Numerical Mathematics and Computing
Fifth Edition

Ward Cheney & David Kincaid
Table of Contents


  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
    11.3 Adams-Moulton Methods

  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



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