NJIT HONOR CODE 

                                
All 
                                Students should be aware that the Department of 
                                Mathematical Sciences takes the NJIT Honor code 
                                very seriously and enforces it strictly.  
                                This means 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. 
 

                                
Mathematics 450-H01:

								Methods of Applied 
								Mathematics - Honors

                                
Fall 
                                2004

                                
 

                                
Days: Tuesday and 
								Thursday 
                                

								

								
								Time: 1:00 pm- 2:25pm

								

								
								Room: Kupfrian 206 

								
 

                                
 

                                
v     
                                Instructor:  
                                Prof.  
                                
								 
                                Bruce Bukiet

                                
v     
                                Office:  
                                Room#518, Cullimore Hall 

                                
v     
                                Phone:  
                                973-596-8392

                                
v     
                                Email:  
                                
								
								
								bukiet@m.njit.edu

                                
v     
                                Office 
                                Hours:    
                                Monday: 4:30 PM – 5:30 
PM; Tuesday and Thursday 2:30-3:30 pm

                                
 

                                
 

                                
Textbook:  
                                
								Mathematical Models: Mechanical Vibrations, 
								Population Dynamics and Traffic Flow

                                
 

                                
 

                                
Grading 
                                Policy:  
                                The final grade in this course 
                                will be determined as follows:

                                
 

                                
 

                                
v     
                                Homework/Projects:                                 
                                
								
								30% 
                                

                                
v     
                                
								
								Midterm 
								and Final Exams: 
                                                    
                                
								 70% 

                                
 

                                
Class 
                                Policies: 
                                

																	
																	
																	Attendance 
																	and 
																	Participation: 
																	
																	
																	Students 
																	must attend 
																	all classes. 
																	Absences 
																	from class 
																	will inhibit 
																	your ability 
																	to fully 
																	participate 
																	in class 
																	discussions 
																	and problem 
																	solving 
																	sessions 
																	and, 
																	therefore, 
																	affect your 
																	grade. 
																	Tardiness to 
																	class is 
																	very 
																	disruptive 
																	to the 
																	instructor 
																	and students 
																	and will not 
																	be 
																	tolerated.
																	
																	

																	
																	Makeup Exam 
																	Policy:
																	
																	There will 
																	be no makeup 
																	exams, 
																	except in 
																	rare 
																	situations 
																	where the 
																	student has 
																	a legitimate 
																	reason for 
																	missing an 
																	exam, 
																	including 
																	illness, 
																	death in the 
																	family, 
																	accident, 
																	requirement 
																	to appear in 
																	court, etc. 
																	The student 
																	must notify 
																	the Math 
																	office and 
																	the 
																	Instructor 
																	that he/she 
																	will miss an 
																	exam. In all 
																	cases, the 
																	student must 
																	present 
																	proof for 
																	missing the 
																	exam, e.g., 
																	a doctor's 
																	note, police 
																	report, 
																	court 
																	notice, 
																	etc., 
																	clearly 
																	stating the 
																	date AND 
																	times.
																	

																	

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

                                

																	

																	Tentative 
																	Course 
																	Outline:

																	

																	 

																	

																	Part 
																	I: Mechanics



	

	Introduction

	

	Spring-Mass Systems

	

	Review of ODEs

	

	Dimensional Analysis

	

	Underdamped, overdamped and critically damped 
	systems

	

	Double mass-spring system

	

	Non-linear oscillations

	

	Phase plane analysis

	

	Numerical methods for ODEs: Euler, Runge-Kutta

	

	Pendulum

	

	Linearization

	

	Spring pendulum



																	

																	Part 
																	II: 
																	Electrostatics



	

	Electrostatic potential in regular and irregular 
	domains

	

	Derivation of LaPlace equation for potential

	

	Discussion of elliptic PDEs

	

	Methods for solving LaPlace's equations

	

	   Separation of Variables

	

	   Finite differences



																	

																	Part 
																	III: Traffic 
																	Flow (time 
																	permitting)



	

	Introduction to traffic flow

	

	Conservation laws

	

	Governing PDE for simple 1-d traffic flow

	

	The linearized equation and its analysis

	

	Traffic waves and characteristics

	

	Special cases

	
 





There will be approximately 5 homework projects assigned 
during the semester

																	

																	Week 8 – 
																	
																	Midterm Exam 

																	

																	Week 
																	16 – 
																	
																	Final Exam 

																	

																	
																	Prepared By: 
																	Bruce Bukiet

																	

																	Last 
																	revised: 
																	08/24/04