MA 797M: Special Topics: Fluid Mechanics Spring 2008

Tu Th 4:30 - 5:45 p.m.   Room:  FOX 140

Instructor: Michael Shearer   http://www4.ncsu.edu/~shearer/home0.html
Office: HA 327     Phone: 515-3298    Email: shearer@ncsu.edu

Office Hours:: Wednesdays, 2:00-3:00pm, and by appointment.

Book:  Elementary Fluid Dynamics, by D.J. Acheson, Oxford University Press, 1990.

Background needed: Undergraduate mechanics (Physics course), vector calculus, matrices, ordinary differential equations,
undergraduate level linear partial differential equations. Other mathematics and physics will be reviewed as needed.

Grading:
1. Weekly Homework Assignments (80% of final grade)   due Thursdays (but not always).
2.  Final take-home exam/project (20% of final grade) due in exam week (date TBA). 

Basic Grading Scale: 90%-100%: A, 80%-89%: B, etc.   (+ and - will also be used.)

In this course, fluid mechanics will be presented from a mathematics perspective.
The equations of fluid mechanics will be introduced, and areas of active research
will be discussed. The course is suitable for graduate students in mathematics,
physics and engineering. Topics will include discussion of physical concepts
such as viscosity and surface tension, and mathematical formulations of
Stokes flow, lubrication theory, boundary layers, potential flow, as well as
presentations on stability and wave propagation. Applications to blood flow
and coating flows will be covered.

Tentative schedule (with sections from Acheson):
4 weeks:  Derivation of equations of fluid flow: Navier-Stokes and Euler. 1.2-5, 2.2, 3.2, 5.1, 6.2-4.
3 weeks: exact solutions and potential flow - complex variables. 2.3-4, 4.2-8
2 weeks: Mette Olufsen, blood flow models and solutions.
5 weeks: Stokes flow, thin films.  7.4-10.
             Water waves, shocks, KdV equation. 3.1-5, 3.9-11.

Notes:
January 10th
Conservation of momentum January 17th
Homework 1 solutions
Homework 2 solutions
Homework 3 solutions
Homework 4 solutions
Homework 5 solutions
Homework 6 solutions
Homework 8 solutions
Homework 9 solutions

Objectives:

This is an introductory course to familiarize you with basic ideas of fluid mechnaics.
Concepts, terminology and calculations will be presented in class, through references to the
textbook and through movies archived at MIT: http://web.mit.edu/fluids/www/Shapiro/ncfmf.html

Homework assignments will be roughly weekly. They will be extensive exercises to practice concepts and
calculations in fluid mechanics, and to extend the material presented in class. At the end of the semester,
you should have a good working knowledge of fluid mechanics, which will enable you to comprehend
research presentations, read advanced materials in fluids, and discuss fluid mechanics concepts with
some confidence.

Link to course announcement

Additional Policies:
1. I encourage you to discuss homework with other students, or with me during office hours. 
2. I expect you to read sections of the book around the time of lectures and homework from those sections. 
3. You are expected to attend all classes on time. Classroom discussion and questions in class help clarify
issues in this course, so please feel free to participate by asking questions.
4. Arriving late for a class or leaving early is very disruptive of class. If you need to leave early, please
let me know at the beginning of class, and sit near the door so you can slip out quietly.
5. Assignments handed in late will not be accepted.

Attendance regulations can be found at
http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.3.php

Academic Integrity Statement: Students are expected to follow university policies on academic integrity
and the Honor Pledge, which may be viewed by following the links at:
http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.7.php

Further Statements: Reasonable accommodations will be made for students with verifiable disabilities.
In order to take advantage of available accommodations, students must register with Disability Services for
Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's
policy on working with students with disabilities, please see the Academic Accommodations for Students
with Disabilities Regulation (REG02.20.1)
There are no pass through charges for this course, such as field trip costs.
Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips: None