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Numerical Methods and Methods of Approximation in Science and Engineering

Author : Karan S. Surana

Publisher : CRC Press

Page : 426 pages

File Size : 47,99 MB

Release : 2018-10-31

Category : Mathematics

ISBN : 0429647867

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Book Description

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors



Approximation Methods in Science and Engineering

Author : Reza N. Jazar

Publisher :

Page : pages

File Size : 29,65 MB

Release : 2020

Category : Approximation theory

ISBN : 9781071604793

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Book Description

Approximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions. Covers practical model-prototype analysis and nondimensionalization of differential equations; Coverage includes approximate methods of responses of nonlinear differential equations; Discusses how to apply approximation methods to analysis, design, optimization, and control problems; Discusses how to implement approximation methods to new aspects of engineering and physics including nonlinear vibration and vehicle dynamics



Numerical Approximation Methods

Author : Harold Cohen

Publisher : Springer Science & Business Media

Page : 493 pages

File Size : 44,41 MB

Release : 2011-09-28

Category : Mathematics

ISBN : 1441998365

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Book Description

This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.



Numerical Methods in Scientific Computing

Author : Germund Dahlquist

Publisher : SIAM

Page : 742 pages

File Size : 26,3 MB

Release : 2008-01-01

Category : Mathematics

ISBN : 0898717787

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Book Description

This new book from the authors of the classic book Numerical methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.



A First Course in Numerical Methods

Author : Uri M. Ascher

Publisher : SIAM

Page : 574 pages

File Size : 12,59 MB

Release : 2011-07-14

Category : Mathematics

ISBN : 0898719976

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Book Description

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



Approximation Theory and Methods

Author : M. J. D. Powell

Publisher : Cambridge University Press

Page : 356 pages

File Size : 35,75 MB

Release : 1981-03-31

Category : Mathematics

ISBN : 9780521295147

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Book Description

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.



Approximate Solution Methods in Engineering Mechanics

Author : Arthur P. Boresi

Publisher : John Wiley & Sons

Page : 284 pages

File Size : 47,5 MB

Release : 2003

Category : Mathematics

ISBN : 9780471402428

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Book Description

The only complete collection of prevalent approximation methods Unlike any other resource, Approximate Solution Methods in Engineering Mechanics, Second Edition offers in-depth coverage of the most common approximate numerical methods used in the solution of physical problems, including those used in popular computer modeling packages. Descriptions of each approximation method are presented with the latest relevant research and developments, providing thorough, working knowledge of the methods and their principles. Approximation methods covered include: * Boundary element method (BEM) * Weighted residuals method * Finite difference method (FDM) * Finite element method (FEM) * Finite strip/layer/prism methods * Meshless method Approximate Solution Methods in Engineering Mechanics, Second Edition is a valuable reference guide for mechanical, aerospace, and civil engineers, as well as students in these disciplines.



Numerical Methods for Engineers and Scientists

Author : Joe D. Hoffman

Publisher : CRC Press

Page : 840 pages

File Size : 33,43 MB

Release : 2018-10-03

Category : Mathematics

ISBN : 1482270609

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Book Description

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."



Numerical Methods for Solving Partial Differential Equations

Author : George F. Pinder

Publisher : John Wiley & Sons

Page : 414 pages

File Size : 28,74 MB

Release : 2018-02-05

Category : Technology & Engineering

ISBN : 1119316383

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Book Description

A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.



Numerical Analysis for Scientists and Engineers

Author : Madhumangal Pal

Publisher : Alpha Science International, Limited

Page : 684 pages

File Size : 38,67 MB

Release : 2007

Category : Mathematics

ISBN :

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Book Description

Develops the subject gradually by illustrating several examples for both the beginners and the advanced readers using very simple language. Classical and recently developed numerical methods are derived from mathematical and computational points of view. Numerical methods to solve ordinary and partial differential equations are also presented.