Course Syllabus

Math 227-001:  Mathematical Modeling

Fall 2009

University Code on Academic Integrity:  All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code very seriously and enforces it strictly.  This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the Honor Code, students are obligated to report any such activities to the Instructor.

 

Instructor:

Prof. Roy Goodman

624 Cullimore Hall

642-4261


Office Hours: Monday 11:30-1:00, Thursday 4:00-5:30 or by appointment


Textbook:  A First Course in Mathematical Modeling, 4th edition, F. Giordano, W. Fox, S. Horton, & M. Weir, Brooks/Cole Publishers, © 2009, ISBN: 0-495-00159-2.


Prerequisites:  Math 112 with a grade of C or better.


Grading Policy:  

▪ Homework/Projects:

40%

▪ 2 Midterm Exams:

15% each

▪ Final Exam:

30%


The final curve remains to be determined, but it might look something like this.

A

90-100

C

60-69

B+

85-89

D

50-59

B

75-84

F

0-49

C+

70-74

 

 

 

Drop Date:  Please note that the Drop Deadline Date November 2, 2009 will be strictly enforced.


Homework: It is therefore vital that you complete all of the homework assignments by the specified dates


Attendance:  Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Department’s Attendance Policy. This policy will be strictly enforced.


MATLAB:  MATLAB is a mathematical software program that is used throughout the science and engineering curricula. Students should download it to their computers from the IST software downloads page.


Exams: There will be two midterm exams during the semester and one comprehensive final exam during the final exam week at the end of the semester. Exams are held in class on the following days.

Exam 1:

October 1, 2009

Exam 2:

November 4, 2009

Final Exam Week:

December 11-17, 2009

The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the department's to Examination Policy. This policy will be strictly enforced. Please note that calculators, cellular phones, beepers, and all other electronic devices may not be used during any exam.


Makeup Exam Policy:  No make-up quizzes or exams will be given.  In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.


Further Assistance:  For further questions, students should contact Prof. Goodman using the above contact information.


Cellular Phones:  All cellular phones and beepers must be switched off during all class times. For consequences see here.


Math Department Course Policies:   All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.


September 7, 2009

M

Labor Day Holiday ~ University Closed.

November 2, 2009

M

Last Day to Withdraw from this Course.

November 24, 2009

T

Classes Follow a Thursday Schedule.

November 25, 2009

W

Classes Follow a Friday Schedule.

November 26-29, 2009

R-Su

Thanksgiving Recess ~ University Closed.

 


Topics, Readings, & Assignments

Week
Dates

Sec.

Topic

Homework Assignments

 

 

 

 

1
8/31 –  9/4

1.1

1.2

1.3  

Difference Equations and Discrete Dynamical Systems

1.1: 10, 12

1.2: 6,8

1.3: 11

Computer Lab 1 Thursday, PC Mall 40

2
9/7 – 9/11

Labor Day--No Class Monday

1.4

2.1

2.2

   2.3   

Systems of Difference Equations

The Modeling Process

Proportionality & Geometric Similarity         

1.4: 4

2.1: 7, 12

2.2: 4, 6, 8, 13

Lab 1 assignments

3
9/14 – 9/18

2.4

3.1

3.2

Gas Mileage Example

Graphical Data Fitting

Analytic Model Fitting

2.3: 3, 4, project 2 (requires some writing)

2.4: 2, 3 (both require writing)

3.1: 2, 3, 6 (plot the variables, transformed if necessary, then use matlab to plot a variety of lines until you find one that looks about right.)

4
9/21 – 9/25

3.3

3.4

Least Squares Fitting

Choosing the Best Model

3.2: 3 (no computation)

Lab 2 problems and solutions

Computer Lab 2, Thursday, PC Mall 40

5
9/28 – 10/2

4.1

4.3

6.3

One-term Experimental Models

Low Order Polynomial Models

Regressions

1,2,7

1,6,8  (Solutions to computational problems)

Exam 1, Thursday, 10/1 (My answers)

6
10/5 – 10/9


4.4

Handout on nonlinear fitting

Splines

 Lab 3 Problems and solutions

Computer Lab 3, Thursday, PC Mall 40

7
10/12 – 10/16

5.1

5.2

5.3

Simulating area under curve

Generating Random Numbers

Simulating Probabilistic Behavior

 

Computer Lab 4, Thursday, PC Mall 40

8
10/19 – 10/23

5.4

6.1

Example of Probabilistic Simulation

Monte Carlo Simulation

Special Guest Lecture Thursday

 Lab 4 Problems, due Wednesday, 11/4

9
10/26 – 10/30

   

9.0

9.1

9.2

UMAP Module 564   

Intro to Dimensions

Dimensions as Products

Dimensional Analysis Process


 QUIZ Monday on Module-related questions

(No questions on 9.0)

2, 3, 5, 7

1 (hint: use 9.1 #3), 4, 6, 9

10
11/2 – 11/6

9.3

9.4

Damped Pendulum

Dimensional Analysis Examples

 1, 2

6a, 7

11
11/9 – 11/13

7.1

7.2

7.3

Optimization

Linear Programming I: Geometry

Linear Programming II: Algebra

2, 5

2, 6, 9, 13b

2, 6

Exam 2 (Thursday, Nov. 12)

12
11/16 – 11/20

7.4

7.5

The Simplex Method

Sensitivity Analysis

 9, 12 (by hand and with my program easyLP.m)
1, project 2

Lab cancelled

13
11/23 – 11/27

Thanksgiving Week: Class Mon & Tues, not Weds. and Thurs.

 7.6

--

Numerical Search Methods

More on Dynamical Systems

1b,2b,3a,4 (do 1-3 by hand or write programs) 

14
11/30 – 12/4

11.1

11.4

11.5

ODE Models

Graphical solutions

Euler's Method

4 (use nonlinear least squares as in Mooney), 7

7, 9, 11

Computer Lab 5, Thursday, PC Mall 40

15
12/7 – 12/9

11.2

 UMAP 69

 Drug dosages, law of cooling

The digestive process of a sheep

(on textbook CD)

Review and Wrap UP

 Study for Final

 

 

Final Exam: Tuesday December 15, 8:30-10:55 am Kupfrian 208

 

 Take the Beginning of Semester Survey here.

Prepared By:  Prof. Roy Goodman

Last revised:  August 25, 2009