Math 340: Differential Equations (Fall 2015)

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  1. 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.

  2. Mathematica-based animations of Differential equations
    There are some interesting examples of animations using Mathematica demonstrations that illustrate Differential Equations concepts on the web

  3. Wolfram Demonstrations of Bifurcations in First-Order ODEs
    Here is a Wolfram Demonstration of supercitical, transcritical and subcritical pitchfork bifurcations.

  4. 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.
  5. 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.
  6. 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.
  7. Visualizing direction fields and solution curves
    This website allows for visualization of simple direction fields. Numerically brittle. 
  8. 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.
  9. Java-based Applet Slope Field Calculator
    This is is a very cool Java-based visual slope field calculator
  10. 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
  11.  Matlab References
    Prof. Anderson at UCLA's Matlab reference documents in
    .html or .pdf format.
    University of Colorado Matlab Tutorial
  12. 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
  13. Blanchard, Devaney & Hall, Differential Equations
    Again thanks to Google, the third edition  of the course textbook is available online!
  14. Boston University Ordinary Differential Equations Project
    This is the official web page of the Blanchard, Devaney & Hall textbook.
  15. Euler's Method
    Here is the Excel spreadsheet that we used in class that does Euler's Method.
  16. Euler's Method and Slope Field from MathScoop
    This program will produce an Euler Table and draw a slope field for you
  17. 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.
  18. Fields of Slopes
    This is the Flash-based Slope Field visualization tool from the Flash and Math website.
  19. Plotting Vector Fields
    This is a cool website by Kevin Mehall that allows you to visualize vector fields.
  20. 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.
  21. 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.
  22. Damped Harmonic Motion Applet
    This is one of the many java applets on the web to illustrated damped harmonic motion.
  23. Paul's Online Math Notes
    A very comprehensive and useful collection of notes that illustrates many of the central concepts in Differential Equations.
  24. 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.
  25. Mathworld's Explanation of Convolution
    An explanation, definition and visualization of convolution from Wolfram's MathWorld
  26. Detailed Explanation of Convolution
    A very detailed explanation (with animated visualization) of the convolution process for an interval signal.
  27. 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.
  28. Videos on  Laplace Transforms
    The Khan Academy has some freely accessible videos which discuss Laplace Transforms.