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Differential Equations Project - Spring 2025

• 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. Graphical solutions are expected including the varying of parameters in the model and/or variations of the given problem. 

• Dates

You will report your group composition and proposed problem on February 24th. A detailed progress report on your work to date is due March 12th. The final full report will be due March 26th. See below for formatting.

February 24th Do some background on the problem that your group will study. Write up a proposal giving a statement of the problem, listing the ket system of differential equations, describing the variables used and sample parameters in the problem.

March 12th This will be a progress report whose form is a draft of your final paper. Here you introduce the problem and the analysis of the problem you have completed to date. What are the equilibrium solutions? What can you say about their stability? Provide plots of solutions indicating important detials.

March 26th Here you continue the work on the draft to turn it into a final product. You should incorporate any suggestions and/or corrections made on the draft paper. Extend the problem by varying parameters, adding interesting terms to the system, etc. Provide important results and discussion of what you learned in the problem as a dynamical system.

• Topics A list of topics can be found in ODE Project PDF.

• 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. Using LaTeX is not only permitted but recommended if you know how to use it. 
   

• 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.