MA 797-002:  Special Topics: Fluid Mechanics
Spring 2010

Tu Th  4:30 - 5:45 p.m.   Room:  SAS 1220

Instructor: Michael Shearer   http://www4.ncsu.edu/~shearer/home0.html
Office: SAS 3228     Phone: 515-3298    Email: shearer@ncsu.edu

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

BookElementary 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.

1. Weekly Homework Assignments (70% of final grade)   due Thursdays (but not always).
2. Quizzes
(10% of final grade): definitions and equations.
3. Final project in pairs (20% of final grade): presentations in last two weeks of class; reports in exam week.

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 waves.

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: water waves. 3.1-3.5
5 weeks: Stokes flow, thin films.  7.4-10.
shock waves, KdV equation.  3.9-11.

Notes: homework solutions; additional materials. Watch this space!
Homework 2 solutions
Homework 3 solutions
Homework 4 solutions
Homework 5 solutions
Homework 6 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

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.

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.
Short in-class quizzes will be
used to keep concepts and definitions of terms sharp. In the last few weeks of class, we will organize the
class into pairs. Each pair will choose a topic to explore, will give a presentation in the last two weeks of
class, and will submit a written report during the final exam period.

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