APM 658, Fall 2004

Mathematical Modelling: Continuous

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Faculty: M. Shillor

Office: 554 SEB

Phone: 370-3439

email: shillor@oakland.edu

Class Time: MW 7:30-9:17 pm

Room: 271 SFH

Section: 45104

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Important Dates:

September 13 - Last day for no-grade drop

November 1 - Last day for official withdrawal (W)

November 23 - Thanksgiving Recess

December 5 - Last day of classes

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Discussion board and chat room

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Prerequisites:

Permission of the Instructor.

Text:

Various sources, most will be presented as needed.

Office Hours:

Monday 5:30--7:00 PM or by individual appointment.

Exams:

There will be no exams, but two projects and possibly one of the as an oral presentation.

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INTENDED SYLLABUS:

We will follow mostly, with some detours, the schedule below.

Week of --- Topics

August 30 --- Conservation of Mass – the continuity equation;
Conservation of Momentum – the equations of motion;
Conservation of Energy – the heat equation.
How to derive general equations to model phenomena.
Initial and boundary conditions.Weak formulations of the problems.

September 4 --- The heat equation, a model problem with initial and boundary conditions

September 11 --- Melting or solidification, thermistors

September 18 --- Spot welding, electropainting, diffusion, diffusion models in biology

September 25 --- Rods, beams, contact, friction, adhesion;

October 2 ---  Elliptic and Parabolic models,

October 9 --  Models with ODEs,  thermostats, oscillations, hysteresis, delays. Sliders and springs, suspensions

October 16 --- Models with ODEs – contnd, population dynamics 

October 23 --- Three-dimensional elasticity, viscoelasticity, and viscoplasticity.

October 30 --- Thermodynamic modelling

November 6 --- Contact problems with friction, adhesion, and wear

November 13 --- Contact problems - contd

November 20 ---  The Navier-Stokes equations, Maxwell’s equations (short)

Have a Good Thanksgiving Break!

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The main topics of the course:

Derivations of modells for continuous processes using ad hoc and the infinitesimal box methods.

Derivations using thermodynamic potentials and pseudopotentials of dissipation.

ODEs 

GOOD LUCK AND BE WELL!