Spring 2010 Syllabus |
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© Leon van Dommelen |
The course will likely cover:
- Vectors and fields. Vectors and fields and their
application to areas fluid mechanics, solid mechanics, and
electromagnetics.
- Vector differentiation. Vector differentiation and its
application to data presentation, geometry, and mechanics.
- Vector integration. Vector integration, gradient, divergence and
curl, and its application to heat transfer, fluid mechanics and
electromagnetics.
- Curvilinear coordinate systems. Curvilinear coordinate systems
and their applications.
- Basic partial differential equations. Basic partial
differential equations, their application areas in mechanical
egineering.
- Qualitative properties. Qualitative properties of solutions of
partial differential equation; smoothness, characteristics, properly
posedness, and their relation to subsonic versus supersonic flows,
wave fronts, Mach lines, acoustics.
- Green’s functions. Green’s functions and their
application to problems in heat conduction and ideal flows.
- Separation of variables. Separation of variables and its use
for solving heat transfer and flow problems in mechanical
engineering.
- Laplace transforms. Laplace transforms and their use for
solving heat transfer and flow problems in mechanical engineering.