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

Preface

1. Introduction 1.1 Preliminary Remarks
1.2 Review of Taylor Series

2. Number Representation and Errors 2.1 Representation of Numbers in Different Bases
2.2 Floating-Point Representation
2.3 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 Definite Integral
5.2 Trapezoid Rule
5.3 Romberg Algorithm

6. More on Numerical Integration 6.1 An Adaptive Simpson's Scheme
6.2 Gaussian Quadrature Formulas

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. 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

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 by B Spines

10. Ordinary Differential Equations 10.0 Initial-Value Problem: Analytical vs. Numerical Solution
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 The 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 16.0 Unconstrained and Constrained Minimization Problems
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: Some Advice on Good Programming Practices

Appendix B: An Overview of Mathematical Software on the WEB

Appendix C: Additional Details on IEEE Floating-Point Arithmetic

Appendix D: Review of Linear Algebra Concepts and Notation

Appendix E: Sir Isaac Newton: Never at Rest

Answers for Selected Problems

Bibliography

Index

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 05/14/2003