NJIT Academic Integrity CODE: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT 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 University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.
Math 227-001: Mathematical Modeling
FALL 2010
Textbook: A First Course in Mathematical Modeling, 4th Edition by 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: The final grade in this course will be determined as follows:
▪ Homework: |
10% |
▪ Labs: |
10% |
▪ Projects: |
25% |
▪ Midterm Examination I: |
10% |
▪ Midterm Examination II: |
10% |
▪ Midterm Examination III: |
10% |
▪ Final Examination: |
25% |
The final curve remains to be determined, but it might look something like this.
A |
90-100 |
C |
70-75 |
B+ |
85-89 |
D |
60-69 |
B |
80-84 |
F |
0-59 |
C+ |
75-79 |
|
|
Drop Date: Please note that the University Drop Date November 1, 2010 deadline will be strictly enforced.
Homework Policy: Homework assignments will be distributed in class.
Graded Work: All work submitted for a grade must be carefully prepared. Incomplete, sloppy or late assignments will not be accepted.
Attendance: On-time attendance is required. 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. Several MATLAB assignments will be given out. These assignments have been designed to help you learn how to use this software in order to visualize many of the concepts taught in class.
Examinations: Three in-class midterm examination and one final examination will be given on the following days:
Exam 1: |
September 16, 2010 |
Exam 2: |
October 14, 2010 |
Exam 3: |
November 8, 2010 |
Final Exam Week: |
December 10-16, 2010 |
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
Examination Policy.
This policy will be
strictly enforced.
Makeup Exam Policy: There will be No make-up QUIZZES OR EXAMS WILL BE GIVEN during the semester. 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 their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
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.
M |
Labor Day Holiday ~ University Closed |
|
M |
Last Day to Withdraw from this course |
|
R-Su |
Thanksgiving Recess ~ University Closed |
|
T |
Classes follow a Thursday Schedule |
|
December 8, 2010 |
W |
Classes follow a Friday Schedule |
Course Outline and Homework Assignments:
Week |
Lect. |
Sections |
Topic |
Homework |
|
||||
Week
1 |
1 |
1.1 & 1.2 |
Springs, Change and Iteration |
8/30: |
2 |
Lab 1 |
Iteration Experiments I |
9/1: |
|
3 |
1.2 & 1.3 |
Cooling and Explicit Solution of Iterations |
9/2: |
|
Week 2 |
└► |
LABOR DAY ~ UNIVERSITY CLOSED |
|
|
4 |
Lab 2 |
Iteration Experiments II |
9/8: |
|
5 |
1.3 & 1.4 |
Explicit Solutions of Iterations & Formulations of Systems |
9/9: |
|
Week 3 |
6 |
1.4 |
Solutions for Linear Difference Equations |
9/13: |
7 |
Lab 3 |
Iteration Experiments III |
9/15: |
|
8 |
└► └► |
MIDTERM EXAM I: September 16, 2010 EXAM I covers all lectures, reading and labs through 9/15 |
||
Week
4 |
9 |
2.1 |
Modeling Processes |
9/20: |
10 |
Lab 4 |
Simulating Mass-Spring Dynamics |
9/22: |
|
11 |
2.2 |
Modeling Using Proportionality |
9/23: |
|
Week 5 |
12 |
2.3 |
Modeling Using Geometric Similarity |
9/27: |
13 |
Lab 5 |
Simulating Planetary Motion |
9/29: |
|
14 |
2.5 |
Biomechanical Modeling |
9/30: |
|
Week
6 |
15 |
3.1 |
Graphical Model Fitting |
10/4: |
16 |
Lab 6 |
Simulating Stock Prices |
10/6: |
|
17 |
3.2 |
L1 and L2 Fitting |
10/7: |
|
Week
7 |
18 |
3.3 |
Least Squares Linear and Nonlinear Models |
10/11: |
19 |
Lab 7 |
Data from a Mass-Spring Experiment |
10/13: |
|
20 |
└► └► |
MIDTERM EXAM II: October 14, 2010 EXAM II covers all lectures, reading and labs through 10/13 |
||
Week
8 |
21 |
5.1 |
Monte Carlo Methods |
10/18: |
22 |
Lab 8 |
Stock Prices and Options |
10/20: |
|
23 |
5.2 |
Random Number Generation |
10/21: |
|
Week 9 |
24 |
5.3 |
Discrete Random Choices and Option Pricing |
10/25: |
25 |
Lab 9 |
Conserved Quantities in Mechanical Systems |
10/27: |
|
26 |
9.1 |
Dimensional Analysis I |
10/28: |
|
Week
10 |
└► |
Last Day to Withdraw from this course |
||
27 |
9.2 |
Dimensional Analysis II |
11/1: |
|
28 |
Lab 10 |
Discrete Systems with Continuum Limits |
11/3: |
|
29 |
9.3 |
Damped Pendulum |
11/4: |
|
Week 11 |
30 |
└► └► |
MIDTERM EXAM III: November 8, 2010 EXAM III covers all lectures, reading and labs through 11/4 |
|
31 |
Lab 11 |
Phase Plane of the Damped Pendulum |
11/10: |
|
32 |
6.1 |
Markov Chains |
11/11: |
|
Week 12 |
33 |
Notes |
Random Walks and Brownian Motion |
11/15: |
34 |
Lab 12 |
Mass-Spring System with Random Forcing |
11/17: |
|
35 |
11.1 |
Population Models |
11/18: |
|
Week 13 |
36 |
11.3 |
Braking Distance |
11/22: |
37 |
Lab 13 |
Heun’s Methods |
11/24: |
|
└► |
[Thurs-Sun: Nov. 25-28] Thanksgiving Recess ~ University Closed |
|||
Week 14 |
38 |
Notes |
Predator-Prey: A Discrete Space-Time Simulation |
11/29: |
39 |
Lab 14 |
Solving ODEs with MATLAB |
12/1: |
|
40 |
Notes |
Predator-Prey: Simulation Properties |
12/2: |
|
Week 15 |
41 |
Notes |
Predator-Prey: Reduced Model |
12/6: |
42 |
Notes |
Predator-Prey: Performance of the Reduced Model |
12/7: |
|
└► |
[TUE & Wed: DEC. 7-8] Classes follow a THURSDAY and FRIDAY Schedule |
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|
||||
Finals |
Final EXAM WEEK: December 10-16, 2010 |
Prepared By: Prof. Jonathan Luke
Last revised: June 1, 2010