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Department of Mathematics
Math 183. Mathematical Modeling
Course Outline
Spring 2013
Time and Place: =
MWF
11:00 am - 11:50 am,
Millikan 207
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 9:00 am - 9:50 am, Tu 9:05 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 throu=
gh
logical, algebraic, analytical or computational means, and assessing what t=
he
solutions imply about the real situation under study. If an analytical or
computational solution is not possible, computer simulations can sometimes =
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 r=
equire
the use of some probability theory and optimization techniques. 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 will be a midterm. Students will also be required to work in teams of two or three on a modeling projec= t in the last part of the course. = The project consists of a term paper describing the construction and analysis of the model. In addition, stude= nts will be required to give a formal presentation on the modeling project at t= he 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; &=
nbsp;
&=
nbsp; &=
nbsp; 20%
&=
nbsp; &nbs=
p; Exams &nb=
sp; =
&nb=
sp; =
&nb=
sp; 50%
&=
nbsp; &nbs=
p; Presentations =
&nb=
sp; &=
nbsp; 15%
&=
nbsp; &nbs=
p; Modeling
term project &=
nbsp; &nbs=
p; &=
nbsp; 15%
Math 183=
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2013
Tentative Schedule of Topics and Prese=
ntations
Date &=
nbsp; &nbs=
p; Topic
W Jan 23 =
span>Introduction
to the process Mathematical Modeling
F &=
nbsp; Jan 25 =
span>Case
Study: Bacterial Growth in a Chemostat
M &n=
bsp; Jan 28 =
span>Nondimensionalization
W Jan 30 =
span>Nondimensionalization
(continued)
F &=
nbsp; Feb 1&n=
bsp; Pro=
blems
M &n=
bsp; Feb 4&n=
bsp; Case
Study: Modeling Traffic Flows
W Feb 6 Traffic
flow models (continued)
W Feb 8&n=
bsp; Pro=
blems
M &n=
bsp; Feb 11 A=
nalysis
of a traffic flow model
W Feb 13 M=
ethod
of characteristics
W Feb 15 M=
ethod
of characteristics (continued)
M &n=
bsp; Feb 18=
S=
hock
waves
W Feb 20=
S=
hock
waves (continued)
W Feb 22=
P=
roblems
M &n=
bsp; Feb 25=
P=
roblems
W Feb 27=
R=
eview
W Mar 1 Exam 1
M &n=
bsp; Mar 4 Case Study: Modeling bacterial mutation=
s
W Mar 6 Stochastic models =
F &=
nbsp; Mar 8 Probability
M &n=
bsp; Mar 11=
<=
span
style=3D'mso-bidi-font-weight:bold'>Probability (continued)
W Mar 13&=
nbsp; Random variables and distributions
F &=
nbsp; Mar
15 Random variables and distributions
(continued)
M &n=
bsp; Mar 18=
S=
pring
Recess!
W Mar 20=
S=
pring
Recess!
F &=
nbsp; Mar 22=
S=
pring
Recess!
M &n=
bsp; Mar
25 Rand=
om
processes
W Mar 27&=
nbsp; Random
processes (continued)
F &=
nbsp; Mar 29 <=
/span>Cesar Chavez Day (no
class)
M &n=
bsp; Apr 1 Problems
W Apr 3 Review
F &=
nbsp; Apr 5 Exam 2
M &n=
bsp; Apr 8 Modeling
Project
W Apr 10=
M=
odeling
Project
F &=
nbsp; Apr 12=
M=
odeling
Project
M &n=
bsp; Apr 15=
M=
odeling
Project Presentations
W Apr 17=
M=
odeling
Project Presentations
F &=
nbsp; Apr 19=
M=
odeling
Project Presentations
M &n=
bsp; Apr 22 M=
odeling
Project Presentations
W Apr 24 M=
odeling
Project Presentations
F &=
nbsp; Apr 26 M=
odeling
Project Presentations
M &n=
bsp; Apr 29 M=
odeling
Project Presentations
W May 1 Mode=
ling
Project Presentations
F &=
nbsp; May 3 Mode=
ling
Project Presentations
M &n=
bsp; May 6&n=
bsp; Modeling
Project Presentations
W May 8 Mode=
ling
Project Presentations