TEACHING NUMERICAL ANALYSIS USING
AN INTRODUCTION TO NUMERICAL ANALYSIS
by KENDALL ATKINSON

E_mail: Kendall-Atkinson@uiowa.edu

GENERAL INFORMATION

• MATLAB RELATED MATERIALS
  • Crash Course in MATLAB, by Tobin Driscoll, University of Delaware
  • Matlab tutorial - University of New Hampshire
  • Matlab tutorial - US Naval Academy
  • Matlab tutorial - University of British Columbia
  • Matlab tutorial - University of Florida
  • Matlab tutorial - University of California at Los Angeles
• 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.
• Maxims about numerical mathematics, science, computers, and life on earth as discussed by L. N. Trefethen.

Lectures and Miscellaneous notes

• Chapter 6 - Numerical Solution of Ordinary Differential Equations
  1. Section 6-1
     Matlab program dirfield.m
     Matlab program linekea.m
  2. Section 6-2
     Matlab program euler.m.
     Fortran program for Euler's method
     Numerical example for Euler's method.
  3. Section 6-3
  4. Section 6-4
  5. Section 6-5
     Matlab program trapzoid.m.
  6. Section 6-6
     Output from DETRAP.
  7. Section 6-7
     Introductory usage comments to ddeabm.f
     ODE solvers available in Matlab.
  8. Section 6-8
  9. Section 6-9
  10. Section 6-10
      Example: Taylor series method
      Runge-Kutta example: Order 2
      The Fortran program fehl45.f. This is a non-automatic implementation of the RFK (4,5) pair of formulas.
  11. Section 6-11
• Chapter 7 - Linear Algebra
  1. Section 7.1
  2. Section 7.2
  3. Section 7.3
  4. Section 7.4
• Chapter 8 - Numerical Solution of Systems of Linear Equations
  1. Section 8.1
  2. Section 8.2
  3. Section 8.3
     LAPACK archive at NETLIB
     The Fortran LINPACK program dgeco.f, along with dgefa.f, dgesl.f, and auxiliary level 1 BLAS.
     The Fortran program tridgl.f for solving tridiagonal systems.
  4. Section 8.4
  5. Section 8.5
     Residual correction example, using a discretization of an integral equation.
     Residual correction example - Output.
     The Fortran program for the residual correction example.
  6. Section 8.6
  7. Section 8.7
  8. Section 8.8
     Poisson equation example
  9. Section 8.9
  10. Section 8.10 - Single-step and Runge-Kutta Methods
  11. Section 8.11 - Boundary value problems
      Notes on collocation methods for solving boundary value problems  (These were originally intended to be included in the second edition of my text An Introduction to Numerical Analysis).
• Chapter 9 - Numerical Solution of Eigenvalue Problems
  1. Section 9.1
  2. Section 9.2
     Fortran program power.f
     Power method example
  3. Section 9.3
  4. Section 9.4
     Proof of Theorem 9.5 on the use of the Sturm sequence properties to locate the eigenvalues of a symmetric tridiagonal matrix. (These notes were originally intended to be included in the second edition of my text An Introduction to Numerical Analysis).
  5. Section 9.5
     QR method - full matrix example
     QR method - tridiagonal matrix example
     Accelerated QR method - tridiagonal matrix example
     Notes on the convergence of the QR method (These were originally intended to be included in the second edition of my text An Introduction to Numerical Analysis).
  6. Section 9.6
  7. Section 9.7

Sketch A Function

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.)

Atkinson's home page