SYST 220:� Discrete Dynamic Systems Modeling
Course Overview
Rajesh Ganesan
Systems
Engineering and Operations Research
An
important problem in engineering is to predict the behavior of systems that
change in time.� Such systems are called dynamical systems.� This course introduces students to a set of
mathematical methods used to model dynamical systems.� In particular, students will learn to:
�
Identify real world problems that can be modeled as dynamical systems.
�
Take such systems and translate them into mathematical models.
�
Predict the behavior of such systems using mathematical analysis and
computation.
Students
will use engineering mathematics as well as computers to simulate the behavior
of dynamical systems and make predictions about the systems. This course
focuses on discrete dynamical models.
Class Hours: Tue / Thu, 10:30 am - 11:45
am, S&T-I 206
Prerequisite:� Math 114
Instructor: ���� Rajesh Ganesan
����������������������� [email protected]
����������������������� 703-993-1693
����������������������� Science & Tech II,
room 323
����������������������� Office hours: Tue , Thu 1:00 to 2:00 PM
Reference book: James T. Sandefur, Discrete
dynamical modeling, Oxford University Press, 1993. ISBN 0-19-508438-1
Class
notes will be posted in advance on website http://classweb.gmu.edu/rganesan.
Please print and bring them to class for better understanding of the lecture.
1. Introduction. Systems engineering. The use of models in Systems Engineering.� Introduction to dynamic modeling.�
2. Introduction to modeling.� Converting
real world problems into mathematical models.�
Solutions and analysis using spreadsheets.� Various applications.� The cobweb model and stability.
3. First order dynamic systems. Linear and nonlinear models.� Solutions and properties. Applications from
linguistics, genetics, finance, and international competition.
4. Probability and dynamical systems.�
Elements of probability.� Simple
Markov chains
5. Dynamic systems with inputs.� Exponential
terms.� Polynomial terms.� Fractal geometry.� Economic systems.
6. Higher order linear systems.� National
economic models. Oscillations and the vibrating string.
7. Nonlinear dynamic systems.�
Linearization; computational models.�
Simulation. Population models; logistics models; predator-prey models.
8. Markov chains.� Regular Markov chains.� Absorbing Markov chains.� Applications.� Simulation.
Student Evaluation Criteria
|
Homework
assignments |
20% |
|
Group
project |
10% |
|
Midterm
1 |
20% |
|
Midterm
2 |
20% |
|
Final
exam |
30% |
|
Thu.
Oct. 5 |
Midterm
Exam 1 |
|
|
Tue.
Nov. 21 |
Midterm
Exam 2 |
Group
project: 1 page progress report due |
|
Thu.
Dec. 14 10:30-1:15
PM |
Final
exam |
Group
project: final report due |
Homework policy:
HW will be posted on the
website http://classweb.gmu.edu/rganesan.
Try to work them by yourself. Working in groups is permitted but you must make
sure that you understand the problems before you turn them in. Each student
must turn in their HW even if worked in groups. Please remember that if you
haven�t learnt the HW problems you may not pass the exams and this will affect
your final grade. All homeworks must be stapled and
submitted on the due date prior to the beginning of the class. Late homework will
be evaluated against 50% credit. Late beyond 2 weeks will receive no credit.
Only 1 problem will be graded in every HW and the HW grade depends on
submitting all assigned HWs and your approach to the
problem that is graded.
Academic Policy:
All academic policies as
given in the Honor System and code will be strictly followed. Visit URL
http://www.gmu.edu/catalog/apolicies/#Anchor12
Grades:
Letter
grades will be decided as follows:�
97% and above �A+, 94-96%- A, 90-93% -A-,
86-89- B+, 83-85%-B, 80-82%-B-,� 76-79%-
C+, 73-75%- C, 70-72%-C-, 66-69%-D+, 63-65%-D,
60-62%-D-, at or below 59%-F
Exams
will only be given at the predetermined dates. Early or late exam taking will
not be allowed, except for very special cases.
Use
of MS Excel is needed for some problems.���������
One 8.5x11in. one sided formula sheet will be allowed in
the midterm and the Final exam. The sheet must be submitted with the test.� ������������� �����������������������
Please
visit http://classweb.gmu.edu/rganesan
to check for announcements, Hw problems, and
solutions.
Please
turn off your cell phones before class and do not use your cell phone during
lecture. Feel free to walk out without distracting the class as and when
needed.
FORMAT
REQUIREMENTS FOR COLLECTED MATERIALS
Identification: all material handed in must have the following
information in the UPPER�
RIGHT -HAND CORNER; Name, last 4 digits of G #.
Multiple pages MUST be stapled. Otherwise pages may get lost and
the instructor and TA�s will not be responsible.
BEST WISHES FOR A GREAT SEMESTER!!