TEACHING NUMERICAL ANALYSIS USING
ELEMENTARY NUMERICAL ANALYSIS
by K. ATKINSON and W. HAN

GENERAL INFORMATION

• MATLAB RELATED MATERIALS
  • Learning MATLAB, by Tobin Driscoll, University of Delaware
  • Matlab tutorial - University of New Hampshire
  • Matlab tutorial - University of British Columbia
  • Matlab tutorial - University of Florida
  • Mathtools.net: a technical computing portal for scientific and engineering needs.
  • Some Unix Commands
  • Some Emacs Keyboard Commands
  • An Overview of Numerical Analysis as discussed by Kendall Atkinson.
  • The Definition of Numerical Analysis as discussed by L. N. Trefethen (pages in reverse order).

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  BOOK CORRECTIONS: We give here a list of corrections for the first printing of the third edition of the textbook Elementary Numerical Analysis.

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  Lectures (in pdf)

  The following notes are to accompany the third edition of the book Elementary Numerical Analysis, by Kendall Atkinson and Weimin Han, published by John Wiley & Sons, Inc.

  • Modeling
    Population model slides.
  • Matlab notes
  • Chapter 1 - Taylor Polynomial Approximations
    • Matlab programs for Chapter 1.
    • Section 1-1
      GUI: There is a MATLAB GUI named Taylor_GUI that can be used to construct Taylor polynomial approximations for degrees 1, 2, and 3 for a limited list of functions. It evaluates the Taylor approximants and computes their error, displaying the results in both tabular form and graphically. To use it, go into MATLAB and simply type Taylor_GUI.
    • Section 1-2
    • Section 1-3
  • Chapter 2 - Error and Computer Arithmetic
    • Appendix E, on binary numbers.
    • Section 2-1
      Disasters due to computer arithmetic error (from Doug Arnold, PSU)
      Software bugs due to computer arithmetic problems (from Thomas Huckle, Munich, Germany).
    • Section 2-2
      Noise example, using IEEE single precision arithmetic.
    • Section 2-3
    • Section 2-4
      Summation example, written in Fortran using IEEE single precision arithmetic.
      The Accuracy Of Floating Point Summation (1993), Nicholas J. Higham.
  • Chapter 3 - Rootfinding
    GUI: Note that you can use the GUI Rootfinding to aid you in working with the following rootfinding methods: bisection (§3.1), Newton (§3.2), secant (§3.3).
    • Matlab programs for Chapter 3.
    • Section 3-1
    • Section 3-2
    • Section 3-3
    • Section 3-4
    • Section 3-5
  • Chapter 4 - Interpolation and Approximation
    • Matlab programs for Chapter 4.
    • Section 4-1
      Graph of quadratic interpolant to cos x.
    • Section 4-2
      Graphs of error polynomial for degrees 6, 7, 8, 9 (see formula (4.55) on page 142 of the text).
      GUI: To aid in developing intuition for polynomial interpolation with evenly spaced interpolation node points, use the GUI Uniform_Interpolation.
    • Section 4-3
      Matlab spline routines.
      Matlab spline example.
      GUI: There is a MATLAB GUI named Spline_GUI that can be used to construct cubic spline interpolatory functions with varying boundary conditions.  The interpolation uses evenly spaced interpolation node points, and the function being interpolated can be chosen from a given pull-down table.
      Interactive interpolation example, comparing polynomial and cubic natural spline interpolation. This is due to Tobias von Petersdorff, University of Maryland.
    • Section 4-4
    • Section 4-5
    • Section 4-6
      GUI: For a comparison of interpolation with evenly spaced nodes and the Chebyshev zeros, use the GUI Uniform_vs_Chebyshev_Interp.
    • Section 4-7
  • Chapter 5 - Numerical Integration and Differentiation
    • Matlab programs for Chapter 5.
    • Section 5-1
      Further examples of the trapezoidal rule and Simpson's rule.
      GUI: To aid in developing intuition for the numerical integration of this section, use the GUI Integrate_GUI.
      Integrate, a Java utility program to do numerical integration examples online. It was written by Kimberly Farrell.
    • Section 5-2
      Examples of the trapezoidal rule, corrected trapezoidal rule, and Richardson's extrapolation.
    • Section 5-3
      Examples of Gaussian quadrature
      Further examples of the trapezoidal rule and Simpson's rule.
      GUI: To aid in developing intuition for the numerical integration of this section, use the GUI Gaussian_Quad.
    • Section 5-4
  • Chapter 6 - Solution of Systems of Linear Equations
    • Matlab programs for Chapter 6.
    • Section 6-1
    • Section 6-2
    • Section 6-3
    • Section 6-4
    • Section 6-5
    • Section 6-6
  • Chapter 7 - Numerical Linear Algebra: Advanced Topics
    • Matlab programs for Chapter 7.
    • Section 7-1
    • Section 7-2
    • Section 7-3
  • Chapter 8 - Numerical Methods for Ordinary Differential Equations
    • Matlab programs for Chapter 8.
    • Section 8-1
    • Section 8-2
    • Section 8-3
      GUI: To aid in developing intuition for Euler's method, use the GUI Euler_ODE_GUI. You can experiment with a variety of differential equations, the solutions to which are listed in the associated help menu.
    • Section 8-4
    • Section 8-5
      Example numerical method based on using a Taylor series.
    • Section 8-6
    • Section 8-7
    • Section 8-8
  • Chapter 9 - Finite Difference Methods for Partial Differential Equations
    • Matlab programs for Chapter 9.
    • Section 9-1
    • Section 9-2
    • Section 9-3

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  Programs:

  • Matlab programs to accompany the course. There are also Matlab GUIs for a number of topics, and they are available on the local Engineering and Mathematical Sciences networks.
  • Sketch A Function. This is a Java utility program to allow online graphing of basic functions.
  • Fortran Programs. These are for the second edition of the book Elementary Numerical Analysis.
  • C Language Programs. These are for the second edition of the book Elementary Numerical Analysis. (Let the buyer beware, as I am not a competent C language programmer.)