SYST 201: 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 bahavior 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 in which time is viewed as a sequence of
steps.
Class
Hours: Tue / Thu,
Prerequisite: MATH 114
Instructor:
Rajesh Ganesan
703-993-1693
Science & Tech II,
room 323
Office hours: Tue , Thu
TA:
Anthony De Cicco
Central Module Room # 17
Wed
Textbook: James T. Sandefur,
Discrete dynamical modeling, Oxford
University Press, 1993.
ISBN 0-19-508438-1
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% |
|
Tue.
Aug. 30 |
Lec. 1, Introduction |
|
|
Thu.
Sep. 1 |
Lec. 2, Modeling |
|
|
Tue.
Sep. 6 |
Lec. 3, Modeling |
|
|
Thu.
Sep. 8 |
Lec. 4, Chapter 1 |
Hmwk #1 due |
|
Tue.
Sep. 13 |
Lec. 5, Chapter 1 |
|
|
Thu.
Sep. 15 |
Lec. 6, Chapter 2 |
Hmwk #2 due |
|
Tue.
Sep. 20 |
Lec. 7, Chapter 2 |
|
|
Thu.
Sep. 22 |
Hmwk #3 due |
|
|
Tue.
Sep. 27 |
Lec. 9, Chapter 3 |
|
|
Thu.
Sep. 29 |
Lec. 10, Chapter 3 |
Hmwk #4 due |
|
Tue.
Oct. 4 |
Review |
|
|
Thu.
Oct. 6 |
Exam
1 ( |
|
|
Tue.
Oct. 11 |
Columbus
Day |
|
|
Thu.
Oct. 13 |
Review
Exam, Project |
|
|
Tue.
Oct. 18 |
Lec. 11, Chapter 8 |
|
|
Thu.
Oct. 20 |
Lec. 12, Chapter 8 |
|
|
Tue.
Oct. 25 |
Lec. 13, Chapter 8 |
Hmwk #5 due |
|
Thu.
Oct. 27 |
Lec. 14, Chapter 4 |
Group
project mid-reports due |
|
Tue.
Nov. 1 |
Lec. 15, Chapter 4 |
|
|
Thu.
Nov. 3 |
Lec. 16, Chapter 4 |
|
|
Tue.
Nov. 8 |
Lec. 17, Chapter 5 |
Hmwk #6 due |
|
Thu.
Nov. 10 |
Lec. 18, Chapter 5 |
|
|
Tue.
Nov. 15 |
Lec. 19, Chapter 5 |
Hmwk #7 due |
|
Thu.
Nov. 17 |
Review |
|
|
Tue.
Nov. 22 |
Exam
2 ( |
Hmwk #8 due |
|
Thu.
Nov. 24 |
Thanksgiving |
|
|
Tue.
Nov. 29 |
Lec. 20, Chapter 6 |
|
|
Thu.
Dec. 1 |
Lec. 21, Chapter 6 |
Group
projects due |
|
Tue.
Dec. 7 |
Review |
Hmwk #9 due |
|
Thu.
Dec. 9 |
Final
exam |
|
|
|
|
|
Homework policy:
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. 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
homework must be stapled and submitted on the due date prior to the beginning
of the class. Late homework carries a penalty. 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:
93% and above –A+, 90-92%- A, 85-89% -A-,
83-84%-B+, 80-82%-B, 75-79%-B-, 73-74%- C+,
70-72%- C, 65-69%-C-, 63-64%-D+, 60-62%-D, 55-59%-D-,
at or below 54%-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.
You
will receive some lecture notes as and when it’s needed. I will approach every
topic by describing the objective, theory, formula and examples. This should make your effort in understanding
the course a lot easier.
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!!