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
    5.4 Gaussian Quadrature Formulas

  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
    7.5 Adams-Bashforth-Moulton Methods

  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

Answers for Selected Exercises



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18 July 2013