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 (5th Ed); Pearson Prentice-Hall, ISBN: 0321797051.
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: |
40% |
▪ Midterm Exam: |
25% |
▪ 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 26, 2013 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 |
|
T-W |
Final Exams |
Course Outline And Homework Assignments:
Week |
Lecture |
Sections |
Topic |
1 |
1 |
1.2 |
Derivation of the Heat Equation in 1D |
2 |
1.3 |
Boundary Conditions |
|
2 |
3 |
1.4 |
Equilibrium Temperature Distribution |
4 |
1.5 |
Derivation of the Heat Equation in Higher Dimensions |
|
3 |
5 |
2.1-2.3 |
Heat Equation, Solution by Separation of Variables |
6 |
2.4 |
Solution by Separation of Variables, Continued |
|
4 |
7 |
2.5 |
Laplace’s Equation, Solution by Separation of
Variables |
8 |
3.1-3.3 |
Fourier Series, Convergence |
|
5 |
9 |
3.4-3.6 |
Fourier Series, Term-by-Term Operations |
10 |
4.1-4.3 |
Derivation of the Wave Equation in 1D, the Vibrating
String |
|
6 |
11 |
4.4 |
Solution by Separation of Variables for the
Vibrating String |
12 |
|
Review for Midterm |
|
7 |
13 |
|
Midterm Exam |
14 |
5.1-5.3 |
Sturm-Liouville Eigenvalue Problems |
|
8 |
15 |
5.4 |
Heat Conduction in a Non-Uniform Rod |
16 |
5.5 |
Self-Adjoint Operators |
|
9 |
17 |
5.6 |
The Rayleigh Quotient |
18 |
5.7 |
Vibration of a Non-Uniform String |
|
10 |
19 |
5.8 |
Mixed Boundary Conditions |
20 |
6.1-6.3 |
Finite Difference Numerical Methods for PDEs |
|
11 |
21 |
7.1-7.3 |
Examples in 2D and 3D, Vibrations of a Rectangular
Membrane |
22 |
7.7 |
Vibration of a Circular Membrane |
|
12 |
23 |
7.8 |
More on Bessel Functions |
24 |
8.1-8.2 |
Heat Conduction with Sources and Nonhomogeneous
Boundary Conditions |
|
13 |
25 |
8.3 |
Eigenfunction Expansion for Nonhomogeneous Problems |
26 |
9.1-9.2 |
Green’s Function for the Heat Equation in 1D |
|
14 |
27 |
9.3 |
Green’s Functions for BVP’s for ODEs |
28 |
|
Review for Final Exam |
Prepared By: Prof. Michael Booty
Last revised: January 4, 2013