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Math 671: Asymptotic Methods I
Fall 2018 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: Asymptotic sequences and series. Use of asymptotic series. Regular and singular perturbation methods. Asymptotic methods for the solution of ODEs, including: boundary layer methods and asymptotic matching, multiple scales, the method of averaging, and simple WKB theory. Asymptotic expansion of integrals, including: Watson's lemma, stationary phase, Laplace's method, and the method of steepest descent.

Number of Credits: 3

Prerequisites: Math 645 or Math 545, and Math 656 or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 671-001 Professor M. Booty

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

Textbook Materials: There is no required textbook for this course. Sources that are relevant to course material will be cited during the course and will be available in the NJIT library.

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 12, 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 Assignments 80%
Final Exam 20%

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. Attendance in all classes is expected. Absences from class may inhibit your ability to learn the material.

Homework Policy: Homework will be assigned in class every few weeks. Because asymptotics problems sometimes take a long time to complete, the course grade will be based primarily on the homework.

Exams: The final exam format is yet to be determined but will be the same for all students in the class. It will either be a written exam during the assigned exam period or an instructor-assigned project that is of interest to the student and may be related to their research. Please read and understand the Math Department's Examination Policy.

Final Exam Period December 15 - 21, 2018

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 2018 Academic Calendar, Registrar)

Date Day Event
September 4, 2018 T First Day of Classes
September 10, 2018 M Last Day to Add/Drop Classes
November 12, 2018 M Last Day to Withdraw
November 20, 2018 T Thursday Classes Meet
November 21, 2018 W Friday Classes Meet
November 22 - 25, 2018 R - Su Thanksgiving Recess
December 12, 2018 W Last Day of Classes
December 13 & 14, 2018 R & F Reading Days
December 15 - 21, 2018 Sa - F Final Exam Period

Course Outline

Week Topic
1 Definitions and notation. Sequences and series, asymptotic versus convergent.  An example, including the use of an asymptotic series in practice.
2 to 4 Asymptotic expansion of integrals:  Watson’s lemma, Laplace’s method, the method of stationary phase, and the method of steepest descent.
5 Examples of regular versus singular perturbation via solution of algebraic equations. Examples of how scaling is determined.
6 to 8 Matched asymptotic expansions.  A singularly perturbed two-point boundary value problem.  Composite expansion.  Further examples.
9 to 11 The method of multiple scales.  Various examples of nonlinear oscillations and parametric excitation.
12 to 14 The WKB method.  Its relation to the method of multiple scales.  Application to singularly perturbed two-point boundary value problems. Turning point problems in wave propagation and other examples.  

Updated by Professor M. Booty - 9/1/2018
Department of Mathematical Sciences Course Syllabus, Fall 2018