Introduction to numerical analysis and scientific computing
By: Nabil Nassif, Dolly Khuwayri Fayyad
Contributors: Fayyad, Dolly Khuwayri, author
Publisher: CRC Press, Taylor & Francis Group
Published: 2014
Place of publication: Boca Raton
Language: eng
Number of pages: 311
ISBN-13: 9781466589483
Copyright date: 2014
Subjects: Numerical analysis; Textbooks; Computer science; Mathematics; MATHEMATICS / Advanced; MATHEMATICS / Applied; MATHEMATICS / Number Systems
Description: "Designed for a one-semester course on the subject, this classroom-tested text presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. Drawing on their years of teaching students in mathematics, engineering, and the sciences, the authors cover floating-point number representations, nonlinear equations, linear algebra concepts, the Lagrange interpolation theorem, numerical differentiation and integration, and ODEs. They also focus on the implementation of the algorithms using MATLAB®"--

"This work is the result of several years of teaching a one-semester course on Numerical Analysis and Scienti c Computing, addressed primarily to stu- dents in Mathematics, Engineering, and Sciences. Our purpose is to provide those students with fundamental concepts of Numerical Mathematics and at the same time stir their interest in the art of implementing and programing Numerical Methods"--
Notes: Includes bibliographical references and index.
Table of contents: title: Preface
pagenum: xi; title: About the Authors
pagenum: xiii; title: List of Figures
pagenum: xv; title: List of Tables
pagenum: xvii; label: 1
title: Computer Number Systems and Floating Point Arithmetic
pagenum: 1; label: 1.1
title: Introduction
pagenum: 1; label: 1.2
title: Conversion from Base 10 to Base 2
pagenum: 3; label: 1.2.1
title: Conversion of the Integral Part
pagenum: 3; label: 1.2.2
title: Conversion of the Fractional Part
pagenum: 7; label: 1.3
title: Conversion from Base 2 to Base 10
pagenum: 9; label: 1.3.1
title: Polynomial Evaluation
pagenum: 9; label: 1.3.2
title: Conversion of the Integral Part
pagenum: 11; label: 1.3.3
title: Conversion of the Fractional Part
pagenum: 11; label: 1.4
title: Normalized Floating Point Systems
pagenum: 12; label: 1.4.1
title: Introductory Concepts
pagenum: 12; label: 1.4.2
title: IEEE Floating Point Systems
pagenum: 18; label: 1.4.3
title: Denormalized Numbers in MATLAB
pagenum: 23; label: 1.4.4
title: Rounding Errors in Floating Point Representation
pagenum: 24; label: 1.5
title: Floating Point Operations
pagenum: 27; label: 1.5.1
title: Algebraic Properties in Floating Point Operations
pagenum: 28; label: 1.5.2
title: The Problem of Absorption
pagenum: 30; label: 1.5.3
title: The Problem of Cancellation or Loss of Precision
pagenum: 31; label: 1.6
title: Computing in a Floating Point System
pagenum: 34; label: 1.6.1
title: Cardinality and Distribution of Floating Point Systems
pagenum: 35; label: 1.6.2
title: A MATLAB Simulation of a Floating Point System
pagenum: 36; label: 1.6.3
title: Tips for Floating Point Computation
pagenum: 36; label: 1.7
title: Exercises
pagenum: 39; label: 1.8
title: Computer Projects
pagenum: 45; label: 2
title: Finding Roots of Real Single-Valued Functions
pagenum: 49; label: 2.1
title: Introduction
pagenum: 49; label: 2.2
title: How to Locate the Roots of a Function
pagenum: 51; label: 2.3
title: The Bisection Method
pagenum: 53; label: 2.4
title: Newton's Method
pagenum: 59; label: 2.5
title: The Secant Method
pagenum: 67; label: 2.6
title: Exercises
pagenum: 73; label: 2.7
title: Computer Projects
pagenum: 78; label: 3
title: Solving Systems of Linear Equations by Gaussian Elimination
pagenum: 85; label: 3.1
title: Mathematical Preliminaries
pagenum: 85; label: 3.2
title: Computer Storage and Data Structures for Matrices
pagenum: 87; label: 3.3
title: Back Substitution for Upper Triangular Systems
pagenum: 88; label: 3.4
title: Gauss Reduction
pagenum: 91; label: 3.4.1
title: Naive Gauss Elimination
pagenum: 93; label: 3.4.2
title: Partial Pivoting: Unscaled and Scaled Partial Pivoting
pagenum: 95; label: 3.5
title: LU Decomposition
pagenum: 104; label: 3.5.1
title: Computing the Determinant of a Matrix
pagenum: 106; label: 3.5.2
title: Computing the Inverse of A
pagenum: 107; label: 3.5.3
title: Solving Linear Systems Using LU Factorization
pagenum: 109; label: 3.6
title: Exercises
pagenum: 111; label: 3.7
title: Computer Projects
pagenum: 117; label: 4
title: Polynomial Interpolation and Splines Fitting
pagenum: 123; label: 4.1
title: Definition of Interpolation
pagenum: 123; label: 4.2
title: General Lagrange Polynomial Interpolation
pagenum: 124; label: 4.3
title: Recurrence Formulae
