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


 Mathematics Preliminaries and FloatingPoint Representation
1.1 Introduction
1.2 Mathematics Preliminaries
1.3 FloatingPoint Representation
1.4 Loss of Significance
 Linear Systems
2.1 Naive Gaussian Elimination
2.2 Gaussian Elimination with Scaled Partial Pivoting
2.3 Tridiagonal and Banded Systems
 Nonlinear 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 Trapezoid Method
5.2 Romberg Algorithm
5.3 Simpson's Rule and NewtonCotes Rule
5.4 Gaussian Quadrature Formulas
 Spline Functions
6.1 FirstDegree and SecondDegree Splines
6.2 Natural Cubic Splines
6.3 B Splines: Interpolation and Approximation
 InitialValue Problems
7.1 Taylor Series Methods
7.2 RungeKutta Methods
7.3 Adaptive RungeKutta and Multistep Method
7.4 Methods for First and HigherOrder Systems
7.5 AdamsBashforthMoulton Methods
 More on Linear Systems
8.1 Matrix Factorizations
8.2 Eigenvalues and Eigenvectors
8.3 Power Methods
8.2 Iterative Solution of Linear Systems
 Least Squares Methods and Fourier Series
9.1 Method of Least Squares
9.2 Orthogonal Systems and Chebyshev Polynomials
9.3 Examples of the Least Squares Principle
9.4 Fourier Series
 Monte Carlo Methods and Simulation
10.1 Random Numbers
10.2 Estimation of Areas and Volumes by Monte Carlo Techniques
10.3 Simulation
 Boundary Value Problems
11.1 Shooting Method
11.2 A Discretization Method
 Partial Differential Equations
12.1 Parabolic Problems
12.2 Hyperbolic Problems
12.3 Elliptic Problems
 Minimization of Functions
13.1 OneVariable Case
13.2 Multivariate Case
 Linear Programming Problems
14.1 Standard Forms and Duality
14.2 Simplex Method
14.3 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 Exercises
 Bibliography
 Index