by KENDALL ATKINSON

Chapters 6-9

**MATLAB RELATED MATERIALS**- 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.

- Chapter 6 -
*Numerical Solution of Ordinary Differential Equations*- Section
6-1

Matlab program dirfield.m

Matlab program linekea.m - Section
6-2

Matlab program euler.m.

Fortran program for Euler's method

Numerical example for Euler's method. - Section 6-3
- Section 6-4
- Section
6-5

Matlab program trapzoid.m. - Section
6-6

Output from*DETRAP*. - Section
6-7

Introductory usage comments to ddeabm.f

ODE solvers available in Matlab. - Section 6-8
- Section 6-9
- 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. - Section 6-11

- Section
6-1
- Chapter 7 -
*Linear Algebra* - Chapter 8 -
*Numerical Solution of Systems of Linear Equations*- Section 8.1
- Section 8.2
- 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. - Section 8.4
- 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. - Section 8.6
- Section 8.7
- Section
8.8

Poisson equation example - Section 8.9
- Section 8.10 - Single-step and Runge-Kutta Methods
- 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*- Section 9.1
- Section 9.2

Fortran program power.f

Power method example - Section 9.3
- 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*). - 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*). - Section 9.6
- Section 9.7

- 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.)