Numerical Mathematics and Computing
Fifth Edition
Ward Cheney & David Kincaid
Table of Contents
 Preface

 Introduction
1.1 Preliminary Remarks
1.2 Review of Taylor Series
 Number Representation and Errors
2.1 Representation of Numbers in Different Bases
2.2 FloatingPoint Representation
2.3 Loss of Significance
 Locating Roots of Equations
3.1 Bisection Method
3.2 Newton's Method
3.3 Secant Method
 Interpolation and Numerical Differentiation
4.1 Polynomial Interpolation
4.2 Errors in Polynomial Interpolation
4.3 Estimating Derivatives and Richardson Extrapolation
 Numerical Integration
5.1 Definite Integral
5.2 Trapezoid Rule
5.3 Romberg Algorithm
 More on Numerical Integration
6.1 An Adaptive Simpson's Scheme
6.2 Gaussian Quadrature Formulas
 Systems of Linear Equations
7.1 Naive Gaussian Elimination
7.2 Gaussian Elimination with Scaled Partial Pivoting
7.3 Tridiagonal and Banded Systems
 More on Systems of Linear Equations
8.1 LU Factorizations
8.2 Iterative Solution of Linear Systems
8.3 Eigenvalues and Eigenvectors
8.4 Power Methods
 Approximation by Spline Functions
9.1 FirstDegree and SecondDegree Splines
9.2 Natural Cubic Splines
9.3 B Splines: Interpolation and Approximation by B Spines
 Ordinary Differential Equations
10.0 InitialValue Problem: Analytical vs. Numerical Solution
10.1 Taylor Series Methods
10.2 RungeKutta Methods
10.3 Stability, Adaptive RungeKutta Methods, and Multistep Methods
 Systems of Ordinary Differential Equations
11.1 Methods for FirstOrder Systems
11.2 HigherOrder Equations and Systems
11.3 AdamsMoulton Methods
 Smoothing of Data and the Method of Least Squares
12.1 The Method of Least Squares
12.2 Orthogonal Systems and Chebyshev Polynomials
12.3 Other Examples of the Least Squares Principle
 Monte Carlo Methods and Simulation
13.1 Random Numbers
13.2 Estimation of Areas and Volumes by Monte Carlo Techniques
13.3 Simulation
 Boundary Value Problems for Ordinary Differential Equations
14.1 Shooting Method
14.2 A Discretization Method
 Partial Differential Equations
15.0 Some Partial Differential Equations from Applied Problems
15.1 Parabolic Problems
15.2 Hyperbolic Problems
15.3 Elliptic Problems
 Minimization of Multivariate Functions
16.0 Unconstrained and Constrained Minimization Problems
16.1 OneVariable Case
16.2 Multivariate Case
 Linear Programming
17.1 Standard Forms and Duality
17.2 Simplex Method
17.3 Approximate Solution of Inconsistent Linear Systems
 Appendix A: Some Advice on Good Programming Practices
 Appendix B: An Overview of Mathematical Software on the WEB
 Appendix C: Additional Details on IEEE FloatingPoint Arithmetic
 Appendix D: Review of Linear Algebra Concepts and Notation
 Appendix E: Sir Isaac Newton: Never at Rest
 Answers for Selected Problems
 Bibliography
 Index