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An Introduction to Numerical Methods and Analysis

An Introduction to Numerical Methods and Analysis Book
Author : James F. Epperson
Publisher : John Wiley & Sons
Release : 2013-06-06
ISBN : 1118626230
Language : En, Es, Fr & De

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Book Description :

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Numerical Analysis

Numerical Analysis Book
Author : Walter Gautschi
Publisher : Springer Science & Business Media
Release : 2011-12-07
ISBN : 0817682597
Language : En, Es, Fr & De

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Book Description :

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

Theoretical Numerical Analysis

Theoretical Numerical Analysis Book
Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Release : 2007-06-07
ISBN : 0387287698
Language : En, Es, Fr & De

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Book Description :

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Introduction to Numerical Analysis

Introduction to Numerical Analysis Book
Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475722729
Language : En, Es, Fr & De

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Book Description :

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

Numerical Analysis

Numerical Analysis Book
Author : Brian Sutton
Publisher : SIAM
Release : 2019-04-18
ISBN : 1611975700
Language : En, Es, Fr & De

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Book Description :

This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.

Numerical Analysis

Numerical Analysis Book
Author : Richard L. Burden,J. Douglas Faires
Publisher : Cengage Learning
Release : 2010-08-09
ISBN : 1133169333
Language : En, Es, Fr & De

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Book Description :

This well-respected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires explain how, why, and when approximation techniques can be expected to work, and why, in some situations, they fail. A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Numerical Analysis or Numerical Method in Symmetry

Numerical Analysis or Numerical Method in Symmetry Book
Author : Clemente Cesarano
Publisher : MDPI
Release : 2020-02-21
ISBN : 3039283723
Language : En, Es, Fr & De

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Book Description :

This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

Guidelines for the Use of Advanced Numerical Analysis

Guidelines for the Use of Advanced Numerical Analysis Book
Author : David Potts,Kenet Axelsson
Publisher : Thomas Telford
Release : 2002
ISBN : 0727731254
Language : En, Es, Fr & De

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Book Description :

It is not easy for engineers to gain all the skills necessary to perform numerical analysis. This book is an authoritative guide that explains in detail the potential restrictions and pitfalls and so help engineers undertake advanced numerical analysis. It discusses the major approximations involved in nonlinear numerical analysis and describes some of the more popular constituitive models currently available and explores their strengths and weaknesses. It also discusses the determination of material parameters for defining soil behaviour, investigates the options for modelling structural components and their interface with the soil and the boundary conditions that are appropriate in geotechnical analysis and the assumptions implied when they are used. Guidelines for the use of Advanced Numerical Analysis also provides guidelines for best practice of specific types of soil-structure interaction that are common in urban development and discusses the role of benchmarking exercises. This authoritative book will be invaluable to practising engineers involved in urban development. It will also be useful tool for geotechnical and structural engineers.

Introductory Numerical Analysis

Introductory Numerical Analysis Book
Author : Mircea Andrecut
Publisher : Universal-Publishers
Release : 2000-02
ISBN : 9781581127577
Language : En, Es, Fr & De

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Book Description :

Synopsis The aim of this book is to provide a simple and useful introduction for the fresh students into the vast field of numerical analysis. Like any other introductory course on numerical analysis, this book contains the basic theory, which in the present text refers to the following topics: linear equations, nonlinear equations, eigensystems, interpolation, approximation of functions, numerical differentiation and integration, stochastics, ordinary differential equations and partial differential equations. Because the students need to quickly understand why the numerical methods correctly work, the proofs of theorems were shorted as possible, insisting more on ideas than on a lot of algebra manipulation. The included examples are presented with a minimum of complications, emphasizing the steps of the algorithms. The numerical methods described in this book are illustrated by computer programs written in C. Our goal was to develop very simple programs which are easily to read and understand by students. Also, the programs should run without modification on any compiler that implements the ANSI C standard. Because our intention was to easily produce screen input-output (using, scanf and printf), in case of WINDOWS visual programming environments, like Visual C++ (Microsoft) and Borland C++ Builder, the project should be console-application. This will be not a problem for DOS and LINUX compilers. If this material is used as a teaching aid in a class, I would appreciate if under such circumstances, the instructor of such a class would send me a note at the address below informing me if the material is useful. Also, I would appreciate any suggestions or constructive criticism regarding the content of these lecture notes.

