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Math 331: Introduction to Partial Differential Equations
Spring 2018 Course Syllabus

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.

Course Information

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.

Number of Credits: 3

Prerequisites: MATH 211 or MATH 213 and MATH 222 all with a grade of C or better.

Course-Section and Instructors

Course-Section Instructor
Math 331-002 Professor C. Turc
Math 331-004 Professor V. Matveev

Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails

Required Textbook:

Title Applied Partial Differential Equations
Author Haberman
Edition 5th
Publisher Pearson
ISBN # 978-0321797056

University-wide Withdrawal Date: The last day to withdraw with a W is Monday, April 2, 2018. It will be strictly enforced.


DMS Course Policies: 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.

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

Homework 15%
Quiz 15%
Midterm Exam I 30%
Final Exam 40%

Your final letter grade will be based on the following tentative curve.

A 89 - 100 C 61 - 67
B+ 82 - 86 D 63 - 60
B 75 - 81 F 0 - 52
C+ 68- 74

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Homework and Quiz Policy: Homework problem sets will be emailed by the instructor each week, and may include problems requiring basic MATLAB coding. Homework is in general due each Wednesday; late work is not accepted. Short quizzes will also be given about once per week, on a pre-announced topic.

Email Policy: 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.

Exams: There will be one midterm exam held in class during the semester and one comprehensive final exam. Exams are held on the following days:

Midterm Exam March 8, 2018
Final Exam Period May 4 - 10, 2018

The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: There will be No make-up QUIZZES OR EXAMS during the semester. In the event an exam is not taken under rare circumstances where the student has a legitimate reason for missing the exam, the student should contact the Dean of Students office and present written verifiable proof of the reason for missing the exam, e.g., a doctor’s note, police report, court notice, etc. clearly stating the date AND time of the mitigating problem. The student must also notify the Math Department Office/Instructor that the exam will be missed.

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

Additional Resources

Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Spring 2018 Hours)

Further Assistance: For further questions, students should contact their instructor. All instructors have regular office hours during the week. These office hours are listed on the Math Department's webpage for Instructor Office Hours and Emails.

All students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. The Department of Mathematical Sciences takes these policies very seriously and enforces them strictly.

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Spring 2018 Academic Calendar, Registrar)

Date Day Event
January 16, 2018 T First Day of Classes
January 22, 2018 M Last Day to Add/Drop Classes
March 11 - 18, 2018 Su - Su Spring Recess - No Classes/ University Closed
March 30, 2018 F Good Friday - No Classes/ University Closed
April 2, 2018 M Last Day to Withdraw
May 1, 2018 T Friday Classes Meet - Last Day of Classes
May 2 - 3, 2018 W - R Reading Days
May 4 - 10, 2018 F - R Final Exam Period

Course Outline

Lecture (Date) Sections Topics
1 (1-16) 3.1-3.3 Intro: visualizing scalar fields (Calculus III), linearity, Fourier series
2 (1-18) 3.4-3.6 Fourier series 
3 (1-23) 3.4-3.6 Fourier series continued: term-by-term operations
4 (1-25) 1.2-1.3 Heat equation: 1D derivation & boundary conditions
5 (1-30) 1.3-1.4 Heat equation: equilibrium temperature distribution
6 (2-1) 1.4-1.5 Heat equation: equilibrium temperature distribution; higher dimensions
7 (2-6) 2.3 Method of separation of variables: boundary value problems
8 (2-8) 2.4.1-2.4.2 Solving heat equation in 1D rod: insulated ends
9 (2-13) 2.4.2-2.4.3 Solving heat equation in 1D rod: circular ring
10 (2-15) 2.5.1 Laplace’s equation inside a rectangle
11 (2-20) 2.5.2, 2.5.4 Laplace’s equation inside a disk; qualitative properties
12 (2-22) 4.1-4.2, 4.4 Wave equation: 1D derivation and vibrating string with fixed ends
13 (2-27) 4.3 Wave equation: boundary conditions and vibrating string continued
14 (3-1) 4.5 Wave equation: vibrating membrane; dissipation
15 (3-6) Exam Review
16 (3-8) Midterm Examination 
17 (3-20) 5.1-5.4 Sturm-Liouville eigenvalue problems: properties; proof of orthogonality
18 (3-22) 5.5 Sturm-Liouville problems: self-adjointness, Lagrange Identity; proofs
19 (3-27) 5.6, 5.8 Rayleigh Quotient and Robin boundary conditions
20 (3-29) 5.6, 5.8 More Rayleigh Quotient examples; Robin boundary conditions
2-Apr Last Day to Withdraw
21 (4-3) 6.1-6.2 Finite difference numerical methods
22 (4-5) 6.2-6.3.2 Euler finite difference method for heat equation; von Neumann stability
23 (4-10) 7.1-7.2 PDE’s in 2+1 dimensions: vibration of a rectangular membrane
24 (4-12) 7.7, 7.8 Bessel equation and Bessel functions
25 (4-17) 7.7 Vibration of a circular membrane
26 (4-19) 10.1-10.3 Heat equation on the line; Fourier Transform derivation
27 (4-24) 10.4, 10.6 Fourier Transform continued
28 (4-26) Final Exam Review

Updated by Professor V. Matveev - 1/18/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018