An Introduction to Numerical Methods in C++

Author: Brian Hilton Flowers,Sir Brian Hilton Flowers

Publisher: Oxford University Press on Demand

ISBN: 9780198506935

Category: Computers

Page: 555

View: 5661

Designed for the many applied mathematicians and engineers who wish to explore computerized numerical methods, this text explores the power of C++ as a tool for work in numerical methods. This revision of the successful first edition includes for the first time information on programming in Windows-based environments. In addition it includes new topics and methods throughout the text that clarify and enhance the treatment of the subject.

An Introduction to Programming and Numerical Methods in MATLAB

Author: Steve Otto,James P. Denier

Publisher: Springer Science & Business Media

ISBN: 9781852339197

Category: Business & Economics

Page: 463

View: 2768

The material presented in this volume provides an introduction to the numerical methods that are typically encountered and used in undergraduate science and engineering courses, and is developed in tandem with MATLAB, which allows rapid prototyping and testing of the methods.

An Introduction to C++ and Numerical Methods

Author: James M. Ortega,Andrew Swift Grimshaw

Publisher: Oxford University Press on Demand

ISBN: 9780195117677

Category: Computers

Page: 273

View: 6656

An introduction to C++ providing explanations of the basics of numerical methods, scientific computing and the basic constructs of C++. Subsequent chapters revisit these topics to treat them in more detail. It also covers numerical methods used in scientific and engineering computation.

Introduction to the Finite Element Method in Electromagnetics

Author: Anastasis C. Polycarpou

Publisher: Morgan & Claypool Publishers

ISBN: 1598290460

Category: Technology & Engineering

Page: 115

View: 8694

This lecture is written primarily for the non-expert engineer or the undergraduate or graduate student who wants to learn, for the first time, the finite element method with applications to electromagnetics. It is also designed for research engineers who have knowledge of other numerical techniques and want to familiarize themselves with the finite element method.Finite element method is a numerical method used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. Author Anastasis Polycarpou provides the reader with all information necessary to successfully apply the finite element method to one- and two-dimensional boundary-value problems in electromagnetics.The book is accompanied by a number of codes written by the author in Matlab. These are the finite element codes that were used to generate most of the graphs presented in this book. Specifically, there are three Matlab codes for the one-dimensional case (Chapter 1) and two Matlab codes for the two-dimensional case (Chapter 2). The reader may execute these codes, modify certain parameters such as mesh size or object dimensions, and visualize the results. The codes are available on the Morgan & Claypool Web site at http://www.morganclaypool.com.

Introduction to Numerical Methods in Differential Equations

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

ISBN: 0387308911

Category: Mathematics

Page: 239

View: 2270

This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

Fortran 77 and Numerical Methods

Author: C. Xavier

Publisher: New Age International

ISBN: 9788122406702

Category: FORTRAN 77 (Computer program language)

Page: 527

View: 1293

Fortran Is The Pioneer Computer Language Originally Designed To Suit Numerical, Scientific And Engineering Computations. In Spite Of The Birth Of Several Computer Languages, Fortran Is Still Used As A Primary Tool For Programming Numerical Computations. In This Book All The Features Of Fortran 77 Have Been Elaborately Explained With The Support Of Examples And Illustrations. Programs Have Been Designed And Developed In A Systematic Way For All The Classical Problems. All The Topics Of Numerical Methods Have Been Presented In A Simple Style And Algorithms Developed. Complete Fortran 77 Programs And More Than One Sets Of Sample Data Have Been Given For Each Method. The Content Of The Book Have Been Carefully Tailored For A Course Material Of A One Semester Course For The Computer Science, Mathematics And Physics Students.

Numerical Analysis with Applications in Mechanics and Engineering

Author: Petre Teodorescu,Nicolae-Doru Stanescu,Nicolae Pandrea

Publisher: John Wiley & Sons

ISBN: 1118614623

Category: Computers

Page: 646

View: 8503

A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.

An Introduction to Numerical Analysis for Electrical and Computer Engineers

Author: Christopher J. Zarowski

Publisher: John Wiley & Sons

ISBN: 9780471650409

Category: Mathematics

Page: 608

View: 1931

This book is an introduction to numerical analysis and intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering Includes MATLAB oriented examples An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

INTRODUCTION TO NUMERICAL METHODS IN CHEMICAL ENGINEERING

Author: PRADEEP AHUJA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120340183