Numerical Methods

Numerical Methods Book
Author : Anne Greenbaum,Tim P. Chartier
Publisher : Princeton University Press
Release : 2012-04-01
ISBN : 1400842670
Language : En, Es, Fr & De

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Book Description :

A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Numerical Analysis

Numerical Analysis Book
Author : D.F. Griffiths
Publisher : Springer
Release : 2006-12-08
ISBN : 3540388818
Language : En, Es, Fr & De

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Book Description :

Download Numerical Analysis book written by D.F. Griffiths, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Analysis

Numerical Analysis Book
Author : J.P. Hennart
Publisher : Springer
Release : 2006-11-14
ISBN : 3540389865
Language : En, Es, Fr & De

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Book Description :

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The Birth of Numerical Analysis

The Birth of Numerical Analysis Book
Author : Adhemar Bultheel,Ronald Cools
Publisher : World Scientific
Release : 2010
ISBN : 9812836268
Language : En, Es, Fr & De

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Book Description :

The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Numerical Analysis of Pierce type Electron Guns

Numerical Analysis of Pierce type Electron Guns Book
Author : Richard T. CLOSE
Publisher : Unknown
Release : 1966
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Digital-computer programs have been used to analyze four Pierce-type electron guns. The numerical analysis has been very successful in identifying the deficiencies of the Pierce-design method when extrapolated to high perveances. It also has been possible to obtain radial phase-space diagrams for the beams from each of the electron guns studied. From these diagrams and by the use of several other computer programs, an estimate of the transverse energy distribution of the electron beams has been made. It has been found that the major contribution to the random transverse energy must be of nonthermal origin. (Author).

Numerical Analysis and Optimization

Numerical Analysis and Optimization Book
Author : Mehiddin Al-Baali
Publisher : Springer Nature
Release : 2022-08-18
ISBN : 3030720403
Language : En, Es, Fr & De

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Book Description :

Download Numerical Analysis and Optimization book written by Mehiddin Al-Baali, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Tea Time Numerical Analysis

Tea Time Numerical Analysis Book
Author : Leon Q. Brin
Publisher : Createspace Independent Publishing Platform
Release : 2014-09-18
ISBN : 9781502365828
Language : En, Es, Fr & De

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Book Description :

A one semester introduction to numerical analysis. Includes typical introductory material, root finding, numerical calculus, and interpolation techniques. The focus is on the mathematics rather than application to engineering or sciences.

Advances in Numerical Analysis Emphasizing Interval Data

Advances in Numerical Analysis Emphasizing Interval Data Book
Author : Tofigh Allahviranloo,Witold Pedrycz,Armin Esfandiari
Publisher : CRC Press
Release : 2022-02-18
ISBN : 1000540316
Language : En, Es, Fr & De

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Book Description :

Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges. The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory. Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

Numerical Analysis and Modelling in Geomechanics

Numerical Analysis and Modelling in Geomechanics Book
Author : John W. Bull
Publisher : CRC Press
Release : 2003-09-02
ISBN : 0203471288
Language : En, Es, Fr & De

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Book Description :

In geomechanics, existing design methods are very much dependent upon sophisticated on-site techniques to assess ground conditions. This book describes numerical analysis, computer simulation and modelling that can be used to answer some highly complex questions associated with geomechanics. The contributors, who are all international experts in the field, also give insights into the future directions of these methods. Numerical Analysis and Modelling in Geomechanics will appeal to professional engineers involved in designing and building both onshore and offshore structures, where geomechanical considerations may well be outside the usual codes of practice, and therefore specialist advice is required. Postgraduate researchers, degree students carrying out project work in this area will also find the book an invaluable resource.

C Algebras and Numerical Analysis

C    Algebras and Numerical Analysis Book
Author : Ronald Hagen,Steffen Roch,Bernd Silbermann
Publisher : CRC Press
Release : 2000-09-07
ISBN : 9780824704605
Language : En, Es, Fr & De

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Book Description :

"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."

Using R for Numerical Analysis in Science and Engineering

Using R for Numerical Analysis in Science and Engineering Book
Author : Victor A. Bloomfield
Publisher : CRC Press
Release : 2014-04-24
ISBN : 1439884498
Language : En, Es, Fr & De

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Book Description :

Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.