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 651-101:
Applied Mathematics I

                                
Fall 
                                2004

                                
 

                                
Day: Monday 
                                

								

								Time: 
								6 pm-9pm

								

								
								Room: Not yet assigned 

								
 

                                
 

                                
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:  
                                
								
								Advanced Engineering Mathematics, Erwin Kreysig 
								8th Edition

                                
 

                                
 

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

                                
 

                                
 

                                
v     
                                Homework:                                 
                                
								
								35% 
                                

                                
v     
                                Quizzes: 
                                                                     
                                
								 35%

                                
v     
                                Final 
                                Exam:                                 
                                
								40%

                                
 

                                
Homework 
                                Policy:  
                                
								
								Selected problems will be collected each week to 
								be graded.

                                
                                
 

                                
 

                                
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 and 
																	Homework 
																	Assignments:

																	

																	 

																	

																	Weeks 
																	1 & 2 – 
																	Review of 
																	First Order 
																	Ordinary 
																	Differential 
																	Equations 
																	and Linear 
																	Higher Order 
																	ODEs – 
																	Chapters 1 & 
																	2

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 13: 11

																	

																	p. 18: 4

																	

																	p. 32: 8,16

																	

																	p. 39: 9, 
																	13, 20

																	

																	p. 58: 4

																	

																	p. 71: 6, 9, 
																	17

																	

																	p. 75: 11, 
																	12

																	

																	p. 80: 8, 14

																	

																	p. 96: 7, 
																	14, 17

																	

																	p. 100: 1, 5

																	

																	p. 103: 3, 
																	11

																	

																	p. 108: 16, 
																	17, 18

																	

																	p. 111: 2, 
																	11

																	

																	p. 137: 12

																	

																	p. 141: 10

																	

																	Find a 
																	general 
																	solution of 
																	y'''-y''-4y'+4y=12 
																	exp(x); 

																	

																	 

																	

																	Week 3 
																	– Review of 
																	Linear 
																	Algebra with 
																	a focus on 
																	Eigenvalues 
																	and 
																	Eigenvectors 
																	- Chapters 6 
																	& 7

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 329: 1, 8

																	

																	p. 357: 7

																	

																	p. 375: 3, 
																	12

																	

																	 

																	

																	Week 4 
																	– Systems of 
																	Ordinary 
																	Differential 
																	Equations - 
																	Chapter 3
																	
																	
																	Homework: 
																	
																	

																	

																	p. 169: 2, 
																	6, 10

																	

																	p. 174: 2, 
																	5, 8

																	

																	p. 183: 6, 7

																	

																	p. 189: 14 - 
																	use 
																	undetermined 
																	coefficients, 
																	variation of 
																	parameters 
																	and 
																	diagonalization

																	

																	p. 198: 3, 6

																	

																	 

																	

																	Week 5 
																	& 6 – Series 
																	Solutions of 
																	ODEs – 
																	Chapter 4
																	

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 204: 
																	(around x=0) 
																	3, 14

																	

																	p. 216: 3, 
																	17 
																	(recognize 
																	the first 
																	answer as 
																	exp(x))

																	

																	p. 238: 4 
																	(don't 
																	verify 
																	orthogonality), 
																	10

																	

																	Write f(x)=x 
																	on [-p,p] using 
																	Fourier 
																	Series

																	
 

																	

																	Week  
																	7 – Review 
																	of Calculus 
																	III: Vector 
																	Differential 
																	Calculus, 
																	Div, Grad, 
																	Curl – 
																	Chapter 8

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 428: 27

																	

																	p. 452: 7, 
																	16, 22, 31

																	

																	p. 456: 3, 
																	15

																	

																	p. 459: 3, 
																	11

																	
 

																	

																	Week 8 
																	– MidTerm 
																	Exam

																	
 

																	

																	Weeks  
																	9 & 10– More 
																	Calculus 
																	III: Vector 
																	Integral 
																	Calculus: 
																	Green's 
																	Tehorem, 
																	Stokes's 
																	Theorem and 
																	Divergence 
																	Theorem – 
																	Chapter 9

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 470: 8, 
																	17

																	

																	p. 477: 6, 
																	16

																	

																	p. 490: 2, 
																	17

																	

																	p. 496: 27

																	

																	p. 503: 1, 
																	6, 14, 15

																	

																	p. 510: 4, 
																	14

																	

																	p. 514: 3

																	

																	p. 520: 5, 8

																	

																	 

																	

																	Week 
																	11 – Fourier 
																	Series – 
																	Chapter 10

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 536: 2, 
																	6, 13

																	

																	p. 540: 4, 
																	15

																	

																	p. 547: 15, 
																	18, 19

																	

																	p. 553: 5, 
																	11

																	

																	p. 557: 13 
																	(use 
																	solution to 
																	section 10.4 
																	#13)

																	
 

																	

																	Week 
																	12 – 
																	Separation 
																	of Variables 
																	for Partial 
																	Differential 
																	Equations – 
																	Chapter 11

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 584: 2, 
																	6, 10, 18

																	

																	p. 594: 2, 
																	and a 
																	PDE-IBVP 
																	given in 
																	class

																	
 

																	

																	Weeks 
																	13 & 14 – 
																	Complex 
																	Numbers and 
																	Complex 
																	Integration 
																	– Chapters 
																	12 and 13

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 662: 6, 
																	16, 21

																	

																	p. 668: 17, 
																	23

																	

																	p. 673: 3, 
																	5, 18, 21

																	

																	p. 678: 14

																	

																	p. 682: 1, 
																	2,6, 11

																	

																	p. 712: 15, 
																	21

																	

																	p. 720: 4c, 
																	13, 19, 23

																	

																	p. 724: 6, 
																	12

																	

																	p. 729: 1, 
																	3, 12

																	
 

																	

																	Week 
																	15 – Complex 
																	Series and 
																	Residue 
																	Integration– 
																	Chapters 14 
																	and 15

																	

																	
																	
																	Homework: 
																	
																	

																	

																	p. 745: 1, 8

																	

																	p. 750: 4

																	

																	p. 757: 2, 
																	10, 19

																	

																	P. 775: 2, 9

																	

																	p. 780: 2, 
																	5, 9

																	

																	p. 786: 1, 
																	7, 12, 15, 
																	17

																	

																	p. 794: 9, 
																	21

																	

																	 

																	

																	Week 
																	16 – 
																	
																	FINAL EXAM 

																	

																	
																	Prepared By: 
																	Bruce Bukiet

																	

																	Last 
																	revised: 
																	08/24/04