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Visualizing Systems
of Ordinary Differential Equations
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
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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.
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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.
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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.
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Java-based Applet Slope Field Calculator
This is is a very cool Java-based visual slope field calculator
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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.
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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.
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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
This is the handout from Class 11 on how to use Matlab and
HPGSystemsSolver to graph the phase portrait of a system of ODEs.
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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.
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Damped Harmonic Motion Applet
This is one of the many java applets on the web to illustrated damped
harmonic motion.
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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.
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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.
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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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