Math 450-H03: Methods of Applied Mathematics I (Capstone I)
Fall 2017 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: Combines mathematical modeling with physical and computational experiments conducted in the Undergraduate Mathematics Computing Laboratory. Effective From: Spring 2009.

Number of Credits: 3

Prerequisites: Math 331 with a grade of C or better, Math 337 with a grade of C or better, and Math 340 with a grade of C or better.

Course-Section and Instructors

Course-Section	Instructor
Math 450-H03	Professor S. Afkhami

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

Course Materials: There is no mandatory text for this section. The following books and materials will be used:

1- Fluid Dynamics: Theory, Computation, and Numerical Simulation, C. Pozrikidis, Springer
2- Numerical Methods with MATLAB: Implementations and Applications, G. Recktenwald, Pearson
3- Practical Applied Mathematics, S. Howison, Cambridge

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

University-wide Withdrawal Date: The last day to withdraw with a W is Monday, November 6, 2017. It will be strictly enforced.

Policies

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:

Projects	50%
Midterm	20%
Final Report and Presentation	30%

Exam: 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 27, 2017
Final Exam Period	December 15 - 21, 2017

Projects: Projects will be given from solving the system of equations and numerical integrations using matlab to solving the Navier-Stokes equations using computational fluid dynamics (CFD) solvers.

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.

Makeup Exam Policy: To properly report their absence during a midterm or final exam, please review the required steps under the DMS Examination Policy found here:

• http://math.njit.edu/students/policies_exam.php

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: Fall 2017 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 lyles@njit.edu. The office is located in Fenster Hall Room 260. 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:

• http://www5.njit.edu/studentsuccess/disability-support-services/

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 conservation laws.
Week 2-3	Units, Dimensions, dimensional analysis, and scaling: Nondimensionalization, examples from fluid flow models.
Week 3-4	Perturbation methods: Regular and singular perturbation methods, boundary layers.
Week 5-6	Lubrication approximation theory: Examples of liquid film flow on surfaces.
Week 7-8	Two-phase flow models.
Week 9-10	Introduction to numerical methods for PDE’s: Finite difference and finite volume methods.
Week 10-11	Finite difference method: Laplace’s equation and linear solvers, unsteady heat equation, explicit and implicit methods.
Week 11-13	Interface problems: Level set and volume-of-fluid methods.

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