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Department of Mathematics
Math 183. Mathematical Modeling
Course Outline
Spring 2012
Time and Place: =
MWF
10:00 am - 10:50 am,
Millikan 211
Instructor:<=
span
style=3D'mso-spacerun:yes'> =
Dr.
Adolfo J. Rumbos
Office:<=
span
style=3D'mso-spacerun:yes'> =
=
Andrew
259
Phone/e-mail:<=
span
style=3D'mso-tab-count:2'> &=
nbsp; ext. 18713 / arumbos@pomona.edu
Course Website: &nb=
sp; http://pages.pomona.edu/~ajr047=
47/
Office Hours:<=
span
style=3D'mso-spacerun:yes'> MWF 11:00 am - 11:50 am; TR 9:00=
am
– 10:00 am;
or
by appointment.
Prerequisites:<=
span
style=3D'mso-spacerun:yes'> Linear
Algebra and Ordinary Differential Equations
Course
Description. The main goal of this =
course
is to provide opportunities for students to construct and analyze mathemati=
cal
models that arise in the physical, biological and social sciences. Mathematical models are usually cr=
eated
in order to obtain understanding of problems and situations arising in the =
real
world; other times, the main goal is to make predictions or to control cert=
ain
processes; finally, some models are created in order to aid in decision mak=
ing.
Construc=
tion
of a mathematical model consists of translating a real world problem into a
mathematical problem involving parameters, variables, functions, equations
and/or inequalities. Analysis=
of
the model involves the solution (if possible) of the mathematical problem
through logical, algebraic, analytical or computational means, and assessing
what the solutions imply about the real situation under study. If an analyt=
ical
or computational solution is not possible, computer simulations can sometim=
es
be used in order to study various scenarios implied or predicted by the
model.
Analysis
techniques can be drawn from many areas of mathematics. In this course, it is assumed that
students have a good working knowledge of Calculus, Linear Algebra and Ordi=
nary
Differential Equations. These=
areas
are adequate for the analysis of some models. However, many modeling situations
require the use of some probability theory and linear programming. These mathematical topics will be
covered in the course. In cal=
culus
and differential equations courses, students have been exposed to some continuous models. In this course, we will also intro=
duce
students to discrete models as =
well.
Course Structure and Requirements. The course will be structured around= a series of case studies that will provide ample opportunity for students to learn about (and to practice) the development and analysis of models raging from the discrete to the continuous, and from the deterministic to the stochastic (or probabilistic), and= in many cases involving mixed-type modeling. Homework problems will be assigned at every meeting and collected= on an alternate basis. There wil= l be a midterm. Students will also be required to work in teams of two or three on a modeling project in the last part of the course. The proje= ct consists of a term paper describing the construction and analysis of the model. In addition, students = will be required to give a formal presentation on a modeling project at the end = of the semester.
Grading
Policy. Grades will be based solutio=
ns to
assigned problems, a midterm, the term paper and the modeling project
presentation. The overall sco=
re
will be computed as follows according to the following distribution:
&=
nbsp; &nbs=
p; Homework =
&=
nbsp; &nbs=
p;
&=
nbsp; &nbs=
p; 20%
&=
nbsp; &nbs=
p; Exams &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; 50%
&=
nbsp; &nbs=
p; Presentations &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; 15%
&=
nbsp; &nbs=
p; Modeling
term project &=
nbsp; &nbs=
p; &=
nbsp; 15%
Math 183=
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2012
Tentative Schedule of Topics and
Presentations
Date &=
nbsp; &nbs=
p; Topic
W Jan 18 =
span>Introduction
to the process Mathematical Modeling
F &=
nbsp; Jan 20 =
span>Case
Study: Bacterial Growth in a Chemostat
M &n=
bsp; Jan 23 =
span>Nondimensionalization
W Jan 25 =
span>Nondimensionalization
(continued)
F &=
nbsp; Jan 27 =
span>Problems
M &n=
bsp; Jan 30 =
span>Case
Study: Modeling Traffic Flows
W Feb 1 Traffic
flow models (continued)
W Feb 3 Problems
M &n=
bsp; Feb 6 Case
Study: Queuing Theory
W Feb 8 Probability
and stochastic models
W Feb 10 P=
robability
and stochastic models (continued)
M &n=
bsp; Feb 13=
P=
robability
and stochastic models (continued)
W Feb 15=
P=
robability
and stochastic models (continued)=
W Feb 17=
P=
roblems
M &n=
bsp; Feb 20=
P=
roblems
W Feb 22=
R=
eview
W Feb 24=
Exam 1
M &n=
bsp; Feb 27=
<=
span
style=3D'mso-bidi-font-weight:bold'>Case Study: An Optimization Problem
W Feb 29=
<=
span
style=3D'mso-bidi-font-weight:bold'>Linear programming
F &=
nbsp; Mar 2 &nbs=
p; Problems
M &n=
bsp; Mar 5 &nbs=
p; Linear programming (continued)
W Mar 7 &nbs=
p; Linear programming
F &=
nbsp; Mar 9 &nbs=
p; Problems
M &n=
bsp; Mar 12=
S=
pring
Recess!
W Mar 14=
S=
pring
Recess!
F &=
nbsp; Mar 16=
S=
pring
Recess!
M &n=
bsp; Mar 19 C=
ase
Study: Testing a Model
W Mar 21 M=
odel
fitting and parameter estimation
F &=
nbsp; Mar 23 P=
roblems
Math 183=
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2012
M &n=
bsp; Mar 26=
R=
eview
W Mar 28=
Exam 2
F &=
nbsp; Mar 30=
Cesar Chavez Day (no class)
M &n=
bsp; Apr 2 Modeling
Project
W Apr 4 Modeling
Project
F &=
nbsp; Apr 6 Modeling
Project
M &n=
bsp; Apr 9 Modeling
Project Presentations
W Apr 11 M=
odeling
Project Presentations
F &=
nbsp; Apr 13
M &n=
bsp; Apr 16 M=
odeling
Project Presentations
W Apr 18 M=
odeling
Project Presentations
F &=
nbsp; Apr 19 M=
odeling
Project Presentations
M &n=
bsp; Apr 23 M=
odeling
Project Presentations
W Apr 25 M=
odeling
Project Presentations
F &= nbsp; Apr 27 <= o:p>
M &n=
bsp; Apr 30 M=
odeling
Project Presentations
W May 2 Mode=
ling
Project Presentations