Numerical Mathematics and Computing
Sixth Edition
Ward Cheney & David Kincaid
Brooks/Cole: Engage Learning
Table of Contents

Preface

 Introduction
1.1 Preliminary Remarks
1.2 Review of Taylor Series
 FloatingPoint Representation and Errors
2.1 FloatingPoint Representation
2.2 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 Lower and Upper Sums
5.2 Trapezoid Rule
5.3 Romberg Algorithm
 Additional Topics on Numerical Integration
6.1 Simpson's Rule and Adaptive Simpson's Rule
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
 Additional Topics on Systems of Linear Equations
8.1 Matrix 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
 Ordinary Differential Equations
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 AdamsBashforthMoulton Methods
 Smoothing of Data and the Method of Least Squares
12.1 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
16.1 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: Advice on Good Programming Practices
 Appendix B: Representation of Numbers in Different Bases
 Appendix C: Additional Details on IEEE FloatingPoint Arithmetic
 Appendix D: Linear Algebra Concepts and Notation
 Answers for Selected Problems
 Bibliography
 Index