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."—Zentralblatt MATH
". . . carefully structured with many detailed worked examples."—The Mathematical Gazette
The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis.
An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higherlevel methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and ClenshawCurtis quadrature, are presented from an introductory perspective, and the Second Edition also features:
Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material
Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises
Widespread exposure and utilization of MATLAB
An appendix that contains proofs of various theorems and other material
The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
Table of Contents
 Cover
 Half Title page
 Title page
 Copyright page
 Dedication
 Preface

Chapter 1: Introductory Concepts and Calculus Review
 1.1 Basic Tools of Calculus
 1.2 Error, Approximate Equality, and Asymptotic Order Notation
 1.3 A Primer on Computer Arithmetic
 1.4 A Word on Computer Languages and Software
 1.5 Simple Approximations
 1.6 Application: Approximating the Natural Logarithm
 1.7 A Brief History of Computing
 1.8 Literature Review
 References

Chapter 2: A Survey of Simple Methods and Tools
 2.1 Horner’s Rule and Nested Multiplication
 2.2 Difference Approximations to the Derivative
 2.3 Application: Euler’s Method for Initial Value Problems
 2.4 Linear Interpolation
 2.5 Application—The Trapezoid Rule
 2.6 Solution of Tridiagonal Linear Systems
 2.7 Application: Simple TwoPoint Boundary Value Problems

Chapter 3: RootFinding
 3.1 The Bisection Method
 3.2 Newton’s Method: Derivation and Examples
 3.3 How to Stop Newton’s Method
 3.4 Application: Division Using Newton’s Method
 3.5 The Newton Error Formula
 3.6 Newton’s Method: Theory and Convergence
 3.7 Application: Computation of the Square Root
 3.8 The Secant Method: Derivation and Examples
 3.9 FixedPoint Iteration
 3.10 Roots of Polynomials, Part 1
 3.11 Special Topics in RootFinding Methods
 3.12 Very HighOrder Methods and the Efficiency Index
 3.13 Literature and Software Discussion
 References

Chapter 4: Interpolation and Approximation
 4.1 Lagrange Interpolation
 4.2 Newton Interpolation and Divided Differences
 4.3 Interpolation Error
 4.4 Application: Muller’s Method and Inverse Quadratic Interpolation
 4.5 Application: More Approximations to the Derivative
 4.6 Hermite Interpolation
 4.7 Piecewise Polynomial Interpolation
 4.8 An Introduction to Splines
 4.9 Application: Solution of Boundary Value Problems
 4.10 Tension Splines
 4.11 Least Squares Concepts in Approximation
 4.12 Advanced Topics in Interpolation Error
 4.13 Literature and Software Discussion
 References

Chapter 5: Numerical Integration
 5.1 A Review of the Definite Integral
 5.2 Improving the Trapezoid Rule
 5.3 Simpson’s Rule and Degree of Precision
 5.4 The Midpoint Rule
 5.5 Application: Stirling’s Formula
 5.6 Gaussian Quadrature
 5.7 Extrapolation Methods
 5.8 Special Topics in Numerical Integration
 5.9 Literature and Software Discussion
 References

Chapter 6: Numerical Methods for Ordinary Differential Equations
 6.1 The Initial Value Problem: Background
 6.2 Euler’s Method
 6.3 Analysis of Euler’s Method
 6.4 Variants of Euler’s Method
 6.5 SingleStep Methods: Runge–Kutta
 6.6 Multistep Methods
 6.7 Stability Issues
 6.8 Application to Systems of Equations
 6.9 Adaptive Solvers
 6.10 Boundary Value Problems
 6.11 Literature and Software Discussion
 References

Chapter 7: Numerical Methods for the Solution of Systems of Equations
 7.1 Linear Algebra Review
 7.2 Linear Systems and Gaussian Elimination
 7.3 Operation Counts
 7.4 The LU Factorization
 7.5 Perturbation, Conditioning, and Stability
 7.6 SPD Matrices and the Cholesky Decomposition
 7.7 Iterative Methods for Linear Systems: A Brief Survey
 7.8 Nonlinear Systems: Newton’s Method and Related Ideas
 7.9 Application: Numerical Solution of Nonlinear Boundary Value Problems
 7.10 Literature and Software Discussion
 References
 Chapter 8: Approximate Solution of the Algebraic Eigenvalue Problem
 Chapter 9: A Survey of Numerical Methods for Partial Differential Equations
 Chapter 10: An Introduction to Spectral Methods
 Appendix A: Proofs of Selected Theorems, and Additional Material
 Index
Product Information
 Title: An Introduction to Numerical Methods and Analysis, 2nd Edition
 Author(s):
 Release date: October 2013
 Publisher(s): Wiley
 ISBN: 9781118407462