Project Materials 

Back

Differential Equations Project - Spring 2021

• The Project Goal

This is a group project. You are expected to work in groups of two. The goal is to take a problem from some application area that can be modeled in terms of an ordinary differential equation and solved numerically using MATLAB, Maple, and/or Simulink. If solutions are available, then numerical solutions should be compared to known exact solutions or other models. Graphical solutions are expected including the varying of parameters in the model. 

• Dates

You will report your group composition and proposed problem on March 12th. A detailed progress report on your work to date is due March 26th. The final full report will be due April 12th. See below for formatting.

• Topics

The first source of topics can be found in Chapter 3 of the text and other ideas may be found in the Simulink notes. Examples:

• Projectile motion - golf balls, soccer balls, missiles, etc.

• Oscillations - masses on springs, circuits, pendula, coupled oscillators, nonlinear oscillators

• Tire Modeling

• Population models (Logistic equation, Lotka-Volterra)

• Chemical Reaction Kinetics: Example,
          Enzyme kinetics:  Michaelis-Menten

• Mixing models

• Epidemic models, (SIR, HIV, Covid)

  • When zombies attack!: modeling of an outbreak of zombie infection - slides, paper, book

• Systems of Differential Equations

• Maple Applications

• Differential Equations and Control Theory - cruise control, bicycle dynamics

• Other ideas or Check here - This might give some ideas, but you may need to discuss with Dr. H. to verify level and if doable.

• Report Format

  All work should be typed with double-spacing and 12 pt font. You will be expected to use correct English grammar and punctuation. This is a report and thus you will use proper sentence and paragraph formatting. You will be graded on the evidence of work, mathematical detail and understanding, proper exposition and neatness. Your work should also be supported with properly labeled and embedded plots and equations. Any references used should be cited as well. These reports will count towards the project component of your grade.

   

  Note, you need to write equations correctly. Do not use * for multiplication. Equation fonts should be consistent with the rest of the paper. Equations are sentences and should be punctuated accordingly. For examples, look at your textbook. Important equations should be numbered and referenced. Figures need captions and should be numbered and referred to in the paper. References are expected and should be cited in the body of the paper.
   

• Structure

A suggested outline of the final report would be: Title page (including Title, Names, Abstract), Introduction to Problem (Statement and Background). Formulation of Model and Method of Solution (Discussion of Simulink Model), Solution Results (Analytical, Numerical, Plots of Solutions), Discussion/Results (Summary and Discussion of Solution), Bibliography.