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Math 715: Mathematical Fluid Dynamics I
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: Introduction to the basic ideas of fluid dynamics, with an emphasis on rigorous treatment of fundamentals and the mathematical developments and issues. The course focuses on the background and motivation for recent mathematical and numerical work on the Euler and Navier-Stokes equations, and presents a mathematically intensive investigation of various model equations of fluid dynamics (e.g., the Korteweg-de-Vries equations). Effective From: Fall 2005.

Number of Credits: 3

Prerequisites: Departmental Approval.

Course-Section and Instructors

Course-Section Instructor
Math 715-001 Professor L. Cummings

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

Required Textbooks:

Title (See Recommended Reading Below)
Author ---
Edition ---
Publisher ---
ISBN # ---
Recommended
  • Viscous Flow (Cambridge Texts in Applied Mathematics), by H. Ockendon and J.R. Ockendon.
  • Elementary Fluid Dynamics (OUP), by D.J. Acheson.
  • 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:

    Homework 40%
    Midterm Paper 25%
    Final Exam 35%

    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.

    Exams: The final exam will be held during the following week

    Final Exam Week 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 lyles@njit.edu. 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

    Weeks Topic
    1-2 Introduction and preamble.  Modeling of a viscous fluid. Derivation of Navier-Stokes equations using Reynolds Transport Theorem. Some simple exact solutions.
    2-3 Concepts of scaling and nondimensionalization. Large and small Reynolds number limits. Relevance and limitations.

    Discussion of boundary conditions (at both rigid and free boundaries).  
    3-4 Flow at high Reynolds number (“inviscid” flow). The Euler equations. Bernouilli’s theorem and Kelvin’s circulation theorem. 2D inviscid flow around obstacles. Potential flow; existence of streamfunction and complex potential. Flow singularities and method of images for flow with obstacles. Simple theory of flight.
    5-6 Water waves in 2D irrotational, inviscid flow. Dispersion relations & group velocity.
    7-9 Viscous boundary layers. Introduction to asymptotic methods for boundary layers. Boundary layer on a flat plate. Boundary layers on more general obstacles.
    9-10 Flow at low Reynolds number. Flow past circular cylinder: the Stokes paradox. Flow past a sphere.
    11-13 Lubrication theory: slider bearings, squeeze films, flow with free surfaces.

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