SYST 201:Discrete Dynamic Systems Modeling

Fall 2005


Course Overview

Rajesh Ganesan

Systems Engineering and Operations Research

George Mason University


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, 10:30 am - 11:45 am, Krug hall #7


Prerequisite:MATH 114


Instructor: ††††††† Rajesh Ganesan


††††††††††††††††††††††† 703-993-1693

††††††††††††††††††††††† Science & Tech II, room 323

††††††††††††††††††††††† Office hours: ††† Tue , Thu 1:00 to 2:00 PM


TA: †††††††††††††††† Anthony De Cicco


††††††††††††††††††††††† Central Module Room # 17

††††††††††††††††††††††† Wed 2:15 - 4:15 PM


Textbook:††††††††† James T. Sandefur, Discrete dynamical modeling, Oxford University Press, 1993.

††††††††††††††††††††††† ISBN 0-19-508438-1


Course Syllabus

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


Group project


Midterm 1


Midterm 2


Final exam



Schedule for Fall 2004


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

Lec. 8, Chapter 3

Hmwk #3 due

Tue. Sep. 27

Lec. 9, Chapter 3


Thu. Sep. 29

Lec. 10, Chapter 3

Hmwk #4 due

Tue. Oct. 4



Thu. Oct. 6

Exam 1 (Ch. 1,2,3)


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



Tue. Nov. 22

Exam 2 (Ch. 8, 4, 5)

Hmwk #8 due

Thu. Nov. 24




Tue. Nov. 29

Lec. 20, Chapter 6


Thu. Dec. 1

Lec. 21, Chapter 6

Group projects due

Tue. Dec. 7


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 havenít 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




Letter grades will be decided as follows:

93% and above ĖA+, 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 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 itís 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.




Identification: all material handed in must have the following information in the UPPERRIGHT -HAND CORNER; Name, last 4 digits of G #. Multiple pages MUST be stapled. Otherwise pages may get lost and the instructor and TAís will not be responsible.