Category: Technology & Engineering

Page: 308

View: 6154

This book is an exhaustive presentation of the numerical methods used in chemical engineering. Intended primarily as a textbook for BE/BTech students of chemical engineering, the book will also be useful to research and development/process professionals in the fields of chemical, biochemical, mechanical and biomedical engineering. The initial chapters discuss the linear and nonlinear algebraic equations. The ensuing chapters cover the problems in chemical engineering thermodynamics as well as initial value problems, boundary value problems and convection–diffusion problems. Topics related to chemical reaction, dispersion and diffusion as well as steady and transient heat conduction are treated in the final chapters. The book covers a large number of numerical methods including tridiagonal matrix algorithm (TDMA) method, Newton’s method, Runge–Kutta fourth-order method, Upwind Difference Scheme (UDS) method and Alternating Direction Implicit (ADI) method. Strong emphasis is given on applications and uses of numerical analysis specifically required at the undergraduate level. The book contains numerous worked-out examples and chapter-end exercises. The answers to all chapter-end exercises are provided. The Appendix contains a total of 33 programs in C++ related to the various numerical methods explained in the book.

Numerical Methods with Worked Examples

Author: C. Woodford,Chris Phillips

Publisher: Springer Science & Business Media

ISBN: 9780412721502

Category: Mathematics

Page: 273

View: 5005

This book is for students following a module in numerical methods, numerical techniques, or numerical analysis. It approaches the subject from a pragmatic viewpoint, appropriate for the modern student. The theory is kept to a minimum commensurate with comprehensive coverage of the subject and it contains abundant worked examples which provide easy understanding through a clear and concise theoretical treatment.

An Introduction to Numerical Methods

A MATLAB Approach, Third Edition

Author: Abdelwahab Kharab,Ronald B. Guenther

Publisher: CRC Press

ISBN: 1439869006

Category: Mathematics

Page: 576

View: 7019

Highly recommended by CHOICE, previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Third Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results so that the main steps are easily visualized and interpreted. New to the Third Edition A chapter on the numerical solution of integral equations A section on nonlinear partial differential equations (PDEs) in the last chapter Inclusion of MATLAB GUIs throughout the text The book begins with simple theoretical and computational topics, including computer floating point arithmetic, errors, interval arithmetic, and the root of equations. After presenting direct and iterative methods for solving systems of linear equations, the authors discuss interpolation, spline functions, concepts of least-squares data fitting, and numerical optimization. They then focus on numerical differentiation and efficient integration techniques as well as a variety of numerical techniques for solving linear integral equations, ordinary differential equations, and boundary-value problems. The book concludes with numerical techniques for computing the eigenvalues and eigenvectors of a matrix and for solving PDEs. CD-ROM Resource The accompanying CD-ROM contains simple MATLAB functions that help students understand how the methods work. These functions provide a clear, step-by-step explanation of the mechanism behind the algorithm of each numerical method and guide students through the calculations necessary to understand the algorithm. Written in an easy-to-follow, simple style, this text improves students’ ability to master the theoretical and practical elements of the methods. Through this book, they will be able to solve many numerical problems using MATLAB.

Solving PDEs in C++

Numerical Methods in a Unified Object-Oriented Approach

Author: Yair Shapira

Publisher: Cambridge University Press

ISBN: 9780898716016

Category: Computers

Page: 500

View: 1109

This comprehensive book not only introduces the C and C++ programming languages but also shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach.The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. This book introduces a unified approach for the implementation of these objects. The code segments and their detailed explanations clearly show how easy it is to implement advanced algorithms in C++. Solving PDEs in C++ contains all the required background in programming, PDEs, and numerical methods; only an elementary background in linear algebra and calculus is required. Useful exercises and solutions conclude each chapter. For the more advanced reader, there is also material on stability analysis and weak formulation. The final parts of the book demonstrate the object-oriented approach in advanced applications.The book is written for researchers, engineers, and advanced students who wish to increase their familiarity with numerical methods and to implement them in modern programming tools. Solving PDEs in C++ can be used as a textbook in courses in C++ with applications, C++ in engineering, numerical analysis, and numerical PDEs at the advanced undergraduate and graduate levels. Because it is self-contained, the book is also suitable for self-study by researchers and students in applied and computational science and engineering. Contents List of Figures; List of Tables; Preface; Part I: Programming. Chapter 1: Introduction to C; Chapter 2: Introduction to C++; Chapter 3: Data Structures; Part II: The Object-Oriented Approach. Chapter 4: Object-Oriented Programming; Chapter 5: Algorithms and Their Object-Oriented Implementation; Chapter 6: Object-Oriented Analysis; Part III: Partial Differential Equations and Their Discretization. Chapter 7: The Convection-Diffusion Equation; Chapter 8: Stability Analysis 209; Chapter 9: Nonlinear Equations; Chapter 10: Application in Image Processing; Part IV: The Finite-Element Discretization Method. Chapter 11: The Weak Formulation; Chapter 12: Linear Finite Elements; Chapter 13: Unstructured Finite-Element Meshes; Chapter 14: Adaptive Mesh Refinement; Chapter 15: High-Order Finite Elements; Part V: The Numerical Solution of Large Sparse Linear Systems of Equations. Chapter 16: Sparse Matrices and Their Implementation; Chapter 17: Iterative Methods for Large Sparse Linear Systems; Chapter 18: Parallelism; Part VI: Applications. Chapter 19: Diffusion Equations; Chapter 20: The Linear Elasticity Equations; Chapter 21: The Stokes Equations; Chapter 22: Electromagnetic Waves; Appendix; Bibliography; Index.

