Mathematical Modeling
MTH 323 - Sec 010

Professor:		Dr. Nathan Louis Gibson
Office:		Kidd 056
Office Hours:		MW 1-1:50
Course Website:		http://www.math.oregonstate.edu/~gibsonn/Teaching/MTH323-010F22
Text Book:		Title: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow Author: Rich Haberman Year: 1998 SIAM Member Price: $55.30

Contents

• Calendar
• Course Description
• Reading Assignments
• Writing Assignments
• Homework Assignments
• Computer Assignments (Optional)
• Term Paper
• Exam
• Grades
• Matlab
• Links

Course Description

Reading Assignments

1. Read for Friday of week 0: Dynamic Models in Biology, Chapter 1
   • Read exercises also, but do not solve.
   • We will not be reading other chapters of this book, but pay attention to what this chapter says about the rest of the book because it will also pertain to the required text for the course.
   • This text is primarily intended for biological models. We will discuss how the concepts and techniques apply to other disciplines.
   • It would be helpful (but is not necessary) to make an outline of important topics.
   Answer the following and bring to class:
   1. What is a model?
   2. What is a dynamic model?
   3. When is a dynamic model preferred over the alternative?

Writing Assignments

The remaining portion of the writing requirement will be comprised of homework assignments and informal in-class assignments pertaining to lecture.

For resources on writing, see Links Section below. Writing Assignments will be posted to Canvas.

Homework Assignments

Computer Assignments (Optional)

Assignments will be posted to Canvas. For resources on MATLAB, see the section below.

Term Paper

1. Topic: (Due Week 4) 10 points This should be roughly a one paragraph description of the problem or application you intend to model. It is fine to list two competing topics in order to get feedback on both. References are not necessary at this point, although they would be helpful. Topics should be typed and uploaded as a pdf file to Canvas.

2. Proposal: (Due Week 5) 20 points The project proposal should be roughly one page (single spaced, 1 inch margins). References may be included. In fact, I suggest you find at least two published papers related to the topic to get a feel for what has been done/what would be involved in modeling. The purpose of the proposal is to clearly present a question regarding your application that you intend to answer using a mathematical model, and to describe why answering that question is important. For the proposal, consider that you are applying for funding/permission to pursue this research topic. As with many funding requests, your proposal will be peer-reviewed. You do not need to have identified the precise methods that you will employ (compare to Introduction section below), however you should try to describe at least what type of equation will be used in the model (e.g., difference vs. differential, ordinary vs. partial, linear vs. nonlinear, stochastic vs. deterministic, etc.). Lastly, please define all uncommon terms and concepts as if the reader is not an expert in the application, but has a mathematical background.

   Please see this sample proposal which is much longer and more detailed than you need to be, but demonstrates the structure and layout of a proposal.

   Your proposal should be typed and uploaded as a pdf file to Canvas.

3. Draft of Introduction: (Due Week 7) 20 points By this point you need to have identified the methods that you will employ in modeling your problem or application. The introduction should include most of the content of the proposal, but in more detail. A background paragraph or two must list previous work in this area, with citations to references. You should make a particular effort to distinguish the current work from previous efforts (e.g., yours is a simplification/generalization of so-and-so's work). Although you likely do not yet have results, it would be a good idea to describe what you expect to happen so as to have had the practice in describing results.

   Please see this sample paper which is much longer and more detailed than you need to be, but demonstrates the structure and layout of each section of a research paper.

4. Rough Draft: (Due Week 9) 40 points See sample above under Introduction. Your rough draft should include an abstract and a bibliography. The introduction of the draft should outline the entire paper. It is appropriate to describe tasks not yet completed and to state hypothesis not yet tested. However, some results are expected for this draft; it should not simply be a longer Introduction.

   Please make use of Writing Resources under Links below.

5. Final Paper: (Due Finals Week) 80 points See sample above under Introduction. Your final draft must include an abstract and a bibliography, possibly figures and tables, and appendices if necessary (could include code used if short, or lenghtly derivations of equations which interrupt flow of narrative). The introduction of the final draft should outline the entire paper. Any tasks not yet completed should be left out (or may be moved to a paragraph in the Conclusions section detailing future work possibilities).

   Please make use of Writing Resources under Links below.

Exam

Grades

Matlab

The following are online resources for learning Matlab:

• Tutorial from Mathworks
• Dr. Higdon's notes on Computational Mathematics
  
• MATLAB Teaching Codes at MIT
  
• Matlab Reference Card
• Matlab Tutorial
• Matlab Introduction
• Sample Matlab diary
• Sample Publishable Script
• Sample Published Script

Matlab demonstrations

cc2plot.m -- This is a Matlab code that I have written to make it easier for you to visualize solutions to 2nd order linear ODEs with constant coefficients. You should have access to Matlab at many of the computer labs on campus. Simply download this file, run Matlab, and at the prompt type help cc2plot. Copy and paste one of the examples to see how it works. Change the input values to try your own examples, or plot those from the book when plots are not provided. See also cc2plotdemo.m, cc4plot.m, coupledspring.m and coupledspring2.m

pensimulate.m -- Damped, driven pendulum

nonlinearpendulum.ppg -- Nonlinear pendulum gallery for use with pplane8 (2014b, 2016b and 2017b versions), originally from Rice University.
See also MyPhysicsLab – Chaotic Pendulum

cobweb.m -- Graphical display of fixed point iterations

logweb.m -- Graphical display of fixed point iterations for logistic map (see paper on period three below)

logphase.m -- Graphical display of fixed point iterations for logistic map (see paper on period three below)

logdelay.m -- Graphical display of solutions for Discrete Logistic with delay.

PDE code

SIR code, SIR code solver

Links

Writing Resources:

• WIC Survival Guide
• Math Department Writing Guide
• The Writing Center
• Latex Templates:
  • simple.tex
  • simple.bib
  • simple.pdf
  • hw.tex

Modeling Resources:

• Dynamic Models in Biology, Chapter 9
• Math modeling from a computational perspective
• Intro to math modeling
• Coupled spring model
  Coupled spring code
  or Coupled spring code (plots position of masses, not displacements)
• Nonlinear Pendulum Analysis
• Birth of Period Three and Birth of Period Three, Revisited
• SZR Model
• Infectious Diseases

Reference Books:

• A Course in Mathematical Modeling by Douglas D. Mooney, Randall J. Swift
• Mathematical Modelling edited by Murray S Klamkin
• Handbook of writing for the mathematical sciences by Nicholas J. Higham
  Author's website

Disclaimers

• While it may not be stated explicitly each day, students are expected to read each section to be covered before class. Students are responsible for any material missed due to absence. Questions not addressed during class time should be asked in office hours.

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