Fortran90, Maple and Java on the accompanying CD in an interactive workbook format

Analysis für Informatiker

Grundlagen, Methoden, Algorithmen

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Author: Michael Oberguggenberger,Alexander Ostermann

Publisher: Springer-Verlag

ISBN: 3540898239

Category: Computers

Page: 328

View: 8640

Bei dem Thema des Buches spielt das algorithmische Denken eine wichtige Rolle. Die Autoren führen in die Analysis ein, indem sie deren Grundlagen aus algorithmischer Sichtweise entwickeln, die Theorie mittels MATLAB- und Maple-Programmen und Java-Applets anschaulich machen und grundlegende Konzepte der numerischen Analysis behandeln. Das Buch wendet sich an Informatiker im ersten Studienabschnitt und kann als Vorlesungsgrundlage, als Begleittext zur Vorlesung oder zum Selbststudium verwendet werden.

Fundamental Algorithms in Computational Fluid Dynamics

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Author: Thomas H. Pulliam,David W. Zingg

Publisher: Springer Science & Business Media

ISBN: 3319050532

Category: Technology & Engineering

Page: 211

View: 5980

Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.

Meshless Methods and Their Numerical Properties

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Author: Hua Li,Shantanu S. Mulay

Publisher: CRC Press

ISBN: 1466517468

Category: Mathematics

Page: 447

View: 7344

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the most important and classical methods, as well as several methods recently developed by the authors. This book also offers a rigorous mathematical treatment of their numerical properties—including consistency, convergence, stability, and adaptivity—to help you choose the method that is best suited for your needs. Get Guidance for Developing and Testing Meshless Methods Developing a broad framework to study the numerical computational characteristics of meshless methods, the book presents consistency, convergence, stability, and adaptive analyses to offer guidance for developing and testing a particular meshless method. The authors demonstrate the numerical properties by solving several differential equations, which offer a clearer understanding of the concepts. They also explain the difference between the finite element and meshless methods. Explore Engineering Applications of Meshless Methods The book examines how meshless methods can be used to solve complex engineering problems with lower computational cost, higher accuracy, easier construction of higher-order shape functions, and easier handling of large deformation and nonlinear problems. The numerical examples include engineering problems such as the CAD design of MEMS devices, nonlinear fluid-structure analysis of near-bed submarine pipelines, and two-dimensional multiphysics simulation of pH-sensitive hydrogels. Appendices supply useful template functions, flowcharts, and data structures to assist you in implementing meshless methods. Choose the Best Method for a Particular Problem Providing insight into the special features and intricacies of meshless methods, this is a valuable reference for anyone developing new high-performance numerical methods or working on the modelling and simulation of practical engineering problems. It guides you in comparing and verifying meshless methods so that you can more confidently select the best method to solve a particular problem.

A First Course in Ordinary Differential Equations

Analytical and Numerical Methods

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Author: Martin Hermann,Masoud Saravi

Publisher: Springer Science & Business

ISBN: 8132218353

Category: Mathematics

Page: 288

View: 8975

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

Fundamentals of Engineering Numerical Analysis

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Author: Parviz Moin

Publisher: Cambridge University Press

ISBN: 1139489550

Category: Technology & Engineering

Page: N.A

View: 7316

Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.

A Primer on Scientific Programming with Python

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Author: Hans Petter Langtangen

Publisher: Springer

ISBN: 3662498871

Category: Computers

Page: 922

View: 2257

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015

Numerical Methods for Chemical Engineering

Applications in MATLAB

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Author: Kenneth J Beers,Kenneth J. Beers

Publisher: Cambridge University Press

ISBN: 9780521859714

Category: Juvenile Nonfiction

Page: 474

View: 6988

Applications of numerical mathematics and scientific computing to chemical engineering.

Numerical Analysis and Scientific Computation

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Author: Jeffery J. Leader

Publisher: Addison-Wesley Longman

ISBN: 9780201734997

Category: Computers

Page: 590

View: 7048

This book offers the following: Quick indtroduction to numerical methods, with roundoff error and computer arithmetic deferred until students ahve gained some experience with real algorithms; mofern approach to numerical linear algebra; explanations to the numerical techniques used by the major computational programs students are likely to use in practice(especally MATLAB, but also Maple and the Netlib library); Appropriate mix of numerical analysis theory and practical sciencfic computation principles; greater than usual emphasis on optimization; numerical experiments so students can gain experience; and efficient and unobtrusice introduction to MATLAB.

Numerical Linear Algebra with Applications

Using MATLAB

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Author: William Ford

Publisher: Academic Press

ISBN: 0123947847

Category: Mathematics

Page: 628

View: 2687

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications