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Numerical methods using MathCAD / Laurene Fausett.

By: Fausett, Laurene V [author].
Material type: materialTypeLabelBookPublisher: New Jersey : Prentice-Hall, 2002Copyright date: ©2002Description: xviii, 702 pages : illustrations ; 25 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 013061081X (hardback); 9780130610812 (hardback).Subject(s): MathCAD | Numerical analysis -- Data processingDDC classification: 518.0285
Contents:
Foundations -- Sample problems and numerical methods -- Some basic issues -- Getting started in Mathcad -- Solving equations of one variable -- Bisection method -- Regula Falsi and Secant methods -- Newton's method -- Muller's method -- Mathcad's methods -- Solving systems of linear equations: direct methods -- Gaussian elimination -- Gaussian elimination with row pivoting -- Gaussian elimination for tridiagonal systems -- Mathcad's methods -- Solving systems of linear equations: iterative methods -- Jacobi method -- Gauss-Seidel method -- Successive overrelaxation -- Mathcad's methods -- Systems of nonlinear equations -- Newton's method for systems of equations -- Fixed-point iteration for nonlinear systems -- Minimum of a nonlinear function -- Mathcad's methods -- LU factorization -- LU factorization from Gaussian elimination -- LU factorization of tridiagonal matrices -- LU factorization with pivoting -- Direct LU factorization -- Applications of LU factorization -- Mathcad's methods -- Eigenvalues, Eigenvectors, and QR factorization -- Power method -- QR factorization -- Finding Eigenvalues using QR factorization -- Mathcad's methods -- Interpolation -- Polynomial interpolation -- Hermite interpolation -- Rational function interpolation -- Spline interpolation -- Mathcad's methods -- Function approximation -- Least squares approximation -- Continuous least-squares approximation -- Function approximation at a point -- Mathcad's methods -- Fourier methods -- Fourier approximation and interpolation -- Fourier transforms for n = 2r -- Fast Fourier transforms for general n -- Mathcad's methods -- Numerical differentiation and integration -- Differentiation -- Basic numerical integration -- Better Numerical integration -- Gaussian quadrature -- Mathcad's methods -- Ordinary differential equations: Initial-value problems -- Taylor methods -- Runge-Kutta methods -- Multistep methods -- Stability -- Mathcad's methods -- Systems of ordinary differential equations -- Higher-order ODEs.

Enhanced descriptions from Syndetics:

This book presents the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences in a way that is both interesting and understandable. Using a wide range of examples and problems, this book focuses on the use of MathCAD functions and worksheets to illustrate the methods used when discussing the following concepts: solving linear and nonlinear equations, numerical linear algebra, numerical methods for data interpolation and approximation, numerical differentiation and integration, and numerical techniques for solving differential equations. For professionals in the fields of engineering, mathematics, computer science, and physical or life sciences who want to learn MathCAD functions for all major numerical methods.

Bibliography: (pages 667-672) and index.

Foundations -- Sample problems and numerical methods -- Some basic issues -- Getting started in Mathcad -- Solving equations of one variable -- Bisection method -- Regula Falsi and Secant methods -- Newton's method -- Muller's method -- Mathcad's methods -- Solving systems of linear equations: direct methods -- Gaussian elimination -- Gaussian elimination with row pivoting -- Gaussian elimination for tridiagonal systems -- Mathcad's methods -- Solving systems of linear equations: iterative methods -- Jacobi method -- Gauss-Seidel method -- Successive overrelaxation -- Mathcad's methods -- Systems of nonlinear equations -- Newton's method for systems of equations -- Fixed-point iteration for nonlinear systems -- Minimum of a nonlinear function -- Mathcad's methods -- LU factorization -- LU factorization from Gaussian elimination -- LU factorization of tridiagonal matrices -- LU factorization with pivoting -- Direct LU factorization -- Applications of LU factorization -- Mathcad's methods -- Eigenvalues, Eigenvectors, and QR factorization -- Power method -- QR factorization -- Finding Eigenvalues using QR factorization -- Mathcad's methods -- Interpolation -- Polynomial interpolation -- Hermite interpolation -- Rational function interpolation -- Spline interpolation -- Mathcad's methods -- Function approximation -- Least squares approximation -- Continuous least-squares approximation -- Function approximation at a point -- Mathcad's methods -- Fourier methods -- Fourier approximation and interpolation -- Fourier transforms for n = 2r -- Fast Fourier transforms for general n -- Mathcad's methods -- Numerical differentiation and integration -- Differentiation -- Basic numerical integration -- Better Numerical integration -- Gaussian quadrature -- Mathcad's methods -- Ordinary differential equations: Initial-value problems -- Taylor methods -- Runge-Kutta methods -- Multistep methods -- Stability -- Mathcad's methods -- Systems of ordinary differential equations -- Higher-order ODEs.

Table of contents provided by Syndetics

  • Preface (p. XI)
  • Examples/Mathcad Functions/Algorithms (p. XIII)
  • 1 Foundations (p. 1)
  • 1.1 Sample Problems and Numerical Methods (p. 4)
  • 1.1.1 Roots of Nonlinear Equations (p. 4)
  • 1.1.2 Fixed-Point Iteration (p. 5)
  • 1.1.3 Linear Systems (p. 6)
  • 1.1.4 Gaussian Elimination (p. 7)
  • 1.1.5 Numerical Integration (p. 8)
  • 1.1.6 Trapezoid Rule (p. 8)
  • 1.2 Some Basic Issues (p. 10)
  • 1.2.1 Key Issues for Iterative Methods (p. 10)
  • 1.2.2 How Good Is the Result? (p. 14)
  • 1.2.3 Getting Better Results (p. 22)
  • 1.3 Getting Started in Mathcad (p. 28)
  • 1.3.1 Overview of the Mathcad Workspace (p. 28)
  • 1.3.2 Mathematical Computations (p. 31)
  • 1.3.3 Operators on the Math Toolbars (p. 32)
  • 1.3.4 Built-In Functions (p. 35)
  • 1.3.5 Programming in Mathcad (p. 38)
  • 2 Solving Equations of One Variable (p. 47)
  • 2.1 Bisection Method (p. 50)
  • 2.1.1 Step-by-Step Computation (p. 50)
  • 2.1.2 Mathcad Function for Bisection (p. 52)
  • 2.1.3 Discussion (p. 54)
  • 2.2 Regula Falsi and Secant Methods (p. 55)
  • 2.2.1 Step-by-Step Computation for Regula Falsi (p. 56)
  • 2.2.2 Mathcad Function for the Regula Falsi Method (p. 58)
  • 2.2.3 Step-by-Step Computation for the Secant Method (p. 60)
  • 2.2.4 Mathcad Function for the Secant Method (p. 62)
  • 2.2.5 Discussion (p. 64)
  • 2.3 Newton's Method (p. 68)
  • 2.3.1 Step-by-Step Computation (p. 68)
  • 2.3.2 Mathcad Function for Newton's Method (p. 70)
  • 2.3.3 Discussion (p. 72)
  • 2.4 Muller's Method (p. 75)
  • 2.4.1 Step-by-Step Computation for Muller's Method (p. 76)
  • 2.4.2 Mathcad Function for Muller's Method (p. 78)
  • 2.4.3 Discussion (p. 80)
  • 2.5 Mathcad's Methods (p. 81)
  • 2.5.1 Using the Built-In Functions (p. 81)
  • 2.5.2 Understanding the Algorithms (p. 84)
  • 3 Solving Systems of Linear Equations: Direct Methods (p. 93)
  • 3.1 Gaussian Elimination (p. 96)
  • 3.1.1 Using Matrix Notation (p. 97)
  • 3.1.2 Step-by-Step Procedure (p. 98)
  • 3.1.3 Mathcad Function for Basic Gaussian Elimination (p. 101)
  • 3.1.4 Discussion (p. 103)
  • 3.2 Gaussian Elimination with Row Pivoting (p. 106)
  • 3.2.1 Step-by-Step Computation (p. 106)
  • 3.2.2 Mathcad Function for Gaussian Elimination with Pivoting (p. 110)
  • 3.2.3 Discussion (p. 113)
  • 3.3 Gaussian Elimination for Tridiagonal Systems (p. 113)
  • 3.3.1 Step-by-Step Procedure (p. 116)
  • 3.3.2 Mathcad Function for the Thomas Method (p. 118)
  • 3.3.3 Discussion (p. 119)
  • 3.4 Mathcad's Methods (p. 122)
  • 3.4.1 Using the Built-In Functions (p. 122)
  • 3.4.2 Understanding the Algorithms (p. 122)
  • 4 Solving Systems of Linear Equations: Iterative Methods (p. 131)
  • 4.1 Jacobi Method (p. 135)
  • 4.1.1 Step-by-Step Procedure for Jacobi Iteration (p. 136)
  • 4.1.2 Mathcad Function for the Jacobi Method (p. 139)
  • 4.1.3 Discussion (p. 142)
  • 4.2 Gauss-Seidel Method (p. 144)
  • 4.2.1 Step-by-Step Computation for Gauss-Seidel Method (p. 145)
  • 4.2.2 Mathcad Function for Gauss-Seidel Method (p. 148)
  • 4.2.3 Discussion (p. 150)
  • 4.3 Successive Overrelaxation (p. 151)
  • 4.3.1 Step-by-Step Computation of SOR (p. 152)
  • 4.3.2 Mathcad Function for SOR (p. 154)
  • 4.3.3 Discussion (p. 155)
  • 4.4 Mathcad's Methods (p. 157)
  • 4.4.1 Using the Built-In Functions (p. 157)
  • 4.4.2 Understanding the Algorithms (p. 159)
  • 5 Systems of Equations and Inequalities (p. 171)
  • 5.1 Newton's Method for Systems of Equations (p. 174)
  • 5.1.1 Matrix-Vector Notation (p. 176)
  • 5.1.2 Mathcad Function for Newton's Method (p. 177)
  • 5.2 Fixed-Point Iteration for Nonlinear Systems (p. 181)
  • 5.2.1 Step-by-Step Computation (p. 182)
  • 5.2.2 Mathcad Function for Fixed-Point Iteration for Nonlinear Systems (p. 182)
  • 5.2.3 Discussion (p. 186)
  • 5.3 Minimum of a Nonlinear Function (p. 187)
  • 5.3.1 Step-by-Step Computation of Minimization by Gradient Descent (p. 187)
  • 5.3.2 Mathcad Function for Minimization by Gradient Descent (p. 188)
  • 5.4 Mathcad's Methods (p. 192)
  • 5.4.1 Using the Built-In Functions (p. 192)
  • 5.4.2 Understanding the Algorithms (p. 193)
  • 6 LU Factorization (p. 201)
  • 6.1 LU Factorization from Gaussian Elimination (p. 203)
  • 6.1.1 A Step-by-Step Procedure for LU Factorization (p. 204)
  • 6.1.2 Mathcad Function for LU Factorization Using Gaussian Elimination (p. 206)
  • 6.2 LU Factorization of Tridiagonal Matrices (p. 207)
  • 6.2.1 Step-by-Step LU Factorization of a Tridiagonal Matrix (p. 207)
  • 6.2.2 Mathcad Function for LU Factorization of a Tridiagonal Matrix (p. 208)
  • 6.3 LU Factorization with Pivoting (p. 209)
  • 6.3.1 Step-by-Step Computation (p. 209)
  • 6.3.2 Mathcad Function for LU Factorization with Row Pivoting (p. 210)
  • 6.3.3 Discussion (p. 212)
  • 6.4 Direct LU Factorization (p. 215)
  • 6.4.1 Direct LU Factorization of a General Matrix (p. 215)
  • 6.4.2 LU Factorization of a Symmetric Matrix (p. 217)
  • 6.5 Applications of LU Factorization (p. 219)
  • 6.5.2 Solving a Tridiagonal System Using LU Factorization (p. 222)
  • 6.5.3 Determinant of a Matrix (p. 224)
  • 6.5.4 Inverse of a Matrix (p. 224)
  • 6.6 Mathcad's Methods (p. 226)
  • 6.6.1 Using the Built-In Functions (p. 226)
  • 6.6.2 Understanding the Algorithms (p. 226)
  • 7 Eigenvalues, Eigenvectors, and QR Factorization (p. 233)
  • 7.1 Power Method (p. 236)
  • 7.1.1 Basic Power Method (p. 237)
  • 7.1.2 Inverse Power Method (p. 242)
  • 7.1.3 Discussion (p. 247)
  • 7.2 QR Factorization (p. 248)
  • 7.2.1 Householder Transformations (p. 248)
  • 7.2.2 Givens Transformations (p. 257)
  • 7.2.3 Basic QR Factorization (p. 261)
  • 7.3 Finding Eigenvalues Using QR Factorization (p. 267)
  • 7.3.1 Basic QR Eigenvalue Method (p. 267)
  • 7.3.2 Better QR Eigenvalue Method (p. 268)
  • 7.3.3 Discussion (p. 270)
  • 7.4 Mathcad's Methods (p. 270)
  • 7.4.1 Using the Built-In Functions (p. 270)
  • 7.4.2 Understanding the Algorithms (p. 271)
  • 8 Interpolation (p. 283)
  • 8.1 Polynomial Interpolation (p. 286)
  • 8.1.1 Lagrange Interpolation Polynomials (p. 286)
  • 8.1.2 Newton Interpolation Polynomials (p. 295)
  • 8.1.3 Difficulties with Polynomial Interpolation (p. 306)
  • 8.2 Hermite Interpolation (p. 310)
  • 8.3 Rational Function Interpolation (p. 316)
  • 8.4 Spline Interpolation (p. 320)
  • 8.4.1 Piecewise Linear Interpolation (p. 321)
  • 8.4.2 Piecewise Quadratic Interpolation (p. 322)
  • 8.4.3 Piecewise Cubic Interpolation (p. 325)
  • 8.5 Mathcad's Methods (p. 334)
  • 8.5.1 Using the Built-In Functions (p. 334)
  • 8.5.2 Understanding the Algorithms (p. 335)
  • 9 Function Approximation (p. 349)
  • 9.1 Least Squares Approximation (p. 352)
  • 9.1.1 Linear Least-Squares Approximation (p. 352)
  • 9.1.2 Quadratic Least-Squares Approximation (p. 359)
  • 9.1.3 Cubic Least-Squares Approximation (p. 364)
  • 9.1.4 Least-Squares Approximation for Other Functional Forms (p. 369)
  • 9.2 Continuous Least-Squares Approximation (p. 373)
  • 9.2.1 Continuous Least-Squares with Orthogonal Polynomials (p. 376)
  • 9.2.2 Gram-Schmidt Process (p. 376)
  • 9.2.3 Legendre Polynomials (p. 378)
  • 9.2.4 Least-Squares Approximation with Legendre Polynomials (p. 379)
  • 9.3 Function Approximation at a Point (p. 381)
  • 9.3.1 Taylor Approximation (p. 381)
  • 9.3.2 Pade Function approximation (p. 382)
  • 9.4 Mathcad's Methods (p. 385)
  • 9.4.1 Using the Built-in Functions (p. 385)
  • 9.4.2 Understanding the Algorithms (p. 386)
  • 10 Fourier Methods (p. 393)
  • 10.1 Fourier Approximation and Interpolation (p. 396)
  • 10.2 Fast Fourier Transforms for n = 2[superscript r] (p. 407)
  • 10.2.1 Discrete Fourier Transform (p. 407)
  • 10.2.2 Fast Fourier Transform (p. 408)
  • 10.3 Fast Fourier Transforms for General n (p. 415)
  • 10.4 Mathcad's Methods (p. 423)
  • 10.4.1 Using the Built-In Functions (p. 423)
  • 10.4.2 Understanding the Algorithms (p. 424)
  • 11 Numerical Differentiation and Integration (p. 436)
  • 11.1 Differentiation (p. 436)
  • 11.1.1 First Derivatives (p. 436)
  • 11.1.2 Higher Derivatives (p. 440)
  • 11.1.3 Partial Derivatives (p. 441)
  • 11.1.4 Richardson Extrapolation (p. 442)
  • 11.2 Basic Numerical Integration (p. 445)
  • 11.2.1 Trapezoid Rule (p. 446)
  • 11.2.2 Simpson Rule (p. 448)
  • 11.2.3 The Midpoint Formula (p. 450)
  • 11.2.4 Other Newton-Cotes Open Formulas (p. 452)
  • 11.3 Better Numerical Integration (p. 452)
  • 11.3.1 Composite Trapezoid Rule (p. 453)
  • 11.3.2 Composite Simpson's Rule (p. 455)
  • 11.3.3 Extrapolation Methods for Quadrature (p. 458)
  • 11.4 Gaussian Quadrature (p. 462)
  • 11.4.1 Gaussian Quadrature on [-1,1] (p. 462)
  • 11.4.2 Gaussian Quadrature on [a,b] (p. 464)
  • 11.5 Mathcad's Methods (p. 468)
  • 11.5.1 Using the Operators (p. 468)
  • 11.5.2 Understanding the Algorithms (p. 469)
  • 12 Ordinary Differential Equations: Initial-Value Problems (p. 477)
  • 12.1 Taylor Methods (p. 479)
  • 12.1.1 Euler's Method (p. 479)
  • 12.1.2 Higher-Order Taylor Methods (p. 484)
  • 12.2 Runge-Kutta Methods (p. 487)
  • 12.2.1 Midpoint Method (p. 487)
  • 12.2.2 Other Second-Order Runge-Kutta Methods (p. 492)
  • 12.2.3 Third-Order Runge-Kutta Methods (p. 494)
  • 12.2.4 Classic Runge-Kutta Method (p. 495)
  • 12.2.5 Other Runge-Kutta Methods (p. 499)
  • 12.2.6 Runge-Kutta-Fehlberg Methods (p. 501)
  • 12.3 Multistep Methods (p. 502)
  • 12.3.1 Adams-Bashforth Methods (p. 502)
  • 12.3.2 Adams-Moulton Methods (p. 508)
  • 12.3.3 Predictor-Corrector Methods (p. 509)
  • 12.4 Stability (p. 514)
  • 12.5 Mathcad's Methods (p. 517)
  • 12.5.1 Using the Built-In Functions (p. 517)
  • 12.5.2 Understanding the Algorithms (p. 520)
  • 13 Systems of Ordinary Differential Equations (p. 529)
  • 13.1 Higher-Order ODEs (p. 532)
  • 13.2 Systems of Two First-Order ODE (p. 534)
  • 13.2.1 Euler's Method for Solving Two ODE-IVPs (p. 534)
  • 13.2.2 Midpoint Method for Solving Two ODE-IVPs (p. 537)
  • 13.3 Systems of First-Order ODE-IVP (p. 541)
  • 13.3.1 Euler's Method for Solving Systems of ODEs (p. 542)
  • 13.3.2 Runge-Kutta Methods for Solving Systems of ODEs (p. 544)
  • 13.3.3 Multistep Methods for Systems (p. 552)
  • 13.4 Stiff ODE and Ill-Conditioned Problems (p. 557)
  • 13.5 Mathcad's Methods (p. 559)
  • 13.5.1 Using the Built-In Functions (p. 559)
  • 13.5.2 Understanding the Algorithms (p. 562)
  • 14 Ordinary Differential Equations--Boundary Value Problems (p. 575)
  • 14.1 Shooting Method for Solving Linear BVP (p. 578)
  • 14.1.1 Simple Boundary Conditions (p. 578)
  • 14.1.2 General Boundary Condition at x = b (p. 583)
  • 14.1.3 General Boundary Conditions at Both Ends of the Interval (p. 584)
