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 331: Introduction to Partial Differential Equations
Number of Credits: 3
Course Description: Partial differential equations in science and engineering. Topics include initial- and boundary-value problems for parabolic, hyperbolic, and elliptic second-order equations. Emphasis is placed on separation of variables, special functions, transform methods, and numerical techniques. Effective From: Fall 2010
Prerequisites: Math 211 or Math 213 and Math 222 with a grade of C or better.
Textbook: Applied Partial Differential Equations by Richard Haberman (4th Ed); Pearson Prentice-Hall, ISBN: 0130652431.
Instructor: (for specific course-related information, follow the link below)
Math 331-002 |
|
Math 331-004 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework & Quiz: |
35% |
▪ Midterm Exam: |
30% |
▪ Final Exam: |
35% |
Your final letter grade will be based on the
following tentative curve.
NOTE: This course needs to be passed with a grade of C or better in order
to proceed to
Math 440, Math 450H, Math 475,
and Math 495.
A |
88-100 |
C |
60-66 |
B+ |
81-87 |
D |
54-59 |
B |
74-80 |
F |
0-53 |
C+ |
67-73 |
|
|
Drop Date: Please note that the University Drop Date March 20, 2012 deadline will be strictly enforced.
Email: It is important that you regularly check your NJIT email account for class assignments and announcements from your instructor. Rutgers students should email the Instructor their preferred email address at the start of the semester.
Homework and Quizzes: Homework assignments listed in the syllabus are tentative. Homework problem sets will be emailed by the instructor after each class. Homework is due on the assigned date; late homework is not accepted. Quizzes are given about once per week on an announced topic.
MATLAB Assignments: Three MATLAB assignments will be given during the semester; for help with MATLAB see the Instructor or MATLAB tutors available in accordance with the posted schedule.
Attendance and Participation: Attendance in this class is mandatory. Please make sure you read and fully understand the Department’s Attendance 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: 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 |
Dr. Martin Luther King, Jr. Day ~ University Closed |
|
Su-Su |
Spring Recess ~ No Classes Scheduled ~ University Open |
|
T |
Last Day to Withdraw from this course |
|
F |
Good Friday ~ University Closed |
|
T |
Classes follow a Friday Schedule, Last Day of Classes |
|
W |
Reading Day |
|
R-W |
Final Exams |
Course Outline And Homework Assignments:
Week |
Lecture,
Section
& Topic |
Assignments |
||
Week 1 |
1 |
3.1-3.3 |
Intro to
PDEs; Review: ODEs, Calculus III, Fourier Series |
Assigned in class |
2 |
3.4-3.6 |
Fourier
Series; Term-by-term Operations |
Assigned in class |
|
Week 2 |
|
|
||
3 |
1.2 |
Heat
Equation: 1D Derivation |
S1.2: 3,5,9 |
|
Week 3 |
4 |
1.3 |
Heat
Equation: Boundary Conditions |
S1.3: 1,2 |
5 |
1.4 |
Heat
Equation: Equilibrium temperature Distribution |
S1.4: 1, 3, 7, 10, 11 |
|
Week 4 |
6 |
1.5 |
Heat
Equation: Higher Dimensions |
S1.5: 5,9,10,11,12,13 |
7 |
2.1-2.3 |
Heat
Equation: 1D Solution I |
S2.2: 2;
S2.3: 1, 2, 3, 8,
|
|
Week 5 |
8 |
2.4 |
Heat
Equation: 1D Solution II |
S2.4: 1, 3, 4
|
9 |
2.5 |
Laplace’s
Equation: Solution |
S2.5: 1, 3, 5(b,c), 7, 8(b),15(a,c) |
|
Week 6 |
10 |
4.1-4.3 |
Wave
Equation: 1D Derivation |
S4.2: 1; S4.3: 1, 2 |
11 |
4.4 |
Wave
Equation: Vibrating String |
S4.4: 1, 2, 3, 5 |
|
Week 7 |
12 |
└► |
REVIEW FOR EXAM #1 |
STUDY FOR EXAM #1 |
13 |
└► |
MIDTERM EXAM I: |
||
Week 8 |
14 |
5.1-5.3 |
Sturm-Liouville Problems |
S5.3: 4, 8, 9 |
15 |
5.4 |
Sturm-Liouville Problem : Heat Flow in Nonuniform
Rod |
S5.4: 1, 2, 3 |
|
Week 9 |
16 |
5.5 |
Sturm-Liouville Problems: Self-Adjointness |
S5.5: 1(d), 8, 9 |
17 |
5.6 |
Sturm-Liouville Problems: Rayleigh Quotient |
S5.6: 1, 2 |
|
Week 10 |
└► |
Last Day to
Withdraw(3/20) from this course |
||
18 |
5.7 |
Sturm-Liouville Problems: Application to Wave
Equation |
S5.7: 1 |
|
19 |
5.8 |
Sturm-Liouville Problems: Mixed Boundary Conditions |
S5.8: 5, 6, 7 |
|
Week 11 |
20 |
6.1-6.3 |
Finite
Difference Numerical Methods for PDEs |
S6.2: 1,2,3,4; S6.3:1 |
21 |
7.1-7.3 |
PDE’s in
2D: Vibration of a Rectangular Membrane |
S7.3: 1, 3, 4 |
|
Week 12 |
22 |
7.7 |
Vibration
of a Circular Membrane |
S7.7: 4, 9, 10 |
23 |
7.8 |
More on
Bessel Functions |
S7.8: 5, 8 |
|
Week 13 |
24 |
8.1-8.2 |
Heat Flow with
Non-homogeneous Boundary Conditions |
Assigned in class |
25 |
8.3 |
Nonhomogeneous Problems:
Eigenfunction Expansion |
S8.3: 6 |
|
Week 14 |
26 |
9.1-9.2 |
Green’s
Functions: 1D Heat Equation |
Assigned in class |
27 |
9.3 |
Green’s Functions: BVP’s
for ODE’s |
Assigned in class |
|
Week 15 |
28 |
└► |
REVIEW FOR FINAL EXAM |
STUDY FOR FINAL EXAM |
|
||||
Finals |
Final EXAM WEEK: may 3-9, 2012 |
Prepared By: Prof. Yassine Boubendir
Last revised: December 9, 2011