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

Preface

1. Introduction 1.1 Preliminary Remarks
1.2 Review of Taylor Series

2. Floating-Point Representation and Errors 2.1 Floating-Point Representation
2.2 Loss of Significance

3. Locating Roots of 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 Lower and Upper Sums
5.2 Trapezoid Rule
5.3 Romberg Algorithm

6. Additional Topics on Numerical Integration 6.1 Simpson's Rule and Adaptive Simpson's Rule

7. Systems of Linear Equations 7.1 Naive Gaussian Elimination
7.2 Gaussian Elimination with Scaled Partial Pivoting
7.3 Tridiagonal and Banded Systems

8. 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

9. Approximation by Spline Functions 9.1 First-Degree and Second-Degree Splines
9.2 Natural Cubic Splines
9.3 B Splines: Interpolation and Approximation

10. Ordinary Differential Equations 10.1 Taylor Series Methods
10.2 Runge-Kutta Methods
10.3 Stability, Adaptive Runge-Kutta Methods, and Multistep Methods

11. Systems of Ordinary Differential Equations 11.1 Methods for First-Order Systems
11.2 Higher-Order Equations and Systems

12. 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

13. Monte Carlo Methods and Simulation 13.1 Random Numbers
13.2 Estimation of Areas and Volumes by Monte Carlo Techniques
13.3 Simulation

14. Boundary Value Problems for Ordinary Differential Equations 14.1 Shooting Method
14.2 A Discretization Method

15. Partial Differential Equations 15.0 Some Partial Differential Equations from Applied Problems
15.1 Parabolic Problems
15.2 Hyperbolic Problems
15.3 Elliptic Problems

16. Minimization of Multivariate Functions 16.1 One-Variable Case
16.2 Multivariate Case

17. 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 Floating-Point Arithmetic

Appendix D: Linear Algebra Concepts and Notation