Mathematical Modeling
MTH 323 - Sec 001

MWF 14:00-14:50
GRAF 307
Spring 2012


Professor:

 

Dr. Nathan Louis Gibson  

Office:

 

Kidd 352

Office Hours:

 

MWF 11:00-11:50AM

Course Website:

 

http://www.math.oregonstate.edu/~gibsonn/Teaching/MTH323-001S12

Text Book:

 
  Title: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow
Series: Classics in Applied Mathematics, Vol. 21
Author: Rich Haberman
Year: 1998
Bookstore Price: $57.04
SIAM Member Price: $43.40

Contents




Course Description

A variety of mathematical modeling techniques will be introduced. Students will formulate models in response to practical problems drawn from the literature of ecology, environmental sciences, engineering or other fields. Informal writing assignments in class and formal written presentation of the models will be required. (Writing Intensive Course) PREREQS: MTH 256 and MTH 341 or instructor approval.

Details

Your goals in this course are to learn how to interpret the mathematical models published in contemporary texts and journals, how to formulate your own mathematical models, and how to present your modeling efforts in a well-written paper.

An approximate outline of topics follows.

Topic Applications Models Concepts
Mechanical Models Spring-mass system
Pendulum 		Ordinary differential equations Linearization
Population Dynamics Discrete one-species systems
Harvesting 		Difference equations
Leslie matrix models
Models with time delays 		Equilibria and Stability
Chaos
Stochasticity
Particle Flow Traffic flow
Heat transfer 		Partial differential equations Waves and shocks

Reading Assignments

Reading assignments will typically involve chapters in the text, but will also include chapters from outside sources, journal articles, and peer-written reports. You may be asked to provide a written summary and/or critique, or participate in classroom/online discussions. Your grade for this component will primarily be based on active participation.

  1. Read for Friday Apr 6: Dynamic Models in Biology, Chapter 1
  2. Peer Reviewing Instructions
The rest will be posted to Blackboard.

Writing Assignments

This is a Writing Intensive Course (WIC), thus you will be required to write at least 5000 words, at least 2000 of which must be polished papers that you have revised after peer review and instructor feedback. This formal writing requirement will be satisfied by producing a term paper, roughly 5 pages in length (not counting figures). See the calendar for deadlines pertaining to this project, and Term Paper for a description of what is expected.

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 below.

  1. Assignment for Friday Apr 13 (Due at noon, upload PDF to Blackboard):
    Describe a system (object, situation, etc.) whose dynamics could reasonably be modeled as a harmonic oscillator, i.e., by using a second order, constant coefficient ordinary differential equation (with or without some "damping"). In your description, be sure to include the following:
    1. Convince me why the dynamics can be modeled as a harmonic oscillator
    2. Discuss the advantages/benefits to using such a model for your system
    3. Discuss the disadvantages/drawbacks to using such a model, e.g., limitations of the model, necessary assumptions.

    Your description must be typed, should be brief (readable in less than 10 mins), and written for a non-expert in the corresponding application field (e.g., explain all non-mathematical concepts and terms).

The rest will be posted to Blackboard.

Computer Assignments (Labs)

This is not a programming course, however many topics are more easily understood by computational experimentation. MATLAB codes will be provided for your use. Your grade for this component will primarily be based on written explanations of what you observe from running the simulations.

Labs will be posted to Blackboard. For resources on MATLAB, see the section below.

Term Paper

This is a Writing Intensive Course (WIC), thus you will be required to write at least 5000 words, at least 2000 of which must be polished papers that you have revised after peer review and instructor feedback. This formal writing requirement will be satisfied by producing a term paper, roughly 5 pages in length (not counting figures).

Deliverables in preparation for the final paper are as follows:

  1. Topic : 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 blackboard.

  2. Proposal : 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 before being evaluated on its merits. 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.

    Instructions for submitting proposal: Your proposal should be typed and exported to PDF format. In order to upload to Blackboard, please follow these instructions:

    Instructions for peer-reviewing proposal

  3. Draft of Introduction : 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.

    Instructions for submitting Draft of Introduction: follow directions above for Proposals.

    Instructions for peer-reviewing Introduction

  4. Rough Draft : 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 proposal.

    Follow directions from Proposals to upload your Rough Draft to the Discussion Board. Please make use of Writing Resources under Links below.

  5. Final Paper : 80 points See sample above under Introduction. Your final draft should 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 (may be moved to a paragraph in the Conclusions section detailing future work possibilities).

    Follow directions from Proposals to upload your Final Paper to the Discussion Board. Please make use of Writing Resources under Links below.

    Exam

    There will be an in-class final exam covering material from lectures.

    Grades

    Grades for each assignment will be posted to the Blackboard Site.

    Grade Distribution

    Reading Assignments 10%
    Writing Assignments 20%
    Computer Assignments 10%
    Term Paper 40%
    Final 20%
    Total 100%

    Matlab

    A scientific programming language is required for this course. Matlab is preferred due to the integration of computation and visualization.

    Oregon State University has subscribed to a Total Academic Headcount (TAH) Site License for MATLAB. This new licensing includes many, but not all MATLAB toolboxes. OSU faculty, staff and students can install on up to 4 personally-owned devices or computers. For more information visit Information Services -- MATLAB or matlab.mathworks.com.

    The following are online resources for learning Matlab:

    Matlab demonstrations
    pensimulate.m -- Damped, driven pendulum
    nonlinearpendulum.ppg -- Nonlinear pendulum gallery (for use with pplane8)
    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)
    logdelay.m -- Graphical display of solutions for Discrete Logistic with delay.

    Links

    Writing Resources:

    Modeling Resources:

    Reference Books:

    Blackboard Site

    Last updated: Thu Oct 24 00:14:47 PDT 2013