Guide to Scientific Computing in C++

Author: Joe Pitt-Francis,Jonathan Whiteley

Publisher: Springer Science & Business Media

ISBN: 1447127366

Category: Computers

Page: 250

View: 2136

This easy-to-read textbook/reference presents an essential guide to object-oriented C++ programming for scientific computing. With a practical focus on learning by example, the theory is supported by numerous exercises. Features: provides a specific focus on the application of C++ to scientific computing, including parallel computing using MPI; stresses the importance of a clear programming style to minimize the introduction of errors into code; presents a practical introduction to procedural programming in C++, covering variables, flow of control, input and output, pointers, functions, and reference variables; exhibits the efficacy of classes, highlighting the main features of object-orientation; examines more advanced C++ features, such as templates and exceptions; supplies useful tips and examples throughout the text, together with chapter-ending exercises, and code available to download from Springer.

Scientific Computing and Differential Equations

An Introduction to Numerical Methods

Author: Gene H. Golub,James M. Ortega

Publisher: Elsevier

ISBN: 0080516696

Category: Mathematics

Page: 344

View: 6268

Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment Contains an introduction to numerical methods for both ordinary and partial differential equations Concentrates on ordinary differential equations, especially boundary-value problems Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level

An Introduction to MATLAB® Programming and Numerical Methods for Engineers

Author: Timmy Siauw,Alexandre Bayen

Publisher: Academic Press

ISBN: 0127999140

Category: Computers

Page: 340

View: 6953

Assuming no prior background in linear algebra or real analysis, An Introduction to MATLAB® Programming and Numerical Methods for Engineers enables you to develop good computational problem solving techniques through the use of numerical methods and the MATLAB® programming environment. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level allowing you to quickly apply results in practical settings. Tips, warnings, and "try this" features within each chapter help the reader develop good programming practices Chapter summaries, key terms, and functions and operators lists at the end of each chapter allow for quick access to important information At least three different types of end of chapter exercises — thinking, writing, and coding — let you assess your understanding and practice what you've learned

Computational Methods in Chemical Engineering with Maple

Author: Ralph E. White,Venkat R. Subramanian

Publisher: Springer Science & Business Media

ISBN: 9783642043116

Category: Science

Page: 860

View: 5056

This book presents Maple solutions to a wide range of problems relevant to chemical engineers and others. Many of these solutions use Maple’s symbolic capability to help bridge the gap between analytical and numerical solutions. The readers are strongly encouraged to refer to the references included in the book for a better understanding of the physics involved, and for the mathematical analysis. This book was written for a senior undergraduate or a first year graduate student course in chemical engineering. Most of the examples in this book were done in Maple 10. However, the codes should run in the most recent version of Maple. We strongly encourage the readers to use the classic worksheet (*. mws) option in Maple as we believe it is more user-friendly and robust. In chapter one you will find an introduction to Maple which includes simple basics as a convenience for the reader such as plotting, solving linear and nonlinear equations, Laplace transformations, matrix operations, ‘do loop,’ and ‘while loop. ’ Chapter two presents linear ordinary differential equations in section 1 to include homogeneous and nonhomogeneous ODEs, solving systems of ODEs using the matrix exponential and Laplace transform method. In section two of chapter two, nonlinear ordinary differential equations are presented and include simultaneous series reactions, solving nonlinear ODEs with Maple’s ‘dsolve’ command, stop conditions, differential algebraic equations, and steady state solutions. Chapter three addresses boundary value problems.

Scientific Computing with MATLAB and Octave

Author: Alfio Quarteroni,Fausto Saleri,Paola Gervasio

Publisher: Springer Science & Business Media

ISBN: 3642453678

Category: Computers

Page: 450

View: 3739

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. From the review: ".... This carefully written textbook, the third English edition, contains substantial new developments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited for readers who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject." Roberto Plato (Siegen), Zentralblatt MATH 1205.65002.