Math 308: Differential Equations

Course Information

Unit Assignments

• Unit 1 Assignment Due Wed 9/11/13:
• Unit 2 Assignment Due Fri 9/20/13:
• Unit 3 Assignment Due Fri 9/27/13:
• Unit 4 Assignment Due Fri 10/4/13:
• Unit 5 Assignment Due End of Wed 10/9/13:
• Unit 6 Assignment Due Fri 10/25/13:
• Unit 7 Assignment Due Fri 11/1/13:
• Unit 8 Assignment Due Mon 11/8/13:
• Unit 9 Assignment Due Mon 12/2/13:
• Unit 10 Assignment Due *Mon 12/9/13* Changed to Wed 12/11/13:
• Unit 11 Assignment Not due. For practice.

Matlab Scripts

• A script to draw direction fields for first order ODEs.
• A script to draw the phase plane for two first order ODEs.

Matlab Info

• Matlab Tutorial used in our in-class session.
• A nice Matlab introduction from MITs webpage.

Other Potentially useful sites

• Function Plotter that can plot multiple plots on one graph.
• System of ODE solver by some good folks at University of Applied Sciences, Dresden Germany.
• Listen to beats at the sound lab put together by ThinkQuest.
• Circuit Simulator to show a driven harmonic oscillator and resonance. There are many more nice java applets to show various differential equation phenomena.
• Resonance Simulator that shows how forced socillators react to different driving frequencies.
• Direction Field java applet for a single first order equation written by Scott Sarra from Marshall University.
• Fun Differential Equations Software released by R.E. Williamson.
• How do I print a Graph drawn by a Java Applet anyway?
• A very nice Phase Plane Potter by Richard Mansfield at Penn State.
• A different interface for the same program. by Frits Beukers in the Netherlands.
• Integrals Online: http://www.integrals.com/
• Also for Integrals and other symbolic manipulation: http://live.sympy.org
• Description of the Taylor Series (Wikipedia).
• Java Applet demo of Taylor Polynomial approximations.
• An applet to simulate the Lorenz Equations demonstrating chaos.
• Another applet for the Lorenz Equations with a simpler interface, but less flexibility.
• A 3D version for the Lorenz Equations which follows many particles simultaneously.

Java Applets for Phase Plane

• Choose the Pplane java applet on this webpage from Rice University.
  This one tells you what it thinks the solution is that the trajectory is heading toward (equilibrium or cycle, etc).
• Another phase plane plotter by Richard Mansfield at Penn State.
  This one plots both the solution vs t and the phase plane at the same time in different windows.

Fun Stuff

• A weather vector fieldshowing Hurricane Katrina. Try to find a saddle point in the Atlantic Ocean. Where are the stable and unstable manifolds? What are the basins of attraction?
• More weather vector fields.
• Tacoma Narrows Bridge footage.
• Binaural beats when driving frequency is close to natural frequency.
• Resonance of particles in a vibrating tube
• Resonance of sound in a tube Here they change the natural frequency instead of the driving frequency, and the resonance is quite clearly heard.
• Resonance: sound breaking glass