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Math 302 Final Project (Fall 2021) Instead of a nal exam,this class has a nal project. You will write a short paper about an application of differential equations to a topic of your choice. Timeline Finalize topic: Tuesday, April 2? Deadline to send draft for comments: Sunday, May 2 hper due: Wednesday, May 12 Summary Differential equations see application in many areas, from ecology to engineering. For the nal project for this class, I want you to pick an application and write a 2 to 5 page paper about this application. You should address the phenomenon you are looking at, what assumptions go into deriving your differential equation{s), how you nd the general solution to the equation(s}, how to nd the particular solution given initial value information, and what these solutions tell you about your problem. For writing your paper, you should consider your classmates as your target audience. You should give enough detail that someone who has taken this class can understand your application and follow the mathematics you present You are not required to use this layout, but here is a suggested way to organize your paper into sections. Section 1: Introduction Introduce your topic. Explain the phenomenon you are looking at and why it is interesting. Section 2: Setting up a differential equation Explain how to set up a differential equation-or possibly multiple equations-which describes your phenomenon. What assumptions underlie the equation? Section 5: Solving the equation Give the mathematical work to solve your equation. Explain what is needed to nd particular solutions. Section 4: Interpreting the solution Now that you've solved the differential equation, how do you apply this to say something about your phenomenon? What are the limits of the application? prks You should pick a topic approachable with the methods from this class. (For example, there are many interesting applications of partial differential equations, but those are beyond the scope of this course.) It's okay if you pick the same topic as someone else in the class, but your work should be your own. By 11pm on Tuesday, April 27, submit via Gradescope one to two paragraphs explaining your topic, why you picked it, and 1what resources you plan to use. Here's some resources for nding a topic: I The textbook has examples of applications of differential equations, in chapters 5 and 6. (But don't pick a topic we covered in class! So no orthogonal trajectories, dilution problems, Newton's law of cooling, nor harmonic motion.) If you pick an application covered by the textbook, you should pick something from the exercises, i.e. where the work is not all already done for you. Here are a few specic places to look: 0 Lesson 15 has applications to geometry. 0 Lesson 16 has applications to kinematics. Lesson 50 has applications to electric circtuits. 0 The library on campus has many books and articles about applications of ODEs to different disciplines. Keywords to search are "[discipline] differential equations" or "[discipline] mathematical modeling". Rubc Here is the breakdown for how your project will be graded: TOTAL 100 Topic Submission 5 Format 5 Mechanics 10 Diff Eq Content 40 Non-Diff Eq Content 40 o pric Submission: Did you submit your topic choice on Gradescope? 0 Format: Does your paper meet the formatting requirements? 0 Mechanics: Does your paper adhere to the standards of academic writing? (Grammar, spelling, etc.) 0 Differential Equations Content Do you clearly and correctly explain the differential equations content for your project? I Non-Differential Equations Content Do you adequately explain the context to your project? Format Your paper should adhere to the following format guidelines. 0 Length: 2-5 pages. Figures and pictures are encouraged where they help explain your ideas, but don't count for meeting the minimum page length. II Use a lpt font, 1.5 inch margins,and single space. I I won't enforce a specic citation style, but you should pick a format and use it consistently. If you use LaTeX to write your paper,l strongly encourage you to use bibTeX for managing your citations. If you are unsure which style you want to use, here is a page about Chicago style citations, and you can google to nd tools to automatically generate citations. MATH 302: FINAL PROJECT TOPIC SUBMISSION Write one to two paragraphs explaining your topic, why you picked it, and what resources you plan to use