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

1. Mathematics Preliminaries and Floating-Point Representation
1.1 Introduction
1.2 Mathematics Preliminaries
1.3 Floating-Point Representation
1.4 Loss of Significance

2. Linear Systems
2.1 Naive Gaussian Elimination
2.2 Gaussian Elimination with Scaled Partial Pivoting
2.3 Tridiagonal and Banded Systems

3. Nonlinear Equations
3.1 Bisection Method
3.2 Newton's Method
3.3 Secant Method

4. Interpolation and Numerical Differentiation
4.1 Polynomial Interpolation
4.2 Errors in Polynomial Interpolation
4.3 Estimating Derivatives and Richardson Extrapolation

5. Numerical Integration
5.1 Trapezoid Method
5.2 Romberg Algorithm
5.3 Simpson's Rule and Newton-Cotes Rule

6. Spline Functions
6.1 First-Degree and Second-Degree Splines
6.2 Natural Cubic Splines
6.3 B Splines: Interpolation and Approximation

7. Initial-Value Problems
7.1 Taylor Series Methods
7.2 Runge-Kutta Methods
7.3 Adaptive Runge-Kutta and Multistep Method
7.4 Methods for First and Higher-Order Systems

8. More on Linear Systems
8.1 Matrix Factorizations
8.2 Eigenvalues and Eigenvectors
8.3 Power Methods
8.2 Iterative Solution of Linear Systems

9. 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

10. Monte Carlo Methods and Simulation
10.1 Random Numbers
10.2 Estimation of Areas and Volumes by Monte Carlo Techniques
10.3 Simulation

11. Boundary Value Problems
11.1 Shooting Method
11.2 A Discretization Method

12. Partial Differential Equations
12.1 Parabolic Problems
12.2 Hyperbolic Problems
12.3 Elliptic Problems

13. Minimization of Functions
13.1 One-Variable Case
13.2 Multivariate Case

14. 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 Floating-Point Arithmetic

Appendix D: Linear Algebra Concepts and Notation