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# An introduction to numerical methods : a MATLAB approach

Author: Abdelwahab Kharab; Ronald B Guenther Boca Raton : CRC Press,  ©2012 eBook : Document : English : Third editionView all editions and formats "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 EditionA chapter on the numerical solution of integral equationsA section on nonlinear partial differential equations (PDEs) in the last chapterInclusion of MATLAB GUIs throughout the textThe 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 ResourceThe 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"--Provided by publisher."Preface This is a textbook designed for an introductory course in numerical methods. It deals with the theory and application of the most commonly used numerical methods for solving numerical problems on microcomputers. It is intended for students in mathematics, science, and engineering who have completed the introductory calculus sequence. In addition, the reader is assumed to have taken a structured programming course. The thrust of this text is to assist the students to become familiar with the most common numerical methods encountered in science and engineering. The content material of this book has been designed to be compatible with any introductory numerical textbook that exists in the market. Students will be able to examine and solve many numerical problems, using MatlabR 1 in a short period of time. Due to the rapid advancement of computer technology and software developments, we have used Matlab as the computing environment throughout all the chapters of the book. Each numerical method discussed in this book is demonstrated through the use of Matlab which is easy to use and has many features such as: 1. Powerful matrix structure, 2. Powerful two- and three-dimensional graphing facilities, 3. A vast number of powerful built-in functions, 4. Matlab's structured programming style that resembles FORTRAN and BASIC. 1Matlab R is a registered trademark of the MathWorks, Inc. Please note, where we have referenced Matlab throughout this book the logo should be Matlab. For product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508-647-7000 Fax: 508-647-7001"--Provided by publisher.  Read more... (not yet rated) 0 with reviews - Be the first.

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Introduces the theory and applications of the most commonly used techniques for solving numerical problems on a computer. This work covers a range of useful algorithms. It includes a chapter on  Read more...

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Praise for Previous EditionsKharab and Guenther offer an attractive, clear, error-free, and well-written introduction to numerical methods ... Highly recommended.-J.H. Ellison, CHOICE

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schema:description "Error of the interpolating polynomial; Lagrange interpolating polynomial; Applied problems Interpolation with Spline Functions ; Piecewise linear interpolation; Quadratic spline; Natural cubic splines; Applied problems The Method of Least Squares ; Linear least squares; Least-squares polynomial; Nonlinear least squares; Trigonometric least-squares polynomial; Applied problems Numerical Optimization ; Analysis of single-variable functions; Line search methods; Minimization using derivatives; Applied problems Numerical Differentiation ; Numerical differentiation; Richardson's formula; Applied problems Numerical Integration; Trapezoidal rule; Simpson's rule; Romberg algorithm; Gaussian quadrature; Applied problems Numerical Methods for Linear Integral."@en ;
schema:description ""Preface This is a textbook designed for an introductory course in numerical methods. It deals with the theory and application of the most commonly used numerical methods for solving numerical problems on microcomputers. It is intended for students in mathematics, science, and engineering who have completed the introductory calculus sequence. In addition, the reader is assumed to have taken a structured programming course. The thrust of this text is to assist the students to become familiar with the most common numerical methods encountered in science and engineering. The content material of this book has been designed to be compatible with any introductory numerical textbook that exists in the market. Students will be able to examine and solve many numerical problems, using MatlabR 1 in a short period of time. Due to the rapid advancement of computer technology and software developments, we have used Matlab as the computing environment throughout all the chapters of the book. Each numerical method discussed in this book is demonstrated through the use of Matlab which is easy to use and has many features such as: 1. Powerful matrix structure, 2. Powerful two- and three-dimensional graphing facilities, 3. A vast number of powerful built-in functions, 4. Matlab's structured programming style that resembles FORTRAN and BASIC. 1Matlab R is a registered trademark of the MathWorks, Inc. Please note, where we have referenced Matlab throughout this book the logo should be Matlab. For product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508-647-7000 Fax: 508-647-7001"--Provided by publisher."@en ;
schema:description "Equations ; Introduction; Quadrature rules; The successive approximation method; Schmidt's method; Volterra-type integral equations; Applied problems Numerical Methods for Differential Equations ; Euler's Method; Error Analysis; Higher-order Taylor series methods; Runge-Kutta methods; Adams-Bashforth methods; Predictor-corrector methods; Adams-Moulton methods; Numerical stability; Higher-order equations and systems of differential equations; Implicit methods and stiff systems; Phase plane analysis: chaotic differential equations; Applied problems Boundary-Value Problems; Finite-difference methods; Shooting methods; Applied problems Eigenvalues and Eigenvectors ; Basic theory; The power method; The quadratic method; Eigenvalues for boundary-value problems; Bifurcations in differential equations; Applied."@en ;
schema:description "Introduction; About MATLAB and MATLAB graphical user interface (GUI); An introduction to MATLAB; Taylor series Number System and Errors ; Floating-point arithmetic; Round-off errors; Truncation error; Interval arithmetic Roots of Equations ; The bisection method; The method of false position; Fixed-point iteration; The secant method; Newton's method; Convergence of the Newton and Secant methods; Multiple roots and the modified Newton method; Newton's method for nonlinear systems; Applied problems System of Linear Equations ; Matrices and matrix operations; Naïve Gaussian elimination; Gaussian elimination with scaled partial pivoting; Lu decomposition; Iterative methods; Applied problems Interpolation; Polynomial interpolation theory; Newton's divided-difference interpolating polynomial; The."@en ;
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schema:description "Problems Partial Differential Equations; Parabolic equations; Hyperbolic equations; Elliptic equations; Nonlinear partial differential equations; Introduction to finite-element method; Applied problems Bibliography and References Appendix A: Calculus Review; Appendix B: MATLAB Built-in Functions; Appendix C: Text MATLAB Functions; Appendix D: MATLAB GUI Answers to Selected Exercises Index."@en ;
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