MATLAB RELATED MATERIALS
BOOK CORRECTIONS: We give
here
a list of corrections for the first printing of the third edition of the
textbook Elementary
Numerical Analysis.
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
- 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).
- 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
- Chapter 7 - Numerical Linear Algebra: Advanced Topics
- Chapter 8 - Numerical Methods for Ordinary Differential Equations
- Chapter 9 - Finite Difference Methods for Partial Differential
Equations
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.)