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Visualizing
Systems of Ordinary Differential Equations (downloads
an executable file)
University of Hartford
Professor
Bob Decker's Mathlet allows you to visualize
solutions of 2-dimensional systems of ordinary differential equations:
plots both solutions, phase portrait and the direction field.
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Mathematica-based animations of Differential
equations
There are some interesting examples of
animations using Mathematica demonstrations that illustrate
Differential Equations concepts on the web
- Wolfram Demonstrations of Bifurcations in First-Order ODEs
Here is a Wolfram Demonstration of supercitical, transcritical and subcritical pitchfork bifurcations.
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How to Plot Direction Fields using Mathematica
This website describes what
Mathematica commands you need to use to generate solution curves and
direction fields, and how to plot them together or separately.
- How to Plot Direction Fields using MATLAB
This website contains a very
cool Matlab m-file called dirfield.m which can be used to
plot direction fields, solution curves, and solution curves with
direction fields. This involves both numerical and symbolic solutions
of DEs.
- The
MATLAB program pplane7
John Polking of Rice University (the man who
brought us dirfield.m) also has another
MATLAB program called pplane7.m, this time
with an advanced Graphical User interface to plot the Phase Plane of
ODEs.
- Visualizing direction fields and solution curves
This website allows for
visualization of simple direction fields. Numerically brittle.
- Fancier program for visualizing direction fields
This website (requires installation
of Java 1.1.6) and uses DFIELD to show direction fields and
solution curves.
- Java-based Applet Slope Field Calculator
This is is a very cool Java-based visual slope field calculator
-
Marek Rychlik's Differential Equations class
at JHU
This has a very useful list of resources for an ODE class at John
Hopkins University similar to ours
- Matlab References
Prof. Anderson at UCLA's Matlab reference documents in
.html or .pdf format.
University of Colorado Matlab Tutorial
- Swift & Wirkus textbook,
A Course In Ordinary Differential Equations
Thanks to the magic of Google, the entire text of the Fall 2007
textbook for Math 341 is available online
- Blanchard, Devaney & Hall, Differential
Equations
Again thanks to Google, the third edition of the
course textbook is available online!
- Boston
University Ordinary Differential Equations Project
This is the official web page of the Blanchard, Devaney & Hall
textbook.
- Euler's Method
Here is the Excel spreadsheet that we used in class that does Euler's
Method.
- Euler's Method and Slope Field from MathScoop
This program will produce an Euler Table and draw a slope field for you
- How
To Plot Slope Fields
This is a handout from Class 4 on how to use Mathematica, Matlab and
the web-based Slope Field Calculator to plot slope fields.
- Fields of
Slopes
This is the
Flash-based Slope Field visualization tool from the Flash and Math website.
- Plotting Vector Fields
This is a cool website by Kevin Mehall that allows you to
visualize vector fields.
- How To
Plot Phase Portraits (Class handout)
This is the handout from Class 11 on how to use Matlab and
HPGSystemsSolver to graph the phase portrait of a system of ODEs.
-
Qualitative Analysis of A Systems of ODEs
Using NullClines
This is a very nice explanation of how to use nullclines to sketch the
phase plane of a DE.
- Damped Harmonic Motion Applet
This is one of the many java applets on the web to illustrated damped
harmonic motion.
-
Paul's Online Math Notes
A very comprehensive and useful collection of notes that illustrates
many of the central concepts in Differential Equations.
- Laplace
Transforms Help Sheet
Here is a copy of the helpsheet that was handed out with the Reading
Quiz which summarizes all we did with Laplace Transforms.
- Mathworld's Explanation of Convolution
An explanation, definition and visualization of convolution from
Wolfram's MathWorld
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Detailed Explanation of Convolution
A very detailed explanation (with animated visualization) of the
convolution process for an interval signal.
-
Animation of Convolution
A nice animation of the convolution process for user-selected signals
is provided at the Joy Of Convolution at Johns Hopkins University.
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Videos on Laplace Transforms
The Khan Academy has some
freely accessible videos which discuss Laplace Transforms.
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