Student Projects in Differential Equations
Instructor: David Arnold
There are files on this site in PDF format. You will need to download a free copy of the Acrobat Reader to read them. Click the following icon to obtain a free copy of the Acrobat Reader.
It is important that you have the most current version of the Acrobat Reader that your system will allow. The above links will take you to the Adobe site. Your system will be automatically analyzed and you will be informed of the optimal version of the reader for your system.
The Scientific Notebook
The Scientific Notebook was used to create some files on this site (Spring 1997 and 1998). You can try to use the free Scientific Viewer to view these files that were created with an older version of Scientific Notebook. No guarantees as this is untested.
Spring 1997
- Romeo and Juliet by Sarah Lewis and Alicia Dominguez
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- Modeling Molecular Vibrations as Simple Harmonic Motion by Bryan George
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- Van Meergeren Art Forgeries by Chris Ogden
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- The Flight of a Discus by Graeme Kling and Scott Lee
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- A Simple Microeconomics Model by Randy Cessna
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- An RLC Circuit by Ron Cummings
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- Autocatalytic Modeling by Nate Claasen and Shalise Radford
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- A Rate of Memorization Model by Todd Douglas
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Spring 1998
The first project of the semester requires students to visit the periodical stacks at Humboldt State University in search of a model involving the use of one or more differential equations. Students are required to explain the model they found, describe the variables and parameters, and give a short explanation of the application. Click here to find samples of this work.
Here are some nice links to potential projects.
- Project Links at Virginia Tech
- Internet Differential Equations Activities (IDEA)
- You might want to browse the differential equations index of the College Mathematics Journal at the MAA. Be sure to scroll down toward the bottom of the page to the differential equations section. These are references to articles in the College Mathematics Journal, a journal specifically aimed at the two-year college student and instructor. This journal is on file in the periodical stacks at the HSU library. So, write down a reference that looks interesting from this link, then head out to HSU to find the article in the periodical stacks.
- There is a wonderful article by Professor Joseph McKenna, University of Connecticut, on the Tacoma Narrows Bridge disaster. You'll need to download the file bridgen.ps, a postscript file about 3 megabytes in size. View the file in GhostView.
- Tacoma Narrows Bridge --- Neva Holladay and Dustin Helliwell
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- Belousov-Zhabotinsky Reaction --- Gabriel Peterson
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- Small Mammal Dispersion --- Tammie Huff and Kristian Cozyris
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- Numerical Solvers --- Eric Rane
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- Skydiving --- Jame Fahey
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- The Battle of Trafalgar--- Athanasios Thomaides, Arne Petersen
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- LRC Circuits--- Karin Glinden, Peggy Morton
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- Pursuit Curves and Matlab --- Peter Gent
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- A Home Heating Model --- Aaron Ambrosini
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- Epidemic Models --- Glenn Kelley
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Spring 1999
The following list of projects are proposed by the students in differential equations.
- Planetary Motion --- Sky McKinley and Craig Anderson
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- Velocity and Aerodynamic Drag --- Adam Heberly
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- Modeling the Angular Velocity of a Spinning Tennis Racket --- Lynn V. McIndoo and Jody S. Hourigan
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- Spirals and Conchospirals in the Flight of Insects --- Jeff Pimentel and Dustin Qualls
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- Rhythm of the Heart --- Megan Levine
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- Lake Pollution Modeling---Darren Tully and Joel Aguirre
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- The Neuron Model --- Josh Herrero and Francis Chan
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- Velocity and Aerodynamic Drag---Adam Heberly
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- Numerical Solutions for Geodesics on Two Dimensional Surfaces---Paul Chesler
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Spring 2000
The following list of projects are proposed by the students in differential equations.
- Force Exerted by a Falling Chain --- Linda Lindsley, Gina Giacone
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- Qualitative Analysis of the Spruce Budworm Outbreak --- Ron Bassar
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- Forced Oscillations and Nuclear Magnetic Resonance -- Dominika Pcion, Tallie Noble
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- Geodesics on an Ellipsoid --- Eric Flocchini
- Double Pendulum --- Scott Mandell, Franziska von Herrath
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- Coupled Oscillators --- Sean Larson, Alex Gagen
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- The Spring Pendulum --- Nick Whitman
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- Lead Levels in the Human Body --- Miyuki Shimokawa
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Spring 2001
The following list of projects are proposed by the students in differential equations.
