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 222H: Honors Differential Equations
Number of Credits: 4
Course Description: Methods for solving ordinary differential equations are studied together with physical applications, Laplace transforms, numerical solutions, and series solutions.
Textbook:
Elementary Differential Equations and Boundary Value Problems, 9th Ed., by Boyce and DiPrima.
Students are required to have a copy of the textbook
available in class at the
start of semester.
Prerequisites: Math 112H with a grade of B or better, or Math 112 with a grade of A.
Instructor: (for specific course-related information, follow the link below)
Math 222-H01 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework & Quizzes: |
17% |
▪ Midterm Exam I: |
17% |
▪ Midterm Exam II: |
17% |
▪ Midterm Exam III: |
17% |
▪ Final Exam: |
32% |
NOTE: This course needs to be passed with a grade of C or better in order
to proceed to
Math 321,
Math 331,
Math 371,
Math 372,
Math 432 or
Math 473.
Drop Date: Please note that the University Drop Date November 3, 2011 deadline will be strictly enforced.
Homework and Quiz Policy: Homework Assignments chosen from the text are listed below. Students are required to work through these problems after each lecture in order to gain a better understanding of the course material. Additional homework sets will be assigned every few weeks.
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. 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.
Exams: Midterm exams are held on Wednesdays on the following days:
Exam 1:
September 21, 2011
Exam 2:
October 26, 2011
Exam 3:
November 16, 2011
Final Exam Week:
December 14-20, 2011
Day sections will have common examinations on the above listed dates from 4:15pm to 5:40pm and evening sections from 5:45pm to 7:10pm. A comprehensive final examination will be given at the end of the semester. The date for this final examination will be announced at the end of the semester.
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 EXAMS 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: In additional to regular office hours during the week,
Teaching Assistants are 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 |
|
R |
Last Day to Withdraw from this course |
|
R-Su |
Thanksgiving Recess ~ University Closed |
Course Outline and Homework Assignments:
Week |
HW |
Sect. |
Topic |
Homework |
1 |
1 |
1.1 |
Some Basic Math Models; Direction Fields |
8,10,17,18,23 |
1 |
2 |
1.2 |
Solutions of Some Differential Equations |
7,9,10,13,16 |
1 |
3 |
1.3
|
Classification of Differential Equations |
1,2,5,8,12
|
2 |
4 |
2.1 |
Integrating Factors |
2c,5c, 14,17
|
2 |
5 |
2.2 |
Separable Equations |
2,4,7,9a,15a |
2 |
6 |
2.3 |
Modeling with First Order Equations |
1,7,14(a,b), 17(a,b)
|
3 |
7 |
2.7 |
Euler's Method |
1 (a,b,d) |
3 |
8 |
3.1 |
Homogeneous Equations with
Constant Coefficients |
3,6,8,10,13
|
3 |
9 |
3.1 |
Homogeneous Equations
with Constant Coefficients |
17,20,22,24 |
4 |
|
|
REVIEW FOR EXAM 1 |
|
4 |
10 |
3.2 |
Solution of Linear Homogeneous
Equations, the,Wronskian |
2,4,8,12,17 |
4 |
11 |
3.2 |
Solution of Linear Homogeneous
Equations, the,Wronskian (cont.) |
18,24,25,26 |
5 |
12 |
3.3 |
Complex Roots of the Characteristic Equation |
3,5, 7,13,19
|
5
|
13 |
3.4 |
Repeated Roots |
1,6,8,11,14 |
5. |
14 |
3.4 |
Reduction of Order |
23,25,28 |
6 |
15 |
3.5 |
Nonhomog. Eqts., Undetermined Coefficients |
3,4,7,14,17 |
6 |
16 |
3.5 |
Nonhomog. Eqts., Undet. Coefficients (cont’d) |
19(a), 23(a), 26(a) |
6 |
17 |
3.6 |
Variation of Parameters |
1,5,9,11 |
7 |
18 |
3.6 |
Variation of Parameters (cont.) |
13,15,19 |
7 |
19 |
3.7 |
Mechanical and Electrical Vibrations
|
1,2,5,7,11,
|
7 |
20 |
3.7 |
Mechanical and Electrical Vibrations (cont.) |
12,17,18,24
|
8 |
21 |
5.1 |
Review of Power Series |
18, 20,21,23 |
8 |
22 |
5.2: |
Solutions to 2nd Order Linear Equations with
Variable
Coefficients: Ordinary Points |
4(a,b), 6(a,b),
7(a,b)
|
8 |
23 |
5.4 |
Euler’s Equation; Regular Singular Points |
1,3,4,12,17,20 |
9 |
24 |
|
REVIEW FOR EXAM 2 |
|
9 |
25 |
6.1 |
Definition of the Laplace Transform |
3,6,8,13,15 |
9 |
26 |
6.2 |
Solution of Initial Value Problems |
1,2,3,7,8 |
10 |
27 |
6.2 |
Solution of Initial Value Problems (cont.) |
13,21,24,29,30 |
10 |
28 |
6.3 |
Step Functions |
2,15,17,20,21 |
10 |
29 |
6.4 |
Differential Equations with Discontinuous Forcing Functions |
2,3,5,7,9 |
11 |
30 |
6.5 |
Impulse Functions |
1,2,5,6,9 |
11 |
31 |
6.6 |
The Convolution Integral |
4,6,8,9,14 |
11 |
32 |
7.1 7.2 |
Introduction &
Review of Matrices |
7.1: 2, 4, 5
7.2: 1,2,22,23 |
12 |
|
|
REVIEW FOR EXAM 3 |
|
12 |
33 |
7.3 |
Linear Algebraic Equations; LI,
Eigenvalues, Eigenvectors (2x2) |
1,5,16,18 |
12 |
34 |
7.5 |
Homogeneous Linear Systems with
Constant Coefficients |
1(a),4(a),7(a),15,16 |
13 |
35 |
7.6 |
Complex Eigenvalues |
2(a),10, 28(a,d) |
13 |
36 |
10.1 |
Two-Point Boundary Value Problems |
1,5,10,14,18 |
|
|
|
THANKSGIVING RECESS |
|
14 |
37 |
10.2 |
Fourier Series |
1,5,13,15 |
14 |
38 |
10.2 |
Fourier Series (cont.) |
16, 22(a,b), 24(a,b) |
14 |
39 |
10.4 |
Even and Odd Functions |
2,4,7,9 15,16
|
15 |
40 |
10.4 |
Even and Odd Functions (cont.) |
21,23(a,b),27(a,b) |
15 |
|
|
REVIEW FOR FINAL EXAM |
|
Prepared By: Prof. John Bechtold
Last revised: August 3, 2011