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Math 613: Advanced Applied Mathematics I: Modeling
Fall 2017 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: Concepts and strategies of mathematical modeling are developed by investigation of case studies in a selection of areas. Consistency of a model, nondimensionalization and scaling, regular and singular effects are discussed. Possible topics include continuum mechanics (heat and mass transfer, fluid dynamics, elasticity), vibrating strings, population dynamics, traffic flow, and the Sommerfeld problem.

Number of Credits: 3

Prerequisites: MATH 331 and MATH 337, or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 613-001 Professor S. Afkhami

Office Hours for All Math Instructors: Fall 2017 Office Hours and Emails

Recommended Textbooks

1- Mathematics Applied to Deterministic Problems in the Natural Sciences, C.C. Lin and L.A. Segel, SIAM
2- Mathematics Applied to Continuum Mechanics, L.A. Segel, SIAM
3- Mathematical Models in the Applied Sciences, A.C. Fowler, Cambridge

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:

Assignments 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 is expected to be handed in on time. Late submissions will be penalized.

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 2017 Academic Calendar, Registrar)

Date Day Event
September 5, 2017 T First Day of Classes
September 11, 2017 M Last Day to Add/Drop Classes
November 6, 2017 M Last Day to Withdraw
November 21, 2017 T Thursday Classes Meet
November 22, 2017 W Friday Classes Meet
November 23 - 26, 2017 R - Su Thanksgiving Break - University Closed
December 13, 2017 W Last Day of Classes
December 14, 2017 R Reading Day
December 15 - 21, 2017 F - R Final Exam Period

Course Outline

Week Topic
Week 1-2 Basics of modeling: Review of basic modeling principles and derivations, examples of some fundamental physical models. Diffusion equation and random walk.
Week 2-3 Units, Dimensions, dimensional analysis, and scaling: Nondimensionalization, examples from various models.
Week 3-4 Perturbation methods: Regular and singular perturbation methods, boundary layers, and multiple scale expansions.
Week 5-6 Wave phenomena: Examples of traffic modeling, method of characteristics, and shocks.
Week 7-8 Problems in continuum mechanics: Conservation of mass and balance of linear and angular momentum.
Week 9-10 Problems in continuum mechanics: Inviscid and viscous fluid flows.
Week 11-12 Problems in continuum mechanics: Elasticity and elastic wave propagation.
Week 12-13 Calculus of variations or two-phase flows (depending on the interest and time).

Updated by Professor S. Afkhami - 9/11/2019
Department of Mathematical Sciences Course Syllabus, Fall 2017