pagenum: 127; label: 4.3.1
title: Neville's Formula
pagenum: 127; label: 4.3.2
title: Newton's Form for the Interpolation Polynomial
pagenum: 129; label: 4.3.3
title: Divided Differences Table and Newton's Formula
pagenum: 131; label: 4.4
title: Equally Spaced Data: Difference Operators
pagenum: 135; label: 4.5
title: Errors in Polynomial Interpolation
pagenum: 138; label: 4.6
title: Local Interpolation: Spline Functions
pagenum: 141; label: 4.6.1
title: Linear Spline Interpolation
pagenum: 141; label: 4.6.2
title: Quadratic Spline Interpolation
pagenum: 143; label: 4.6.3
title: Cubic Spline Interpolation
pagenum: 146; label: 4.6.4
title: Solving a Tridiagonal System
pagenum: 152; label: 4.6.5
title: Errors in Spline Interpolation
pagenum: 153; label: 4.7
title: Concluding Remarks
pagenum: 154; label: 4.8
title: Exercises
pagenum: 155; label: 4.9
title: Computer Projects
pagenum: 162; label: 5
title: Numerical Differentiation and Integration
pagenum: 167; label: 5.1
title: Introduction
pagenum: 167; label: 5.2
title: Mathematical Prerequisites
pagenum: 168; label: 5.3
title: Numerical Differentiation
pagenum: 169; label: 5.3.1
title: Approximation of First Derivatives: Error Analysis
pagenum: 170; label: 5.3.2
title: Approximation of Second Derivatives: Error Analysis
pagenum: 174; label: 5.4
title: Richardson Extrapolation
pagenum: 176; label: 5.5
title: Richardson Extrapolation in Numerical Differentiation
pagenum: 178; label: 5.5.1
title: Richardson Extrapolation for First Derivatives
pagenum: 178; label: 5.5.2
title: Richardson Extrapolation for Second Derivatives
pagenum: 182; label: 5.6
title: Numerical Integration
pagenum: 183; label: 5.6.1
title: The Rectangular Rules
pagenum: 185; label: 5.6.2
title: The Trapezoidal Rule
pagenum: 186; label: 5.6.3
title: The Midpoint Rectangular Rule
pagenum: 188; label: 5.6.4
title: Recurrence Relation for the Trapezoidal Rule
pagenum: 190; label: 5.6.5
title: Simpson's Rule
pagenum: 191; label: 5.7
title: Romberg Integration
pagenum: 194; label: 5.8
title: Appendix: Error Term for Midpoint Rule, \(h = \frac{b - a}{2^l}\)
pagenum: 197; label: 5.9
title: Exercises
pagenum: 199; label: 5.10
title: Computer Projects
pagenum: 207; label: 6
title: Advanced Numerical Integration
pagenum: 211; label: 6.1
title: Numerical Integration for Non-Uniform Partitions
pagenum: 211; label: 6.1.1
title: Generalized Formulae and Error Analysis
pagenum: 211; label: 6.1.2
title: The Case for Adaptive Numerical Integration
pagenum: 213; label: 6.1.3
title: Adaptive Simpson's Integration
pagenum: 213; label: 6.2
title: Numerical Integration of Functions of Two Variables
pagenum: 218; label: 6.2.1
title: Double Integrals over Rectangular Domains
pagenum: 218; label: 6.2.2
title: Double Rectangular Rule
pagenum: 219; label: 6.2.3
title: Double Trapezoidal and Midpoint Rules
pagenum: 220; label: 6.2.4
title: Double Simpson's Rule
pagenum: 220; label: 6.2.5
title: Error Estimates
pagenum: 221; label: 6.2.6
title: Double Integrals over Convex Polygonal Domains
pagenum: 223; label: 6.3
title: Monte Carlo Simulations for Numerical Quadrature
pagenum: 228; label: 6.3.1
title: On Random Number Generation
pagenum: 228; label: 6.3.2
title: Estimation of Integrals through Areas and Volumes
pagenum: 229; label: 6.3.3
title: Estimating Mean Values
pagenum: 232; label: 6.4
title: Exercises
pagenum: 234; label: 6.5
title: Computer Exercises
pagenum: 236; label: 7
title: Numerical Solutions of Ordinary Differential Equations (ODEs)
pagenum: 237; label: 7.1
title: Introduction
pagenum: 237; label: 7.2
title: Analytic Solutions to ODEs
pagenum: 240; label: 7.3
title: Mathematical Settings for Numerical Solutions to ODEs
pagenum: 244; label: 7.4
title: Explicit Runge-Kutta Schemes
pagenum: 249; label: 7.4.1
title: Euler Explicit Method
pagenum: 250; label: 7.4.2
title: Second-Order Explicit Runge-Kutta Methods
pagenum: 252; label: 7.4.3
title: General Explicit Runge-Kutta Methods
pagenum: 256; label: 7.4.4
title: Control of the Time-Step Size
pagenum: 261; label: 7.5
title: Adams Multistep Methods
pagenum: 266; label: 7.5.1
title: Adams Schemes of Order 1
pagenum: 267; label: 7.5.2
title: Adams Schemes of Order 2
pagenum: 268; label: 7.5.3
title: Adams Schemes of Order 3
pagenum: 268; label: 7.5.4
title: Adams Methods of Order 4
pagenum: 269; label: 7.6
title: Multistep Backward Difference Formulae
pagenum: 270; label: 7.7
title: Approximation of a Two-Points Boundary Value Problem
pagenum: 272; label: 7.8
title: Exercises
pagenum: 275; label: 7.9
title: Computer Exercises
pagenum: 277; title: Answers to Odd-Numbered Exercises
pagenum: 279; title: Bibliography
pagenum: 307; title: Index
pagenum: 309