  • 14.2 Shooting Method for Solving Nonlinear BVP (p. 585)
  • 14.2.1 Nonlinear Shooting Based on the Secant Method (p. 585)
  • 14.2.2 Nonlinear Shooting Using Newton's Method (p. 588)
  • 14.3 Finite-Difference Method for Solving Linear BVP (p. 592)
  • 14.4 Finite-Difference Method for Nonlinear BVP (p. 599)
  • 14.5 Mathcad's Methods (p. 602)
  • 14.5.1 Using the Built-In Functions (p. 602)
  • 14.5.2 Understanding the Algorithms (p. 604)
  • 15 Partial Differential Equations (p. 609)
  • 15.1 Classification of PDE (p. 613)
  • 15.2 Heat Equation: Parabolic PDE (p. 614)
  • 15.2.1 Explicit Method for Solving the Heat Equation (p. 615)
  • 15.2.2 Implicit Method for Solving the Heat Equation (p. 623)
  • 15.2.3 Crank-Nicolson Method for Solving the Heat Equation (p. 628)
  • 15.2.4 Heat Equation with Insulated Boundary (p. 632)
  • 15.3 Wave Equation: Hyperbolic PDE (p. 633)
  • 15.3.1 Explicit Method for Solving Wave Equations (p. 634)
  • 15.3.2 Implicit Method for Solving Wave Equation (p. 638)
  • 15.4 Poisson Equation: Elliptic PDE (p. 640)
  • 15.5 Finite-Element Method for Solving an Elliptic PDE (p. 645)
  • 15.6 Mathcad's Methods (p. 658)
  • 15.6.1 Using the Built-In Functions (p. 658)
  • 15.6.2 Understanding the Algorithms (p. 659)
  • Bibliography (p. 667)
  • Answers to Selected Problems (p. 673)
  • Index (p. 695)

Excerpt provided by Syndetics

The purpose of this text is to present the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences in a manner that is both interesting and understandable to undergraduate and beginning graduate students in those fields. The organization of the chapters, and of the material within each chapter, the use of Mathcad worksheets and functions to illustrate the methods, and the exercises provided are all designed with student learning as the primary objective. The first chapter sets the stage for the material in the rest of the text, by giving a brief introduction to the long history of numerical techniques, and a "preview of coming attractions" for some of the recurring themes of the remainder of the text. It also presents enough description of Mathcad to allow students to use the Mathcad functions presented for each of the numerical methods discussed in the other chapters. An algorithmic statement of each method is also included; the algorithm may be used as the basis for computations using a variety of types of technological support, ranging from paper and pencil, to calculators, Mathcad worksheets or developing computer programs. Each of the subsequent chapters begins with a one-page overview of the subject matter, together with an indication as to how the topics presented in the chapter are related to those in previous and subsequent chapters. Introductory examples are presented to suggest a few of the types of problems for which the topics of the chapter may be used. Following the sections in which the methods are presented, each chapter concludes with a summary of the most important formulas, a selection of suggestions for further reading, and an extensive set of exercises. The first group of problems provide fairly routine practice of the techniques; the second group are applications adapted from a variety of fields, and the final group of problems encourage students to extend their understanding of either the theoretical or the computational aspects of the methods. The presentation of each numerical technique is based on the successful teaching methodology of providing examples and geometric motivation for a method, and a concise statement of the steps to carry out the computation, before giving a mathematical derivation of the process or a discussion of the more theoretical issues that are relevant to the use and understanding of the topic. Each topic is illustrated by examples that range in complexity from very simple to moderate. Geometrical or graphical illustrations are included whenever they are appropriate. A simple Mathcad function is presented for each method, which also serves as a clear step-by-step description of the process; discussion of theoretical considerations is placed at the conclusion of the section. The last section of each chapter gives a brief discussion of Mathcad's built-in functions for solving the kinds of problems covered in the chapter. The chapters are arranged according to the following general areas: Chapters 2-5 deal with solving linear and nonlinear equations. Chapters 6 and 7 treat topics from numerical linear algebra. Chapters 8-10 cover numerical methods for data interpolation and approximation. Chapters 11 presents numerical differentiation and integration. Chapters 12-15 introduce numerical techniques for solving differential equations. For much of the material, a calculus sequence that includes an introduction to differential equations and linear algebra provides adequate background. For more in depth coverage of the topics from linear algebra (especially the QR method for eigenvalues) a linear algebra course would be an appropriate prerequisite. The coverage of Fourier approximation and FFT (Chapter 10) and partial differential equations (Chapter 15) also assumes that the students have somewhat more mathematical maturity than the other chapters, since the material in intrinsically more challenging. The subject matter included is suitable for a two-semester sequence of classes, or for any of several different one-term courses, depending on the desired emphasis, student background, and selection of topics. Many people have contributed to the development of this text. My colleagues at Florida Institute of Technology, the Naval Postgraduate School, the University of South Carolina Aiken, and Georgia Southern University have provided support, encouragement, and suggestions. I especially want to thank Jacalyn Huband for the development of the Mathcad functions and examples. I also wish to thank three other colleagues for their particular contributions: Jane Lybrand for the data from classroom experiments used in several examples and exercises in Ch 9. Jack Leifer for providing data, as well as helpful discussions on engineering applications and the use of Mathcad in engineering; Pierre Larochelle for the example of robot motion in Ch 13.1 also appreciate the many contributions my students have made to this text, which was after all written with them in mind. The comments made by the reviewers of the text have helped greatly in the fine-tuning of the final presentation. The editorial and production staff at Prentice Hall, as well as Patty Donovan, and the rest of the staff at Pinetree Composition, have my heartfelt gratitude for their efforts in insuring that the text is as accurate and as well designed as possible. And, saving the most important for last, I thank my husband and colleague, Don Fausett, for his patience and support. Laurene Fausett Excerpted from Numerical Methods Using MathCAD by Laurene V. Fausett All rights reserved by the original copyright owners. Excerpts are provided for display purposes only and may not be reproduced, reprinted or distributed without the written permission of the publisher.