# Mathematical Modelling (MATH 4090)

** Time and Place **

Winter 2019

MWF: 11:30-12:30

CB 120

** Starting Jan 23, Weds lectures are in the Gauss Lab. **

** Description **

This course will introduce the student to discrete, continuous and probabilistic modeling of problems from industry, finance and the life and physical sciences. The emphasis will be on the process of generating an appropriate model for the problem in question, so that the student can gradually develop intuition about the strengths and limits of modeling approaches. The student will complete a research project, developing and analyzing a model of a system of their choice.

** Syllabus: ** found here pdf file

** Lecture January 11 ** Class on Friday January 11 will be in Ross N619, the Mathematics & Statistics Control Lab. We will be studying random walks using Lego Mindstorm Robots.

** Project Presentations: Due April 3 - post a video of your project presentation (10 - 15 minutes length) to a dropbox folder that will be emailed to you (for security). Please note that the folder only allows uploading and viewing - no revision is allowed.**

** Project information: ** Sample proposal and outline pdf file

** Project Rubric: ** Marking scheme pdf file

** Project Peer Evaluation Form - Presentations: ** Marking scheme pdf file

Possible topics: pdf file

Matlab refresher - Lab questions

** Homework Questions: ** pdf file

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** Test 1 ** - Posted on CrowdMark on Feb 25th at 9am. You have until Feb 26th 9pm to submit it on CrowdMark, but you can only work on it for 16 continuous hours. Check you email so that you don't miss it!

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Lab 1 - A man walks along a four-block stretch of Yonge St. If he is at corner 1, 2, or 3, then he walks to the left or right with equal probability. He continues until he reaches corner 4, which is a bar, or corner 0, which is his home. If he reaches either home or the bar, he stays there.

Questions:

What is the probability that the process will eventually reach an absorbing state?

What is the probability that the process will end up in a given absorbing state?

On average, how long will it take for the process to be absorbed?

On average, how many times will the process be in each transient state?

Extra notes: pdf file

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Lab 2 - Snakes and Ladders - Download the matlab code here doc file (Open the code in matlab and save it as a .m file.

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Lab 3 - Elevator Code - copy and paste into a Matlab script. Run the simulation before the lab on Wednesday and try to understand what it is doing.

doc file (Open the code in matlab and save it as a .m file.

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Lab 4 - discrete time dynamical systems pdf file, and some maple code maple code

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Lab 5 - Computer lab questions pdf_file, and phase plane diagram example pdf_file

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Lab 6 - Computer lab questions pdf_file

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Lab 7 - Open up the matlab files attached (copy and past into matlab). Extend this model to the SEIR model that we will discuss today in the computer lab. callSIRodes, and SIRodes. Finally, write your own Maple worksheet to find the fixed points and eigenvalues for the SIR and SEIR models.

** As of March 19, 2019 - there are no more computer labs **