MAT 3130 - Introduction to Differential Equations
Spring 2021 - Projects
Projects
All submissions must be in pdf format as a single file (not a compressed folder or group of files - one file) and submitted via a shared google drive folder. No other formats will receive credit. The name of the file should be "yourlastname_labX.pdf". The file should be placed in a google drive folder named "yourlastname_ode" which should be shared with the instructor.The write-up for a project must be typed (LaTeX preferred but not required) and have the following:
1. Title, Author, Date
2. Titled sections for Introduction, Methods, Results, Discussion, References. More sections may be needed depending on the project.
3. Any code should be included and labelled in a section titled Appendix
4. Any graph, plot, or figure must have a numbered figure caption with a careful description of the figure and its relevant features as pertaining to the project. All figures must be included within the writeup. Figures in the Appendix will only be used to assess partial credit for incorrect plots contained in the main sections.
5. Web references should include "date accessed" in the reference in addition to the other standard documentation.
Projects that are turned in late will count a maximum of 80% of the full points if they are turned in late, but within a week. Projects turned in later than the same week in which it is due will be worth a maximum of 50% of the full points. No project (including the extra credit) will be accepted for credit after reading day.
Laboratory 1 (individual, but help is ok)
In a single pdf file, submit a photo you have taken and a short poem that you write about math. Your name should be at the top of the file. The file should have the name: "yourlastname_lab0.pdf".
Laboratory 2 (teams - my choice)
Create, with your team, a manual on how to solve differential equations and display their solution. You can do this in Maple, Mathematica, or R. The manual should include equations, plots and screen capture images, and detailed instructions. More requirements will be provided as we get close.
Laboratory 3 (teams - my choice)
Create two animations of a two dimensional bifurcation as a parameter is changed. The parameter should be changed through at least two bifurcations, although it may be the same one if the parameter does not return to the same values. Examples of acceptable bifurcations are:
- moving from a saddle to a node and on to a spiral.
- moving from a node to a spiral and back to a node.
- moving away from and back to the same place in the trace-determinant plane but with different equations.
- making a circuit of the origin in the trace-determinant plane.
The animation should include the two dimensional phase plane with null clines, directional arrows, and sample solutions for different initial conditions. A simultaneous animation of the location of the steady state in the trace-determinant plane in the same figure will earn extra credit. Music incorporated into the animation will earn extra credit.
The write-up should include a detailed analysis of what the animation shows including a careful examination of the stability of the steady state(s). Also provide a commentary on the process of developing the animation and an explanation on how to create the animation.
The animation must be done in Maple but the animation may be modified using other software packages.
Laboratory 4 (teams - your choice) Balancing Point
The caber toss is a traditional Scottish athletics event. Model the caber toss and determine the optimal release angle and direction of force. Document all assumptions and equations of motion. Also document your development process as you worked on the model and tested different simulations.
Laboratory Extra Credit (solo, extra credit, up to 2%)
Coming soon ...