Syllabi Header

Math 675: Partial Differential Equations
Spring 2019 Graduate 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: This course is intended to provide a modern introduction to the theory of partial differential equations, based on the notion of weak solutions and to develop existence and regularity theory for several prototypical examples. Specifically, first order PDEs, as well as second order elliptic, parabolic and hyperbolic PDEs will be discussed within appropriate functional settings.

Number of Credits: 3

Prerequisites: Math 690 or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 675-002 Professor C. Muratov

Office Hours for All Math Instructors: Spring 2019 Office Hours and Emails

Required Textbooks:

Title Partial Differential Equations
Author L. C. Evans
Edition 2nd Ed.
Publisher AMS
ISBN # 0-821849743

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 8, 2019. 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 30%
Midterm Exam 30%
Final Exam 40%

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 Policy: Homework will be assigned during class times and collected every few weeks.

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 TBA
Final Exam Period May 10 - 16, 2019

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: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

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

Additional Resources

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 2019 Academic Calendar, Registrar)

Date Day Event
January 22, 2019 T First Day of Classes
February 1, 2019 F Last Day to Add/Drop Classes
March 17 - 24, 2019 Su - Su Spring Recess - No Classes, NJIT Open
April 8, 2019 M Last Day to Withdraw
April 19, 2019 F Good Friday - No Classes, NJIT Closed
May 7, 2019 T Friday Classes Meet/ Last Day of Classes
May 8 & 9, 2019 W & R Reading Days
May 10 - 16, 2019 F - R Final Exam Period

Course Outline

Title HW Problems
1 Introduction, examples, strategies
2 First order ODEs, the method of characteristics
3 Sobolev spaces: definitions and basic properties
4 Approximations by smooth functions, extensions, traces
5 Sobolev inequalities
6 Compactness
7 Second order linear elliptic PDEs, weak solutions
8 Regularity: motivation and interior regularity
9 Boundary regularity
10 Maximum principles
11 Second order linear parabolic equations
12 Second order linear hyperbolic equations
13 Nonlinear PDEs and calculus of variations
14 Review

Updated by Professor C. Muratov - 1/21/2019
Department of Mathematical Sciences Course Syllabus, Spring 2019