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Mathematical
Methods for Engineers
(10. 539/24.539)
List of Matlab Demos
This
page contains a summary list of the Matlab demos available for this
course. The list is organized roughly by topic and by the order
that the files are discussed in the Lecture Notes. Some of these
files will be discussed in detail in class, but all of them are
discussed to some extent in the notes. They hopefully can serve
as a guide for many of the Matlab assignments given throughout the
semester. Careful study of these sample files should introduce you
to a variety of Matlab programming features and also give you a
solid understanding of the various mathematical problemsolving
strategies and techniques discussed over the course of the semester.
You can view a particular Matlab file or download it by simply clicking
the right mouse button
on the link over the file name. From here you can either choose
"open in new window" to view the file online or "save
target as" to download the file directly to your PC (note that
these commands might differ slightly depending on your choice of
web browser). In any case, once the file is on your machine, you
can run it just like any other Matlab script file (make sure you
do not inadvertently change any file names).
Review
of Introductory Differential Equations and Linear Algebra


Plotting
and function evaluation with Matlab for the sliding chain problem
in Example 1.5. 

Plotting
and function evaluation with Matlab for the orthogonal trajectory
problem in Example 1.6. 

Sample
problem to illustrate Picard’s iteration method. 

Demo
that illustrates the solution of a single IVP with the use of
Matlab’s ode23 routine. These
files, which are discussed in Example 1.7, also show how to
use fzero to plot an analytical solution
if it is given in implicit form. 

Files
for Example 1.8 to illustrate the solution of a single IVP with
the use of Matlab’s ode23 routine. 

Files
associated with Example 1.9: Flow from a Damaged Oil
Tank. 

Simple
demo to illustrate some linear algebra capability in Matlab
(see Chapter 3 in the Lecture Notes). 
General
Solution to IVPs 

Simulation
of a simple mechanical system. This demo is discussed as part
of Example 4.4, which illustrates how to use ode23
to solve of system of ODEs. 

Simulation
of the Dynamics of a SemiBatch Chemical Reactor as discussed
in Example 4.5 (a typical IVP). 
General
Solution to BVPs 

Demo
to illustrate the solution of a 2nd order BVP via the Shooting
Method. These files implement the manual method discussed in
Example 5.1. 

This
is a generalpurpose routine that implements an automated solution
procedure based on the Shooting Method for 2nd order BVPs. In
its present form, it is restricted to problems with linear
BCs. 

This
is the automated version of Example 5.1 (uses bvp2sh.m). 

Example of Finite Difference method for solving BVPs. These
files are associated with two versions of the solution to Example
5.2. 

Solution
to Example 5.3A: Shooting Method Solution for the Circular
Fin Problem. These files use bvp2sh.m. 

Solution
to Example 5.3B: Finite Difference Solution for the
Circular Fin Problem. 
Numerical
Solution of Algebraic Equations 

Function
file to implement a simple version (no partial pivoting) of
the Gauss Seidel iteration scheme with successive relaxation
(SR) for solving linear equations. 

Demo
to illustrate the behavior of the SR method for a simple 3x3
system as discussed in Example 6.3. Uses the sr.m
routine. 
Power
Series Solution Method 

Demo
to illustrate the evaluation of infinite power series expansions
using a recurrence relation as discussed in Chapter 7. 
Special
Functions and Orthogonality 

Demo
to plot several loworder Legendre polynomials and to demonstrate
their orthogonality property. Uses Matlab’s quadl
routine to do the numerical integration. 

Script
file to plot some loworder Bessel functions. 

Analytical
solution, which involves Bessel functions, for the Cylindrical
Fin Problem. This file is associated with Example 8.3
in the Lecture Notes. 
SturmLiouville
Theory and Generalized Fourier Series 

Demo
of Fourier Series Representation for f(x) = 1. 

Demo
of Fourier Series Representation for f(x) = x(Lx). 

Demo
for using Fourier Series for solving BVPs. This file is associated
with Case 1 of Example 9.2. 

Demo
for using Fourier Series for solving BVPs. This file is associated
with Case 2 of Example 9.2. 
Analytical
Solution of PDEs 

Heat Transfer
in a 1D Finite Bar using the Separation of Variables (SOV)
method (Example 10.1 in Class Notes). 

Heat
Transfer in a 1D Finite Bar using the (SOV) method (Example
10.2 in Class Notes). 

Heat
Transfer in a 1D Finite Bar using the (SOV) method (Example
10.3 in Class Notes). 

2D Heat
Conduction in a Rectangular Block via the SOV method (Example
10.5 in Class Notes). 
Numerical
Solution of PDEs using Finite Difference Methods 

Heat
Transfer in a 1D Finite Bar using the EXPLICIT FD method
(Example 11.1 in Class Notes). This is HT Example #2 which
is solved using several techniques  here we use the explicit
Euler method. 

Heat
Transfer in a 1D Finite Bar using the IMPLICIT FD method
(Example 11.2 in Class Notes). This is HT Example #2 which
is solved using several techniques  here we use the implicit
CrankNicolson method. 

Heat
Transfer in a 1D Finite Bar using the StateSpace FD method
(Example 11.3 in Class Notes). This is HT Example #2 which
is solved using several techniques  here we FD the spatial
part and use ode23 to solve the
system of 1st order ODEs. 

Heat
Transfer in a 1D Finite Bar using the StateSpace FD method
(Example 11.4 in Class Notes). This is HT Example #3 which has
a timedependent BC on the right side. This was solved earlier
using the Eigenfunction Expansion Method (similar to SOV method),
but here we FD the spatial part and use ode23
to solve the resulting system of 1st order ODEs. 

2D
Heat Conduction in a 2D Rectangular Block via the FD method
(Example 11.5 in Class Notes). This was solved previously using
the SOV method in Example 10.5. 
Numerical
Solution of PDEs using FEMLAB 

Heat
Transfer in a 1D Finite Bar using FEMLAB (ver 3.0.a). This
is HT Example #2 which has already been solved using several
techniques (see above). Here we simply demonstrate how to
solve a parabolic PDE in 1D within FEMLAB. The zip file contains
a *.fl file which can be opened in FEMLAB and a *.m file with
an example of some simple postprocessing of the FEMLAB results
in Matlab. 

Heat
Transfer in a 1D Finite Bar using FEMLAB (ver 3.0.a). This
is HT Example #3 (Example 10.4 and 11.4 in Class Notes) which
has a timedependent BC on the right side. This is another
example of how to solve a parabolic PDE in 1D within FEMLAB.
The zip file contains a *.fl file which can be opened in FEMLAB
and a *.m file with an example of some simple postprocessing
of the FEMLAB results in Matlab. 

2D
Heat Conduction in a 2D Rectangular Block using FEMLAB. This
was solved previously using the SOV method in Example 10.5 and
the FD method in Example 11.5. The zip file given here contains
a *.mat file that was saved during the FEMLAB (ver 2.3a) run,
so the exact setup within FEMLAB can be reproduced. Some postprocessing
is also done in Matlab with the *.m file (see comments within
the file) contained within the zip archive. 
Note:
The Matlab demos listed here are related directly to the examples
in the Math Methods Lecture Notes. Some of the Matlab files associated
with the examples done in class are also available under the Additional
Resources link. In addition, several other of my courses also
have a series of Matlab related demos that may be of interest to
the student studying this material. These files can be found at
the following URL: www.profjrwhite.com/courses.htm.
Last
updated by Prof. John R. White (Sept. 2005)
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