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Math 651: Methods of Applied Mathematics I
Fall 2016 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: A survey of mathematical methods for the solution of problems in the applied sciences and engineering. Topics include: ordinary differential equations and elementary partial differential equations. Fourier series, Fourier and Laplace transforms, and eigenfunction expansions.

Number of Credits: 3

Prerequisites: MATH 222 or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 651-001 Professor Y.-N. Young

Office Hours for All Math Instructors: Fall 2016 Office Hours and Emails

Required Textbooks: (NO BOOK)

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 6, 2017. 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 40%
Midterm Exam 30%
Final Exam 30%

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

A 90 - 100 C 70 - 75
B+ 86 - 89 D 60 - 69
B 80 - 85 F 0 - 59
C+ 76 - 79    

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 assignments/projects will be given frequently. Each assignment must be handed in at the beginning of class on the due date. Late assignments are NOT accepted.

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 October 26, 2017
Final Exam Period December 15 - 21, 2017

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: Fall 2016 Academic Calendar, Registrar)

Date Day Event
September 6, 2016 T First Day of Classes
September 12, 2016 M Last Day to Add/Drop Classes
November 7, 2016 M Last Day to Withdraw
November 22, 2016 T Thursday Classes Meet
November 23, 2016 W Friday Classes Meet
November 24 - 27, 2016 R - Su Thanksgiving Holiday, University Closed
December 14, 2016 W Last Day of Classes
December 15, 2016 R Reading Day
December 16 - 22, 2016 F - R Final Exam Period

Course Outline

Week Dates Topic
1 9/8 Linear Ordinary Differential Equations: Theory (existence & uniqueness)
2 9/11 & 9/14 Linear ODEs: Methods for homogeneous ODEs
3 9/18 & 9/21 Linear ODEs: Methods for inhomogeneous ODEs
4 9/25 & 9/28 Local analysis of Linear ODEs (series solutions)
5 10/2 & 10/5 Sturm-Liouville Boundary Value Problems
6 10/9 & 10/12 Nonlinear ODEs
7 10/16 & 10/19 Linear Partial Differential Equations: Introduction and classification.
8 10/23 & 10/26 MIDTERM (OCTOBER 26)
9 10/30 & 11/2 Wave equation and characteristics
10 11/6 & 11/9 Heat equation and separation of variables
11 11/13 & 11/16 Solution by eigenfunction expansion
12 11/20 & 11/23 Laplace’s equation (FOLLOWS THURSDAY SCHEDULE, NO CLASS 11/23)
13 11/27 & 11/30 Transform methods
14 12/4 & 12/7 Green’s functions
15 12/11 Review and/or additional topics

Updated by Professor Y.-N. Young - 9/11/2017
Department of Mathematical Sciences Course Syllabus, Fall 2016