Mathematical Modeling
MTH 323  Sec 010
MWF 11:0011:50
BEXL 328
Spring 2017
Professor:   
Office:   Kidd 056

Office Hours:   MW 1212:50

Course Website:
  http://www.math.oregonstate.edu/~gibsonn/Teaching/MTH323010S17

Text Book:
 

Contents
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.
Learning Outcomes: After completing this class, successful students will be able to:
 Apply fundamental principles to new problems
 Put together chains of reasoning
 Design experimental investigations to investigate phenomena, to test
hypotheses, or to solve practical problems
 Identify the assumptions a model, equation, or claim relies upon, and
make a judgment about the validity of the assumptions
 Conduct unit/dimensional analysis to test the selfconsistency of an
equation
 Make a reasonable prediction from and devise a test of a proposed
hypothesis
 Devise multiple explanations for observations and modify them in light
of new data
 Analyze a relevant limiting/special case for a given model, equation,
claim
 Organize information, ideas, and solutions
 Communicate explanations and results both in writing and verbally
 Exhibit other communication skills: peer review, presentation, paper
 Attain scientific literacy: making sense of scientific news and journal
articles
 Perform programming and computational modeling
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
wellwritten paper.
An approximate outline of topics follows.
Topic 
Applications 
Models 
Concepts 
Mechanical Models
 Springmass system
Pendulum
 Ordinary differential equations
 Linearization

Population Dynamics
 Discrete onespecies 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 will typically involve chapters in the text, but will
also include chapters from outside sources, journal articles, and
peerwritten 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.
 Read for Friday of week 1: 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:
 What is a model?
 What is a dynamic model?
 When is a dynamic model preferred over the alternative?
The rest will be posted to Canvas.
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 a polished paper
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 Section for a description of what is expected.
The remaining portion of the writing requirement will be
comprised of homework assignments and informal inclass assignments
pertaining to lecture.
For resources on writing, see Links Section below.
Writing Assignments will be posted to Canvas.
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 Canvas.
For resources on MATLAB, see the section below.
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 a polished paper
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:
 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.
 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 peerreviewed.
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.
 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 soandso'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 peerreviewing Introduction
 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.
Instructions for peerreviewing Rough Draft
 Final Paper: (Due Finals Week) 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).
Please make use of Writing Resources under Links below.
There will be an inclass final exam covering material from lectures. Sample exam problems will be posted on Canvas.
Grades for each assignment will be posted on Canvas
Grade Distribution
Reading Assignments  10%

Writing Assignments  20%

Computer Assignments  10%

Term Paper  40%

Final  20%

Total  100%

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 personallyowned devices or computers.
For more information visit Information Services  MATLAB.
The following are online resources for learning Matlab:
 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
 Writing Resources:

 Modeling Resources:

 Reference Books:

 Canvas Site
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.
Students are expected to be familiar with
Oregon State University's
Statement of
Expectations for Student Conduct
“Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 5417374098 or at http://ds.oregonstate.edu. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.”
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and
Academic Calendars
Last updated:
Thu Jan 11 17:31:02 PST 2018