- Celestial Orbits --- Ottopaskal Rice, Adrienne Carter
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- Tacoma Narrows Bridge --- Ken Menkveld, William O. Pence
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- Analysis of Communications Channels --- Richard Oremus, Maurissa Salas
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- A Rowing Model for a Four --- Al Abrahamsen
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- An Overview of Bifrucating Iterators and Chaos --- Matthew Lincoln
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- Buckling of a Yard Stick and Boundary Value Problem --- Jesse Trutna, T. Trutna
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- Lanchester's Law Modelling the Battle of the Atlantic --- Greg Brown, Shavez Kaleem
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Spring 2002
The following list of projects are proposed by the students in differential equations.
- The Optimal Height for Releasing Paratroopers --- Greg Ames
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- The Three Body Problem --- Shinichi Tokoro
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- The Double Pendulum --- LiHong Huang Herman
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- The Two Body Problem --- Noah Brisby and Robin R. Rumple
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- Poe's Pendulum --- Emilia Brinckhaus and Liya Zhu
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- The Heat Equation --- Adam Abrahamsen and David Richards
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- Presentation Slides
- Paper
- Dave and Adam also offer the following M-files for your viewing. The file pdex211.m is commented nicely, while the others are offered as is.
- Variable Step Size Differential Equation Solver --- Jason Brewer and George Little
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- Enzyme Kinetics --- Jonathan Gent and Doug Saucedo
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- The Brachistochrone --- Rhyan Pino
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- Modeling Mercury Concentrations in Clear Lake --- Anders Carlson
Spring 2003
The following list of projects were completed by the students in differential equations during the spring semester of 2003.
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The Tacoma Narrows Bridge---Sean Donohoe and Matt Bates
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A Differential Look at the Watt's Governor---Seth Stone and Tim Honn
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The Vibrating String---Tara Puzin and Mike Land
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Rigid Body Rotations---David Frank
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Computers, Lies, and the Fishing Season---Liz Arnold
Spring 2004
The following list of projects were completed by the students in differential equations during the spring semester of 2004.
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Basic Coupled Oscillator Theory Applied to the Wilberforce Pendulum---Misay Partnof and Steve Richards
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Low Pass Filters, Sinusoidal Input, and Steady State Output---Jaimie Stephens and Michael Bruce
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Analysis of the Motion of Pumping on a Swing---Jonathan Jackson
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Differential Equations and the Parachute Problem---Ron Phoebus and Cole Reilly
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Double Spring Pendulum---Jordan Pierce
- Presentation
- Paper
- Download project.m, a Matlab file that animates the system. You will also need to download animate.m in order to produce the animation on your system. Place both of these files in a folder on your system, open Matlab, change the current directory in Matlab to the folder. For example, if you store the files project.m and animate.m in c:\myprograms, then open Matlab and type cd c:\myprograms. Then, at the Matlab prompt, enter project. The animation will run. Feel free to change the source code to get different looks at the animation.
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Predator-Prey Modelling---Eric Anopolsky
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Modeling A Simple Toy---Alex Bame
- Presentation
- Paper
- Alex also has written a matlab gui for the animation. The gui will also write the output to a file odeouput.txt, which is used later by the POVRAY program. Get the following files:
- Alex has also written a POVRAY animation (1.4 MB) which is classic.
Spring 2005
- Bethany Adams and Keren Crum: "Vegetation Erosion Model Using Differential Equations."
- Aaron Kavanaugh and Travis Moe: "Poe's Pendulum."
- Presentation
- Paper
- Aaron and Travis have also written a Matlab file which animates the descending pendulum of Edgar Allen Poe. Get the following file:
- Ken Huffman, Tacoma Narrows and the Gradient Vector
- Presentation
- Paper
- Ken has written a number of Matlab m-files whose use is described in his paper. Get the following files:
- Becky Wieczorek and Shawn Rutan, Modern Siege Weapons: Mechanics of the Trebuchet.
- Presentation
- Paper
- A number of Maple worksheets contributed to this project, including some animations of three models of the trebuchet presented in this paper.
- Boden Hegdal and Mike Moore, Using Differential Equations to Model a Vibrating String
Spring 2008
- Josh Altic: "The Double Pendulum"
- Brianne Gill: The SIRS Model Approach to Host/Parasite Relationships"
- Graham Steinke: "The Josephson Effect"
- Hans Parshall: "Modeling an Economy's Growth"
- Ryan Seng and Mike Meeks: "Bead on a Rotating Hoop"
- Molly Severdia: "Pursuit Curves"
- Eddie Koch: "The Spruce Budworm"